Search Results

Documents authored by Kovács, Laura

Found 2 Possible Name Variants:

Kovacs, Laura

Document
Invited Talk
DOI: 10.4230/LIPIcs.SAT.2026.1
SAT in Saturation: A Satisfied Match (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
Saturation is the leading concept behind the proof-search algorithms of state-of-the-art first-order theorem provers [Filip Bártek et al., 2025; Christoph Weidenbach et al., 2009; Stephan Schulz et al., 2019]. The key idea behind saturation-based proof search is to reduce the problem of proving validity of a first-order formula to the problem of establishing unsatisfiability of the respective formula, by using a sound inference system, such as resolution and superposition [Leo Bachmair and Harald Ganzinger, 2001; Robert Nieuwenhuis and Albert Rubio, 2001]. Central to efficient saturation-based proof search is the implementation of redundancy in the form of simplification rules [John Alan Robinson, 1965; Laura Kovács and Andrei Voronkov, 2013]: such rules do not add new formulas to search space, but instead simplify/delete redundant formulas from the search space, while not loosing refutational completeness of superposition. Redundancy in first-order theorem proving is controlled via term/clause ordering and literal selection functions in extension of standard superposition: redundant clauses are logical consequences of smaller clauses with respect to the considered ordering. While redundancy is essential for efficient proof search, establishing whether an arbitrary first-order formula is redundant is as hard as proving whether it is valid. First-order provers therefore implement sufficient conditions towards proving redundancy, so that these conditions can be efficiently checked, ideally using only syntactic arguments over formulas. One such condition comes with the notion of subsumption, yielding one of the most important simplification rules in automated reasoners [Leo Bachmair and Harald Ganzinger, 1994]. It is common that millions of subsumption checks are performed during a single solver run [Jakob Rath et al., 2022]. However, in contrast to propositional subsumption as used by SAT solvers and implemented using sophisticated polynomial algorithms, first-order subsumption in first-order theorem proving involves NP-complete search queries, turning the efficient use of first-order subsumption into a huge practical burden. This talks presents a tailored integration of SAT solving for detecting variants of subsumption in superposition. Key to our approach is retrieving clauses from the search space and checking whether subsumption with retrieved clauses can be applied, using multi-literal matching. A solution to our SAT-based encoding gives a concrete application of (variants of) subsumption, allowing the first-order prover to apply that instance of subsumption as a simplification rule during saturation [Bernhard Gleiss et al., 2020; Jakob Rath et al., 2022; Robin Coutelier et al., 2025]. Our SAT encoding captures subset relations among literals/clauses and formalizes matching of literals between inference premises/conclusions. We show that SAT encodings improve literal matching, and thus subsumption, in first-order theorem proving. In particular, our experimental results using the Vampire prover demonstrate the practical benefits of using SAT solving for variants of first-order subsumption.
Cite as

Laura Kovács. SAT in Saturation: A Satisfied Match (Invited Talk). In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.SAT.2026.1,
  author =	{Kov\'{a}cs, Laura},
  title =	{{SAT in Saturation: A Satisfied Match}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.1},
  URN =		{urn:nbn:de:0030-drops-263076},
  doi =		{10.4230/LIPIcs.SAT.2026.1},
  annote =	{Keywords: Automated Reasoning, First-Order Theorem Proving, Superposition, Subsumption, Redundancy, SAT Solving, Vampire}
}
Document
DOI: 10.4230/LIPIcs.SAT.2026.14
Generalizing CDCL with Graph Backtracking

Authors: Robin Coutelier, Thomas Hader, and Laura Kovács

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
We present graph backtracking, a novel, fine-grained backtracking scheme for CDCL-based SAT solving, parametrized by a user-defined weight function. For conflict repair, we challenge the decision level abstraction and use the implication graph as a precise guiding structure to minimize the weight of literals that are unassigned. Graph backtracking is sound, complete, and terminating. We show that it is a generalization of chronological and non-chronological backtracking by simulating them with specific weight functions. Our approach is implemented in the experimental solver NapSAT. Empirical results show that graph backtracking requires fewer literal propagations than standard approaches, leading to improved solver runtime.
Cite as

Robin Coutelier, Thomas Hader, and Laura Kovács. Generalizing CDCL with Graph Backtracking. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{coutelier_et_al:LIPIcs.SAT.2026.14,
  author =	{Coutelier, Robin and Hader, Thomas and Kov\'{a}cs, Laura},
  title =	{{Generalizing CDCL with Graph Backtracking}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.14},
  URN =		{urn:nbn:de:0030-drops-263203},
  doi =		{10.4230/LIPIcs.SAT.2026.14},
  annote =	{Keywords: SAT Solving, Backtracking, Conflict Analysis, CDCL}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2026.36
Lean on Vampire Proofs (Short Paper)

Authors: Jonas Bodingbauer, Márton Hajdu, Laura Kovács, Axel Polaczek, and Michael Rawson

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampire’s output. We describe ongoing efforts in reconstructing Vampire proofs as trusted proofs in Lean. Our experiments showcase feasibility of generating trusted Vampire proofs that are validated in Lean.
Cite as

