79 Search Results for "Zhang, Lijun"

Volume

LIPIcs, Volume 118

29th International Conference on Concurrency Theory (CONCUR 2018)

CONCUR 2018, September 4-7, 2018, Beijing, China

Editors: Sven Schewe and Lijun Zhang

Document
DOI: 10.4230/LIPIcs.CSL.2026.40
The Groupoid-Syntax of Type Theory Is a Set

Authors: Thorsten Altenkirch, Ambrus Kaposi, and Szumi Xie

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the traditional notion of CwFs is the requirement to set-truncate types, which excludes models based on univalent categories, such as the standard set model. To address this limitation, we introduce the concept of a Groupoid Category with Families (GCwF). This framework truncates types at the groupoid level and incorporates coherence equations, providing a natural extension of the CwF framework when starting from a 1-category. We demonstrate that the initial GCwF for a type theory with a base family of sets and Π-types (groupoid-syntax) is set-truncated. Consequently, this allows us to utilize the conventional intrinsic syntax of type theory while enabling interpretations in semantically richer and more natural models. All constructions in this paper were formalised in Cubical Agda.
Cite as

Thorsten Altenkirch, Ambrus Kaposi, and Szumi Xie. The Groupoid-Syntax of Type Theory Is a Set. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 40:1-40:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{altenkirch_et_al:LIPIcs.CSL.2026.40,
  author =	{Altenkirch, Thorsten and Kaposi, Ambrus and Xie, Szumi},
  title =	{{The Groupoid-Syntax of Type Theory Is a Set}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{40:1--40:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.40},
  URN =		{urn:nbn:de:0030-drops-254650},
  doi =		{10.4230/LIPIcs.CSL.2026.40},
  annote =	{Keywords: Categorical models of type theory, category with families, groupoids, coherence, homotopy type theory}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.47
Useful Call-by-Value: A Semantic Interpretation via Quantitative Types

Authors: Pablo Barenbaum, Delia Kesner, and Mariana Milicich

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Useful evaluation is an optimised evaluation mechanism for functional programming languages. It relies on representing terms with sharing and imposing a restricted notion of useful substitutions, that intuitively disallows copying subterms that do not contribute to the progress of the computation. In particular, useful call-by-value evaluation optimises the standard call-by-value strategy by preserving its original semantics. This preservation result has been shown by means of syntactical rewriting techniques, difficult to adapt to alternative variants of the calculi at play. In this work, we present the first semantic model of useful call-by-value evaluation through the non-idempotent intersection type system 𝒰. Our first contribution is a characterisation of termination for useful call-by-value evaluation via system 𝒰. That is, a term is typable in system 𝒰 if and only if it terminates in the useful call-by-value strategy. As a second contribution, we show that system 𝒰 provides a quantitative interpretation for useful call-by-value evaluation, offering exact step-count information for program evaluation. Our third contribution is that termination in call-by-value and useful call-by-value are equivalent. This ensures in particular that call-by-value, which is (potentially) erasing, and useful call-by-value, which is non-erasing, are observationally equivalent. Even though the specification of the operational semantics of useful evaluation is highly complex, system 𝒰 is notably simple. As far as we know, system 𝒰 is one of the scarce quantitative type systems capturing exactly the substitution step-count for variables and abstractions in an open call-by-value strategy.
Cite as

Pablo Barenbaum, Delia Kesner, and Mariana Milicich. Useful Call-by-Value: A Semantic Interpretation via Quantitative Types. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 47:1-47:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barenbaum_et_al:LIPIcs.CSL.2026.47,
  author =	{Barenbaum, Pablo and Kesner, Delia and Milicich, Mariana