Jonas Bodingbauer, Márton Hajdu, Laura Kovács, Axel Polaczek, and Michael Rawson. Lean on Vampire Proofs (Short Paper). In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 36:1-36:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bodingbauer_et_al:LIPIcs.ITP.2026.36,
  author =	{Bodingbauer, Jonas and Hajdu, M\'{a}rton and Kov\'{a}cs, Laura and Polaczek, Axel and Rawson, Michael},
  title =	{{Lean on Vampire Proofs}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{36:1--36:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.36},
  URN =		{urn:nbn:de:0030-drops-270102},
  doi =		{10.4230/LIPIcs.ITP.2026.36},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Provers, Automated Theorem Provers, Lean, Vampire, Proof Reconstruction}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2026.2
Saturation-Guided Inductive Synthesis (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
Proof by induction is common-place in mathematics [Josef Urban and Geoff Sutcliffe, 2010; Martin Desharnais et al., 2022], formal verification [Raven Beutner and Bernd Finkbeiner, 2024; Wolfgang Ahrendt et al., 2000; Pamina Georgiou et al., 2022], cybersecurity [Simon Jeanteur et al., 2024; Evan Laufer et al., 2024], and many more areas. This talk overviews recent progress in automating inductive reasoning in quantified logic, with applications to code synthesis. Key to our work is saturation-based first-order theorem proving [Laura Kovács and Andrei Voronkov, 2013], using variants of the superposition calculus [Robert Nieuwenhuis and Albert Rubio, 2001]. We show that induction and synthesis are better together in saturation, allowing us not only to prove quantified properties F, but also generate a functional implementation of F during proof search. We showcase our results using the first-order theorem prover Vampire [Filip Bártek et al., 2025], a completely automatic push-button theorem prover for first-order logic with theories, including arithmetic, inductively defined datatypes, induction, and higher-order logic. We structure our talk within three inter-connected parts. First, we overview the main ingredients behind saturation provers [Filip Bártek et al., 2025; Stephan Schulz et al., 2019; Christoph Weidenbach et al., 2009] using superposition. Such provers work by negating an input conjecture F, transforming ¬ F into a clausal normal form, and using superposition inferences to derive new clauses from existing ones until a contradiction is reached; when a contradiction is derived, validity of F is established. Many years of development in saturation-based theorem proving have gone into making this process as efficient as possible, while deriving new clauses only when needed in order to tame growth of the search space. Doing so, highly-efficient superposition calculi parametrized by so-called clause selection functions have been proposed, in order to make as few inferences between clauses as possible. Redundancy elimination techniques further prune the search space. Next, we show how to formalize applications of induction in the saturation process [Márton Hajdú et al., 2022], without bringing drastic changes into the overall framework of first-order proving. A natural choice for implementing induction would be by reducing goals to subgoals, in particular by proving a base case and an inductive step case of a valid induction principle. For example, a goal ∀ x. F(x) over natural numbers x can be proven using structural induction: we prove F[0] (base case) and ∀ x. F(x) ⇒ F(x+1) (step case). However, saturation theorem proving is not about reducing goals to subgoals: in principle, each clause in the search space can be chosen during any step of saturation. We therefore automate induction in saturation as follows. When a clause F(x) is chosen and inductive reasoning over F should be applied (for example, because F uses inductively defined data types x, such as natural numbers), we combine the application of a valid induction schema over F(x) with resolution. Put it simply, induction and resolution are combined in one step of saturation, allowing us to use parts of F(x) as subgoals of F(x). Interestingly with this approach is that clauses generated during saturation may be stronger than the induction schema and, most importantly, are friendly to saturation provers: they are mostly quantifier-free Horn clauses and their (at most one) positive equality cannot be used in many inferences during saturation. Thus, applying many induction inferences during proof search would hardly affect the performance of a saturation prover. Figure 1 lists a property over natural numbers: every natural number x is the half of another natural number y. Proving this property in saturation, and in particular using Vampire, can be achieved by (structural) induction over x. Finally, we extend saturation proof search with code synthesis [Petra Hozzová et al., 2024]. While proving formula F, we track the constructive parts of the proof of F using so-called answer literals [Cordell Green, 1969]. We use these parts to synthesize a program satisfying F and use the applications of induction in saturation to construct recursive programs satisfying F. In a nutshell, the base case and inductive case steps of induction in saturation express how to construct the desired program for the next recursive step using the program for the previous recursive step; we capture this information via answer literals. When we apply induction in saturation, we introduce a special term into the answer literal and record the program corresponding to the induction step. As we prove induction steps, we capture their corresponding programs in the answer literal. Finally, we convert the special tracker terms from the answer literals into recursive functions, and obtain a program satisfying property F. For example, from the proof of property of Figure 1, our approach implemented in Vampire infers the following functional implementation of a recursive function r, while using only the signature of Figure 1: 𝗋(0) & := 0 𝗋(s(x)) & := s(s(𝗋(x))) The above inferred function r satisfies the property of Figure 1 and, for each input natural number x, computes a natural number 𝗋(x) such that x is half of 𝗋(x). In summary, induction and synthesis are better together in saturation-based theorem proving using the superposition calculus. Soundness and practical use of our work has been addressed and experimented using the Vampire theorem prover, both in the case of automating induction [Márton Hajdú et al., 2022; Márton Hajdú et al., 2024] and program synthesis [Petra Hozzová et al., 2023; Petra Hozzová et al., 2024]. Interesting questions regarding completeness arise: if a program satisfying a given property exists, can we derive it from saturation-based proof search? Our recent results [Hajdu et al., 2026] answer this question for recursion-free program using additional assumptions of realizability. A natural direction for future work is to identify realizability assumptions for recursive program synthesis and induction.
Cite as

Laura Kovács. Saturation-Guided Inductive Synthesis (Invited Talk). In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.FSCD.2026.2,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Saturation-Guided Inductive Synthesis}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{2:1--2:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.2},
  URN =		{urn:nbn:de:0030-drops-263521},
  doi =		{10.4230/LIPIcs.FSCD.2026.2},
  annote =	{Keywords: automated reasoning, first-order theorem proving, saturation, induction, program synthesis}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2026.2
Moments in Time: Algebraic Analysis for Solvable Loops (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
With substantial progress in automated reasoning, algebraic approaches emerged to automatically analyse program loops in an exact manner. In this invited talk, we discuss recent results in characterizing the functional behaviour of loops with polynomial arithmetic and probabilistic updates. This problem remains unsolved even when we restrict consideration to loops that are non-nested, without conditionals, and/or without exit conditions [Ehud Hrushovski et al., 2023; Julian Müllner and others, 2024]. We are motivated by applications of computer-aided verification, in particular to assess the safety, security, and sensitivity of computer systems [M. Z. Kwiatkowska et al., 2011; Gilles Barthe et al., 2012; Gilles Barthe and others, 2018; Marcel Moosbrugger et al., 2023; Alessandro Abate et al., 2023; Andrey Kofnov and others, 2024]. We are interested in modeling, deciding, and solving loop analysis. The key to our work are moment-computable loops [L. Kovács, 2008; Marcel Moosbrugger et al., 2022] which allow us to set limits on what is decidable and solvable in loop analysis. Our approach combines algebra, statistics, and automated reasoning to mechanize loop analysis. Various techniques, such as martingale theory and quantifier elimination, can be seen as examples of moment-computable loop analysis. This talk is structured within three inter-connected parts. We first bring moment-based loop analysis into the landscape of {loop invariant synthesis} and extend moment-computable loops with {termination guarantees}. We next automate the reasoning about (probabilistic) loops by summarizing loop semantics as (probabilistic) algebraic recurrences, whose closed-form solutions capture (higher-order) moments, and hence invariants, among loop variables. These recurrences together with loop tests yield moment-based (super)martingales necessary to prove loop termination and compute probability bounds on termination. We finally describe moment-computable loops whose invariant synthesis {decidable} or as {hard} as open problems, such as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008].
Cite as

Laura Kovács. Moments in Time: Algebraic Analysis for Solvable Loops (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.STACS.2026.2,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Moments in Time: Algebraic Analysis for Solvable Loops}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.2},
  URN =		{urn:nbn:de:0030-drops-254910},
  doi =		{10.4230/LIPIcs.STACS.2026.2},
  annote =	{Keywords: program analysis, algebraic reasoning, symbolic computation, loop invariants}
}
Document
DOI: 10.4230/DagRep.14.10.22
SAT and Interactions (Dagstuhl Seminar 24421)

Authors: Olaf Beyersdorff, Laura Kovács, Meena Mahajan, Martina Seidl, and Kaspar Kasche

Published in: Dagstuhl Reports, Volume 14, Issue 10 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar "SAT and Interactions" (24421). The seminar brought together theoreticians and practitioners from the areas of proof complexity, SAT and QBF solving, and first-order theorem proving, who discussed recent developments in their fields and embarked on an interdisciplinary exchange of ideas and techniques between these neighbouring subfields of SAT.
Cite as

Olaf Beyersdorff, Laura Kovács, Meena Mahajan, Martina Seidl, and Kaspar Kasche. SAT and Interactions (Dagstuhl Seminar 24421). In Dagstuhl Reports, Volume 14, Issue 10, pp. 22-38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@Article{beyersdorff_et_al:DagRep.14.10.22,
  author =	{Beyersdorff, Olaf and Kov\'{a}cs, Laura and Mahajan, Meena and Seidl, Martina and Kasche, Kaspar},
  title =	{{SAT and Interactions (Dagstuhl Seminar 24421)}},
  pages =	{22--38},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{14},
  number =	{10},
  editor =	{Beyersdorff, Olaf and Kov\'{a}cs, Laura and Mahajan, Meena and Seidl, Martina and Kasche, Kaspar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.10.22},
  URN =		{urn:nbn:de:0030-drops-230243},
  doi =		{10.4230/DagRep.14.10.22},
  annote =	{Keywords: SAT, QBF, proof complexity, solving, first-order logic, automated theorem proving}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.9
Lazy Reimplication in Chronological Backtracking

Authors: Robin Coutelier, Mathias Fleury, and Laura Kovács

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Chronological backtracking is an interesting SAT solving technique within CDCL reasoning, as it backtracks less aggressively upon conflicts. However, chronological backtracking is more difficult to maintain due to its weaker SAT solving invariants. This paper introduces a lazy reimplication procedure for missed lower implications in chronological backtracking. Our method saves propagations by reimplying literals on demand, rather than eagerly. Due to its modularity, our work can be replicated in other solvers, as shown by our results in the solvers CaDiCaL and Glucose.
Cite as

Robin Coutelier, Mathias Fleury, and Laura Kovács. Lazy Reimplication in Chronological Backtracking. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{coutelier_et_al:LIPIcs.SAT.2024.9,
  author =	{Coutelier, Robin and Fleury, Mathias and Kov\'{a}cs, Laura},
  title =	{{Lazy Reimplication in Chronological Backtracking}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.9},
  URN =		{urn:nbn:de:0030-drops-205313},
  doi =		{10.4230/LIPIcs.SAT.2024.9},
  annote =	{Keywords: Chronological Backtracking, CDCL, Invariants, Watcher Lists}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.41
Linear Loop Synthesis for Quadratic Invariants

Authors: S. Hitarth, George Kenison, Laura Kovács, and Anton Varonka

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather than generating invariants for given loops, in this paper we synthesise loops that exhibit a predefined behaviour given by an invariant. From the perspective of formal loop verification, the synthesised loops are thus correct by design and no longer need to be verified. To overcome the hardness of reasoning with arbitrarily strong invariants, in this paper we construct simple (non-nested) while loops with linear updates that exhibit polynomial equality invariants. Rather than solving arbitrary polynomial equations, we consider loop properties defined by a single quadratic invariant in any number of variables. We present a procedure that, given a quadratic equation, decides whether a loop with affine updates satisfying this equation exists. Furthermore, if the answer is positive, the procedure synthesises a loop and ensures its variables achieve infinitely many different values.
Cite as

S. Hitarth, George Kenison, Laura Kovács, and Anton Varonka. Linear Loop Synthesis for Quadratic Invariants. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 41:1-41:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hitarth_et_al:LIPIcs.STACS.2024.41,
  author =	{Hitarth, S. and Kenison, George and Kov\'{a}cs, Laura and Varonka, Anton},
  title =	{{Linear Loop Synthesis for Quadratic Invariants}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{41:1--41:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.41},
  URN =		{urn:nbn:de:0030-drops-197512},
  doi =		{10.4230/LIPIcs.STACS.2024.41},
  annote =	{Keywords: program synthesis, loop invariants, verification, Diophantine equations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2023.4
Algebraic Reasoning for (Un)Solvable Loops (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Loop invariants describe valid program properties that hold before and after every loop iteration. As such, loop invariants are the workhorses in formalizing loop semantics and automating the formal analysis and verification of programs with loops. While automatically synthesizing loop invariants is, in general, an uncomputable problem, when considering only single-path loops with linear updates (linear loops), the strongest polynomial invariant is in fact computable [Michael Karr, 1976; Markus Müller-Olm and Helmut Seidl, 2004; Laura Kovács, 2008; Ehud Hrushovski et al., 2018]. Yet, already for loops with "only" polynomial updates, computing the strongest invariant has been an open challenge since 2004 [Markus Müller-Olm and Helmut Seidl, 2004]. In this invited talk, we first present computability results on polynomial invariant synthesis for restricted polynomial loops, called solvable loops [Rodríguez-Carbonell and Kapur, 2004]. Key to solvable loops is that one can automatically compute invariants from closed-form solutions of algebraic recurrence equations that model the loop behaviour [Laura Kovács, 2008; Andreas Humenberger et al., 2017]. We also establish a technique for invariant synthesis for classes of loops that are not solvable, termed unsolvable loops [Daneshvar Amrollahi et al., 2022]. We next study the limits of computability in deriving the (strongest) polynomial invariants for arbitrary polynomial loops. We prove that computing the strongest polynomial invariant of arbitrary, single-path polynomial loops is very hard [Julian Müllner, 2023] - namely, it is at least as hard as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008], a prominent algebraic problem in the theory of linear recurrences. Going beyond single-path loops, we show that the strongest polynomial invariant is uncomputable already for multi-path polynomial loops with arbitrary quadratic polynomial updates [Laura Kovács and Anton Varonka, 2023].
Cite as

Laura Kovács. Algebraic Reasoning for (Un)Solvable Loops (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.MFCS.2023.4,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Algebraic Reasoning for (Un)Solvable Loops}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.4},
  URN =		{urn:nbn:de:0030-drops-185385},
  doi =		{10.4230/LIPIcs.MFCS.2023.4},
  annote =	{Keywords: Symbolic Computation, Formal Methods, Loop Analysis, Polynomial Invariants}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CONCUR.2020
LIPIcs, Volume 171, CONCUR 2020, Complete Volume

Authors: Igor Konnov and Laura Kovács

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
LIPIcs, Volume 171, CONCUR 2020, Complete Volume
Cite as

31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 1-984, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@Proceedings{konnov_et_al:LIPIcs.CONCUR.2020,
  title =	{{LIPIcs, Volume 171, CONCUR 2020, Complete Volume}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{1--984},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020},
  URN =		{urn:nbn:de:0030-drops-128115},
  doi =		{10.4230/LIPIcs.CONCUR.2020},
  annote =	{Keywords: LIPIcs, Volume 171, CONCUR 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.CONCUR.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Igor Konnov and Laura Kovács

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{konnov_et_al:LIPIcs.CONCUR.2020.0,
  author =	{Konnov, Igor and Kov\'{a}cs, Laura},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.0},
  URN =		{urn:nbn:de:0030-drops-128125},
  doi =		{10.4230/LIPIcs.CONCUR.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2017.3
First-Order Interpolation and Grey Areas of Proofs (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract
Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and optimizing interpolants based on transformations of what we call the “grey area” of local proofs. Local changes in proofs can change the extracted interpolant. Our method can describe properties of extracted interpolants obtained by such proof changes as a pseudo-boolean constraint. By optimizing solutions of this constraint we also improve the extracted interpolants. Unlike many other interpolation techniques, our technique is very general and applies to arbitrary theories. Our approach is implemented in the theorem prover Vampire and evaluated on a large number of benchmarks coming from first-order theorem proving and bounded model checking using logic with equality, uninterpreted functions and linear integer arithmetic. Our experiments demonstrate the power of the new techniques: for example, it is not unusual that our proof transformation gives more than a tenfold reduction in the size of interpolants. While local proofs admit efficient interpolation algorithms, standard complete proof systems, such as superposition, for theories having the interpolation property are not necessarily complete for local proofs. In this talk we therefore also investigate interpolant extraction from non-local proofs in the superposition calculus and prove a number of general results about interpolant extraction and complexity of extracted interpolants. In particular, we prove that the number of quantifier alternations in first-order interpolants of formulas without quantifier alternations is unbounded. This result has far-reaching consequences for using local proofs as a foundation for interpolating proof systems - any such proof system should deal with formulas of arbitrary quantifier complexity.
Cite as

Laura Kovács. First-Order Interpolation and Grey Areas of Proofs (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.CSL.2017.3,
  author =	{Kov\'{a}cs, Laura},
  title =	{{First-Order Interpolation and Grey Areas of Proofs}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.3},
  URN =		{urn:nbn:de:0030-drops-76912},
  doi =		{10.4230/LIPIcs.CSL.2017.3},
  annote =	{Keywords: theorem proving, interpolation, proof transformations, constraint solving, program analysis}
}
Document
DOI: 10.4230/OASIcs.WCET.2013.53
The Auspicious Couple: Symbolic Execution and WCET Analysis

Authors: Armin Biere, Jens Knoop, Laura Kovács, and Jakob Zwirchmayr

Published in: OASIcs, Volume 30, 13th International Workshop on Worst-Case Execution Time Analysis (2013)

Abstract
We have recently shown that symbolic execution together with the implicit path enumeration technique can successfully be applied in the Worst-Case Execution Time (WCET) analysis of programs. Symbolic execution offers a precise framework for program analysis and tracks complex program properties by analyzing single program paths in isolation. This path-wise program exploration of symbolic execution is, however, computationally expensive, which often prevents full symbolic analysis of larger applications: the number of paths in a program increases exponentially with the number of conditionals, a situation denoted as the path explosion problem. Therefore, for applying symbolic execution in the timing analysis of programs, we propose to use WCET analysis as a guidance for symbolic execution in order to avoid full symbolic coverage of the program. By focusing only on paths or program fragments that are relevant for WCET analysis, we keep the computational costs of symbolic execution low. Our WCET analysis also profits from the precise results derived via symbolic execution. In this article we describe how use-cases of symbolic execution are materialized in the r-TuBound toolchain and present new applications of WCET-guided symbolic execution for WCET analysis. The new applications of selective symbolic execution are based on reducing the effort of symbolic analysis by focusing only on relevant program fragments. By using partial symbolic program coverage obtained by selective symbolic execution, we improve the WCET analysis and keep the effort for symbolic execution low.
Cite as

Armin Biere, Jens Knoop, Laura Kovács, and Jakob Zwirchmayr. The Auspicious Couple: Symbolic Execution and WCET Analysis. In 13th International Workshop on Worst-Case Execution Time Analysis. Open Access Series in Informatics (OASIcs), Volume 30, pp. 53-63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{biere_et_al:OASIcs.WCET.2013.53,
  author =	{Biere, Armin and Knoop, Jens and Kov\'{a}cs, Laura and Zwirchmayr, Jakob},
  title =	{{The Auspicious Couple: Symbolic Execution and WCET Analysis}},
  booktitle =	{13th International Workshop on Worst-Case Execution Time Analysis},
  pages =	{53--63},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-54-5},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{30},
  editor =	{Maiza, Claire},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2013.53},
  URN =		{urn:nbn:de:0030-drops-41225},
  doi =		{10.4230/OASIcs.WCET.2013.53},
  annote =	{Keywords: WCET analysis, Symbolic execution, WCET refinement, Flow Facts}
}
Document
DOI: 10.4230/DagRep.2.11.45
Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461)

Authors: Nikolaj Bjorner, Krishnendu Chatterjee, Laura Kovacs, and Rupak M. Majumdar

Published in: Dagstuhl Reports, Volume 2, Issue 11 (2013)

Abstract
This report documents the program and the outcomes of the Dagstuhl Seminar 12461 "Games and Decisions for Rigorous Systems Engineering". The seminar brought together researchers working in rigorous software engineering, with a special focus on the interaction between synthesis and automated deduction. This event was the first seminar of this kind and a kickoff of a series of seminars organised on rigorous systems engineering. The theme of the seminar was close in spirit to many events that have been held over the last decades. The talks scheduled during the seminar naturally reflected fundamental research themes of the involved communities.
Cite as

Nikolaj Bjorner, Krishnendu Chatterjee, Laura Kovacs, and Rupak M. Majumdar. Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461). In Dagstuhl Reports, Volume 2, Issue 11, pp. 45-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@Article{bjorner_et_al:DagRep.2.11.45,
  author =	{Bjorner, Nikolaj and Chatterjee, Krishnendu and Kovacs, Laura and Majumdar, Rupak M.},
  title =	{{Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461)}},
  pages =	{45--65},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{2},
  number =	{11},
  editor =	{Bjorner, Nikolaj and Chatterjee, Krishnendu and Kovacs, Laura and Majumdar, Rupak M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.11.45},
  URN =		{urn:nbn:de:0030-drops-39092},
  doi =		{10.4230/DagRep.2.11.45},
  annote =	{Keywords: Systems Engineering, Software Verification, Reactive Synthesis, Automated Deduction}
}

Kovács, Laura

Document
Invited Talk
DOI: 10.4230/LIPIcs.SAT.2026.1
SAT in Saturation: A Satisfied Match (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
Saturation is the leading concept behind the proof-search algorithms of state-of-the-art first-order theorem provers [Filip Bártek et al., 2025; Christoph Weidenbach et al., 2009; Stephan Schulz et al., 2019]. The key idea behind saturation-based proof search is to reduce the problem of proving validity of a first-order formula to the problem of establishing unsatisfiability of the respective formula, by using a sound inference system, such as resolution and superposition [Leo Bachmair and Harald Ganzinger, 2001; Robert Nieuwenhuis and Albert Rubio, 2001]. Central to efficient saturation-based proof search is the implementation of redundancy in the form of simplification rules [John Alan Robinson, 1965; Laura Kovács and Andrei Voronkov, 2013]: such rules do not add new formulas to search space, but instead simplify/delete redundant formulas from the search space, while not loosing refutational completeness of superposition. Redundancy in first-order theorem proving is controlled via term/clause ordering and literal selection functions in extension of standard superposition: redundant clauses are logical consequences of smaller clauses with respect to the considered ordering. While redundancy is essential for efficient proof search, establishing whether an arbitrary first-order formula is redundant is as hard as proving whether it is valid. First-order provers therefore implement sufficient conditions towards proving redundancy, so that these conditions can be efficiently checked, ideally using only syntactic arguments over formulas. One such condition comes with the notion of subsumption, yielding one of the most important simplification rules in automated reasoners [Leo Bachmair and Harald Ganzinger, 1994]. It is common that millions of subsumption checks are performed during a single solver run [Jakob Rath et al., 2022]. However, in contrast to propositional subsumption as used by SAT solvers and implemented using sophisticated polynomial algorithms, first-order subsumption in first-order theorem proving involves NP-complete search queries, turning the efficient use of first-order subsumption into a huge practical burden. This talks presents a tailored integration of SAT solving for detecting variants of subsumption in superposition. Key to our approach is retrieving clauses from the search space and checking whether subsumption with retrieved clauses can be applied, using multi-literal matching. A solution to our SAT-based encoding gives a concrete application of (variants of) subsumption, allowing the first-order prover to apply that instance of subsumption as a simplification rule during saturation [Bernhard Gleiss et al., 2020; Jakob Rath et al., 2022; Robin Coutelier et al., 2025]. Our SAT encoding captures subset relations among literals/clauses and formalizes matching of literals between inference premises/conclusions. We show that SAT encodings improve literal matching, and thus subsumption, in first-order theorem proving. In particular, our experimental results using the Vampire prover demonstrate the practical benefits of using SAT solving for variants of first-order subsumption.
Cite as

Laura Kovács. SAT in Saturation: A Satisfied Match (Invited Talk). In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.SAT.2026.1,
  author =	{Kov\'{a}cs, Laura},
  title =	{{SAT in Saturation: A Satisfied Match}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.1},
  URN =		{urn:nbn:de:0030-drops-263076},
  doi =		{10.4230/LIPIcs.SAT.2026.1},
  annote =	{Keywords: Automated Reasoning, First-Order Theorem Proving, Superposition, Subsumption, Redundancy, SAT Solving, Vampire}
}
Document
DOI: 10.4230/LIPIcs.SAT.2026.14
Generalizing CDCL with Graph Backtracking

Authors: Robin Coutelier, Thomas Hader, and Laura Kovács

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
We present graph backtracking, a novel, fine-grained backtracking scheme for CDCL-based SAT solving, parametrized by a user-defined weight function. For conflict repair, we challenge the decision level abstraction and use the implication graph as a precise guiding structure to minimize the weight of literals that are unassigned. Graph backtracking is sound, complete, and terminating. We show that it is a generalization of chronological and non-chronological backtracking by simulating them with specific weight functions. Our approach is implemented in the experimental solver NapSAT. Empirical results show that graph backtracking requires fewer literal propagations than standard approaches, leading to improved solver runtime.
Cite as

Robin Coutelier, Thomas Hader, and Laura Kovács. Generalizing CDCL with Graph Backtracking. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{coutelier_et_al:LIPIcs.SAT.2026.14,
  author =	{Coutelier, Robin and Hader, Thomas and Kov\'{a}cs, Laura},
  title =	{{Generalizing CDCL with Graph Backtracking}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.14},
  URN =		{urn:nbn:de:0030-drops-263203},
  doi =		{10.4230/LIPIcs.SAT.2026.14},
  annote =	{Keywords: SAT Solving, Backtracking, Conflict Analysis, CDCL}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2026.36
Lean on Vampire Proofs (Short Paper)

Authors: Jonas Bodingbauer, Márton Hajdu, Laura Kovács, Axel Polaczek, and Michael Rawson

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampire’s output. We describe ongoing efforts in reconstructing Vampire proofs as trusted proofs in Lean. Our experiments showcase feasibility of generating trusted Vampire proofs that are validated in Lean.
Cite as

Jonas Bodingbauer, Márton Hajdu, Laura Kovács, Axel Polaczek, and Michael Rawson. Lean on Vampire Proofs (Short Paper). In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 36:1-36:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bodingbauer_et_al:LIPIcs.ITP.2026.36,
  author =	{Bodingbauer, Jonas and Hajdu, M\'{a}rton and Kov\'{a}cs, Laura and Polaczek, Axel and Rawson, Michael},
  title =	{{Lean on Vampire Proofs}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{36:1--36:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.36},
  URN =		{urn:nbn:de:0030-drops-270102},
  doi =		{10.4230/LIPIcs.ITP.2026.36},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Provers, Automated Theorem Provers, Lean, Vampire, Proof Reconstruction}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2026.2
Saturation-Guided Inductive Synthesis (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
Proof by induction is common-place in mathematics [Josef Urban and Geoff Sutcliffe, 2010; Martin Desharnais et al., 2022], formal verification [Raven Beutner and Bernd Finkbeiner, 2024; Wolfgang Ahrendt et al., 2000; Pamina Georgiou et al., 2022], cybersecurity [Simon Jeanteur et al., 2024; Evan Laufer et al., 2024], and many more areas. This talk overviews recent progress in automating inductive reasoning in quantified logic, with applications to code synthesis. Key to our work is saturation-based first-order theorem proving [Laura Kovács and Andrei Voronkov, 2013], using variants of the superposition calculus [Robert Nieuwenhuis and Albert Rubio, 2001]. We show that induction and synthesis are better together in saturation, allowing us not only to prove quantified properties F, but also generate a functional implementation of F during proof search. We showcase our results using the first-order theorem prover Vampire [Filip Bártek et al., 2025], a completely automatic push-button theorem prover for first-order logic with theories, including arithmetic, inductively defined datatypes, induction, and higher-order logic. We structure our talk within three inter-connected parts. First, we overview the main ingredients behind saturation provers [Filip Bártek et al., 2025; Stephan Schulz et al., 2019; Christoph Weidenbach et al., 2009] using superposition. Such provers work by negating an input conjecture F, transforming ¬ F into a clausal normal form, and using superposition inferences to derive new clauses from existing ones until a contradiction is reached; when a contradiction is derived, validity of F is established. Many years of development in saturation-based theorem proving have gone into making this process as efficient as possible, while deriving new clauses only when needed in order to tame growth of the search space. Doing so, highly-efficient superposition calculi parametrized by so-called clause selection functions have been proposed, in order to make as few inferences between clauses as possible. Redundancy elimination techniques further prune the search space. Next, we show how to formalize applications of induction in the saturation process [Márton Hajdú et al., 2022], without bringing drastic changes into the overall framework of first-order proving. A natural choice for implementing induction would be by reducing goals to subgoals, in particular by proving a base case and an inductive step case of a valid induction principle. For example, a goal ∀ x. F(x) over natural numbers x can be proven using structural induction: we prove F[0] (base case) and ∀ x. F(x) ⇒ F(x+1) (step case). However, saturation theorem proving is not about reducing goals to subgoals: in principle, each clause in the search space can be chosen during any step of saturation. We therefore automate induction in saturation as follows. When a clause F(x) is chosen and inductive reasoning over F should be applied (for example, because F uses inductively defined data types x, such as natural numbers), we combine the application of a valid induction schema over F(x) with resolution. Put it simply, induction and resolution are combined in one step of saturation, allowing us to use parts of F(x) as subgoals of F(x). Interestingly with this approach is that clauses generated during saturation may be stronger than the induction schema and, most importantly, are friendly to saturation provers: they are mostly quantifier-free Horn clauses and their (at most one) positive equality cannot be used in many inferences during saturation. Thus, applying many induction inferences during proof search would hardly affect the performance of a saturation prover. Figure 1 lists a property over natural numbers: every natural number x is the half of another natural number y. Proving this property in saturation, and in particular using Vampire, can be achieved by (structural) induction over x. Finally, we extend saturation proof search with code synthesis [Petra Hozzová et al., 2024]. While proving formula F, we track the constructive parts of the proof of F using so-called answer literals [Cordell Green, 1969]. We use these parts to synthesize a program satisfying F and use the applications of induction in saturation to construct recursive programs satisfying F. In a nutshell, the base case and inductive case steps of induction in saturation express how to construct the desired program for the next recursive step using the program for the previous recursive step; we capture this information via answer literals. When we apply induction in saturation, we introduce a special term into the answer literal and record the program corresponding to the induction step. As we prove induction steps, we capture their corresponding programs in the answer literal. Finally, we convert the special tracker terms from the answer literals into recursive functions, and obtain a program satisfying property F. For example, from the proof of property of Figure 1, our approach implemented in Vampire infers the following functional implementation of a recursive function r, while using only the signature of Figure 1: 𝗋(0) & := 0 𝗋(s(x)) & := s(s(𝗋(x))) The above inferred function r satisfies the property of Figure 1 and, for each input natural number x, computes a natural number 𝗋(x) such that x is half of 𝗋(x). In summary, induction and synthesis are better together in saturation-based theorem proving using the superposition calculus. Soundness and practical use of our work has been addressed and experimented using the Vampire theorem prover, both in the case of automating induction [Márton Hajdú et al., 2022; Márton Hajdú et al., 2024] and program synthesis [Petra Hozzová et al., 2023; Petra Hozzová et al., 2024]. Interesting questions regarding completeness arise: if a program satisfying a given property exists, can we derive it from saturation-based proof search? Our recent results [Hajdu et al., 2026] answer this question for recursion-free program using additional assumptions of realizability. A natural direction for future work is to identify realizability assumptions for recursive program synthesis and induction.
Cite as

Laura Kovács. Saturation-Guided Inductive Synthesis (Invited Talk). In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.FSCD.2026.2,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Saturation-Guided Inductive Synthesis}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{2:1--2:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.2},
  URN =		{urn:nbn:de:0030-drops-263521},
  doi =		{10.4230/LIPIcs.FSCD.2026.2},
  annote =	{Keywords: automated reasoning, first-order theorem proving, saturation, induction, program synthesis}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2026.2
Moments in Time: Algebraic Analysis for Solvable Loops (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
With substantial progress in automated reasoning, algebraic approaches emerged to automatically analyse program loops in an exact manner. In this invited talk, we discuss recent results in characterizing the functional behaviour of loops with polynomial arithmetic and probabilistic updates. This problem remains unsolved even when we restrict consideration to loops that are non-nested, without conditionals, and/or without exit conditions [Ehud Hrushovski et al., 2023; Julian Müllner and others, 2024]. We are motivated by applications of computer-aided verification, in particular to assess the safety, security, and sensitivity of computer systems [M. Z. Kwiatkowska et al., 2011; Gilles Barthe et al., 2012; Gilles Barthe and others, 2018; Marcel Moosbrugger et al., 2023; Alessandro Abate et al., 2023; Andrey Kofnov and others, 2024]. We are interested in modeling, deciding, and solving loop analysis. The key to our work are moment-computable loops [L. Kovács, 2008; Marcel Moosbrugger et al., 2022] which allow us to set limits on what is decidable and solvable in loop analysis. Our approach combines algebra, statistics, and automated reasoning to mechanize loop analysis. Various techniques, such as martingale theory and quantifier elimination, can be seen as examples of moment-computable loop analysis. This talk is structured within three inter-connected parts. We first bring moment-based loop analysis into the landscape of {loop invariant synthesis} and extend moment-computable loops with {termination guarantees}. We next automate the reasoning about (probabilistic) loops by summarizing loop semantics as (probabilistic) algebraic recurrences, whose closed-form solutions capture (higher-order) moments, and hence invariants, among loop variables. These recurrences together with loop tests yield moment-based (super)martingales necessary to prove loop termination and compute probability bounds on termination. We finally describe moment-computable loops whose invariant synthesis {decidable} or as {hard} as open problems, such as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008].
Cite as

Laura Kovács. Moments in Time: Algebraic Analysis for Solvable Loops (Invited Talk). In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.STACS.2026.2,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Moments in Time: Algebraic Analysis for Solvable Loops}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.2},
  URN =		{urn:nbn:de:0030-drops-254910},
  doi =		{10.4230/LIPIcs.STACS.2026.2},
  annote =	{Keywords: program analysis, algebraic reasoning, symbolic computation, loop invariants}
}
Document
DOI: 10.4230/DagRep.14.10.22
SAT and Interactions (Dagstuhl Seminar 24421)

Authors: Olaf Beyersdorff, Laura Kovács, Meena Mahajan, Martina Seidl, and Kaspar Kasche

Published in: Dagstuhl Reports, Volume 14, Issue 10 (2025)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar "SAT and Interactions" (24421). The seminar brought together theoreticians and practitioners from the areas of proof complexity, SAT and QBF solving, and first-order theorem proving, who discussed recent developments in their fields and embarked on an interdisciplinary exchange of ideas and techniques between these neighbouring subfields of SAT.
Cite as

Olaf Beyersdorff, Laura Kovács, Meena Mahajan, Martina Seidl, and Kaspar Kasche. SAT and Interactions (Dagstuhl Seminar 24421). In Dagstuhl Reports, Volume 14, Issue 10, pp. 22-38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@Article{beyersdorff_et_al:DagRep.14.10.22,
  author =	{Beyersdorff, Olaf and Kov\'{a}cs, Laura and Mahajan, Meena and Seidl, Martina and Kasche, Kaspar},
  title =	{{SAT and Interactions (Dagstuhl Seminar 24421)}},
  pages =	{22--38},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{14},
  number =	{10},
  editor =	{Beyersdorff, Olaf and Kov\'{a}cs, Laura and Mahajan, Meena and Seidl, Martina and Kasche, Kaspar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.10.22},
  URN =		{urn:nbn:de:0030-drops-230243},
  doi =		{10.4230/DagRep.14.10.22},
  annote =	{Keywords: SAT, QBF, proof complexity, solving, first-order logic, automated theorem proving}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.9
Lazy Reimplication in Chronological Backtracking

Authors: Robin Coutelier, Mathias Fleury, and Laura Kovács

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Chronological backtracking is an interesting SAT solving technique within CDCL reasoning, as it backtracks less aggressively upon conflicts. However, chronological backtracking is more difficult to maintain due to its weaker SAT solving invariants. This paper introduces a lazy reimplication procedure for missed lower implications in chronological backtracking. Our method saves propagations by reimplying literals on demand, rather than eagerly. Due to its modularity, our work can be replicated in other solvers, as shown by our results in the solvers CaDiCaL and Glucose.
Cite as

Robin Coutelier, Mathias Fleury, and Laura Kovács. Lazy Reimplication in Chronological Backtracking. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{coutelier_et_al:LIPIcs.SAT.2024.9,
  author =	{Coutelier, Robin and Fleury, Mathias and Kov\'{a}cs, Laura},
  title =	{{Lazy Reimplication in Chronological Backtracking}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.9},
  URN =		{urn:nbn:de:0030-drops-205313},
  doi =		{10.4230/LIPIcs.SAT.2024.9},
  annote =	{Keywords: Chronological Backtracking, CDCL, Invariants, Watcher Lists}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.41
Linear Loop Synthesis for Quadratic Invariants

Authors: S. Hitarth, George Kenison, Laura Kovács, and Anton Varonka

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather than generating invariants for given loops, in this paper we synthesise loops that exhibit a predefined behaviour given by an invariant. From the perspective of formal loop verification, the synthesised loops are thus correct by design and no longer need to be verified. To overcome the hardness of reasoning with arbitrarily strong invariants, in this paper we construct simple (non-nested) while loops with linear updates that exhibit polynomial equality invariants. Rather than solving arbitrary polynomial equations, we consider loop properties defined by a single quadratic invariant in any number of variables. We present a procedure that, given a quadratic equation, decides whether a loop with affine updates satisfying this equation exists. Furthermore, if the answer is positive, the procedure synthesises a loop and ensures its variables achieve infinitely many different values.
Cite as

S. Hitarth, George Kenison, Laura Kovács, and Anton Varonka. Linear Loop Synthesis for Quadratic Invariants. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 41:1-41:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hitarth_et_al:LIPIcs.STACS.2024.41,
  author =	{Hitarth, S. and Kenison, George and Kov\'{a}cs, Laura and Varonka, Anton},
  title =	{{Linear Loop Synthesis for Quadratic Invariants}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{41:1--41:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.41},
  URN =		{urn:nbn:de:0030-drops-197512},
  doi =		{10.4230/LIPIcs.STACS.2024.41},
  annote =	{Keywords: program synthesis, loop invariants, verification, Diophantine equations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2023.4
Algebraic Reasoning for (Un)Solvable Loops (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Loop invariants describe valid program properties that hold before and after every loop iteration. As such, loop invariants are the workhorses in formalizing loop semantics and automating the formal analysis and verification of programs with loops. While automatically synthesizing loop invariants is, in general, an uncomputable problem, when considering only single-path loops with linear updates (linear loops), the strongest polynomial invariant is in fact computable [Michael Karr, 1976; Markus Müller-Olm and Helmut Seidl, 2004; Laura Kovács, 2008; Ehud Hrushovski et al., 2018]. Yet, already for loops with "only" polynomial updates, computing the strongest invariant has been an open challenge since 2004 [Markus Müller-Olm and Helmut Seidl, 2004]. In this invited talk, we first present computability results on polynomial invariant synthesis for restricted polynomial loops, called solvable loops [Rodríguez-Carbonell and Kapur, 2004]. Key to solvable loops is that one can automatically compute invariants from closed-form solutions of algebraic recurrence equations that model the loop behaviour [Laura Kovács, 2008; Andreas Humenberger et al., 2017]. We also establish a technique for invariant synthesis for classes of loops that are not solvable, termed unsolvable loops [Daneshvar Amrollahi et al., 2022]. We next study the limits of computability in deriving the (strongest) polynomial invariants for arbitrary polynomial loops. We prove that computing the strongest polynomial invariant of arbitrary, single-path polynomial loops is very hard [Julian Müllner, 2023] - namely, it is at least as hard as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008], a prominent algebraic problem in the theory of linear recurrences. Going beyond single-path loops, we show that the strongest polynomial invariant is uncomputable already for multi-path polynomial loops with arbitrary quadratic polynomial updates [Laura Kovács and Anton Varonka, 2023].
Cite as

Laura Kovács. Algebraic Reasoning for (Un)Solvable Loops (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.MFCS.2023.4,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Algebraic Reasoning for (Un)Solvable Loops}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.4},
  URN =		{urn:nbn:de:0030-drops-185385},
  doi =		{10.4230/LIPIcs.MFCS.2023.4},
  annote =	{Keywords: Symbolic Computation, Formal Methods, Loop Analysis, Polynomial Invariants}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CONCUR.2020
LIPIcs, Volume 171, CONCUR 2020, Complete Volume

Authors: Igor Konnov and Laura Kovács

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
LIPIcs, Volume 171, CONCUR 2020, Complete Volume
Cite as

31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 1-984, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@Proceedings{konnov_et_al:LIPIcs.CONCUR.2020,
  title =	{{LIPIcs, Volume 171, CONCUR 2020, Complete Volume}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{1--984},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020},
  URN =		{urn:nbn:de:0030-drops-128115},
  doi =		{10.4230/LIPIcs.CONCUR.2020},
  annote =	{Keywords: LIPIcs, Volume 171, CONCUR 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.CONCUR.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Igor Konnov and Laura Kovács

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{konnov_et_al:LIPIcs.CONCUR.2020.0,
  author =	{Konnov, Igor and Kov\'{a}cs, Laura},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.0},
  URN =		{urn:nbn:de:0030-drops-128125},
  doi =		{10.4230/LIPIcs.CONCUR.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2017.3
First-Order Interpolation and Grey Areas of Proofs (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract
Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and optimizing interpolants based on transformations of what we call the “grey area” of local proofs. Local changes in proofs can change the extracted interpolant. Our method can describe properties of extracted interpolants obtained by such proof changes as a pseudo-boolean constraint. By optimizing solutions of this constraint we also improve the extracted interpolants. Unlike many other interpolation techniques, our technique is very general and applies to arbitrary theories. Our approach is implemented in the theorem prover Vampire and evaluated on a large number of benchmarks coming from first-order theorem proving and bounded model checking using logic with equality, uninterpreted functions and linear integer arithmetic. Our experiments demonstrate the power of the new techniques: for example, it is not unusual that our proof transformation gives more than a tenfold reduction in the size of interpolants. While local proofs admit efficient interpolation algorithms, standard complete proof systems, such as superposition, for theories having the interpolation property are not necessarily complete for local proofs. In this talk we therefore also investigate interpolant extraction from non-local proofs in the superposition calculus and prove a number of general results about interpolant extraction and complexity of extracted interpolants. In particular, we prove that the number of quantifier alternations in first-order interpolants of formulas without quantifier alternations is unbounded. This result has far-reaching consequences for using local proofs as a foundation for interpolating proof systems - any such proof system should deal with formulas of arbitrary quantifier complexity.
Cite as

Laura Kovács. First-Order Interpolation and Grey Areas of Proofs (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{kovacs:LIPIcs.CSL.2017.3,
  author =	{Kov\'{a}cs, Laura},
  title =	{{First-Order Interpolation and Grey Areas of Proofs}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.3},
  URN =		{urn:nbn:de:0030-drops-76912},
  doi =		{10.4230/LIPIcs.CSL.2017.3},
  annote =	{Keywords: theorem proving, interpolation, proof transformations, constraint solving, program analysis}
}
Document
DOI: 10.4230/OASIcs.WCET.2013.53
The Auspicious Couple: Symbolic Execution and WCET Analysis

Authors: Armin Biere, Jens Knoop, Laura Kovács, and Jakob Zwirchmayr

Published in: OASIcs, Volume 30, 13th International Workshop on Worst-Case Execution Time Analysis (2013)

Abstract
We have recently shown that symbolic execution together with the implicit path enumeration technique can successfully be applied in the Worst-Case Execution Time (WCET) analysis of programs. Symbolic execution offers a precise framework for program analysis and tracks complex program properties by analyzing single program paths in isolation. This path-wise program exploration of symbolic execution is, however, computationally expensive, which often prevents full symbolic analysis of larger applications: the number of paths in a program increases exponentially with the number of conditionals, a situation denoted as the path explosion problem. Therefore, for applying symbolic execution in the timing analysis of programs, we propose to use WCET analysis as a guidance for symbolic execution in order to avoid full symbolic coverage of the program. By focusing only on paths or program fragments that are relevant for WCET analysis, we keep the computational costs of symbolic execution low. Our WCET analysis also profits from the precise results derived via symbolic execution. In this article we describe how use-cases of symbolic execution are materialized in the r-TuBound toolchain and present new applications of WCET-guided symbolic execution for WCET analysis. The new applications of selective symbolic execution are based on reducing the effort of symbolic analysis by focusing only on relevant program fragments. By using partial symbolic program coverage obtained by selective symbolic execution, we improve the WCET analysis and keep the effort for symbolic execution low.
Cite as

Armin Biere, Jens Knoop, Laura Kovács, and Jakob Zwirchmayr. The Auspicious Couple: Symbolic Execution and WCET Analysis. In 13th International Workshop on Worst-Case Execution Time Analysis. Open Access Series in Informatics (OASIcs), Volume 30, pp. 53-63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{biere_et_al:OASIcs.WCET.2013.53,
  author =	{Biere, Armin and Knoop, Jens and Kov\'{a}cs, Laura and Zwirchmayr, Jakob},
  title =	{{The Auspicious Couple: Symbolic Execution and WCET Analysis}},
  booktitle =	{13th International Workshop on Worst-Case Execution Time Analysis},
  pages =	{53--63},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-54-5},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{30},
  editor =	{Maiza, Claire},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2013.53},
  URN =		{urn:nbn:de:0030-drops-41225},
  doi =		{10.4230/OASIcs.WCET.2013.53},
  annote =	{Keywords: WCET analysis, Symbolic execution, WCET refinement, Flow Facts}
}
Document
DOI: 10.4230/DagRep.2.11.45
Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461)

Authors: Nikolaj Bjorner, Krishnendu Chatterjee, Laura Kovacs, and Rupak M. Majumdar

Published in: Dagstuhl Reports, Volume 2, Issue 11 (2013)

Abstract
This report documents the program and the outcomes of the Dagstuhl Seminar 12461 "Games and Decisions for Rigorous Systems Engineering". The seminar brought together researchers working in rigorous software engineering, with a special focus on the interaction between synthesis and automated deduction. This event was the first seminar of this kind and a kickoff of a series of seminars organised on rigorous systems engineering. The theme of the seminar was close in spirit to many events that have been held over the last decades. The talks scheduled during the seminar naturally reflected fundamental research themes of the involved communities.
Cite as

Nikolaj Bjorner, Krishnendu Chatterjee, Laura Kovacs, and Rupak M. Majumdar. Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461). In Dagstuhl Reports, Volume 2, Issue 11, pp. 45-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@Article{bjorner_et_al:DagRep.2.11.45,
  author =	{Bjorner, Nikolaj and Chatterjee, Krishnendu and Kovacs, Laura and Majumdar, Rupak M.},
  title =	{{Games and Decisions for Rigorous Systems Engineering (Dagstuhl Seminar 12461)}},
  pages =	{45--65},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{2},
  number =	{11},
  editor =	{Bjorner, Nikolaj and Chatterjee, Krishnendu and Kovacs, Laura and Majumdar, Rupak M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.11.45},
  URN =		{urn:nbn:de:0030-drops-39092},
  doi =		{10.4230/DagRep.2.11.45},
  annote =	{Keywords: Systems Engineering, Software Verification, Reactive Synthesis, Automated Deduction}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact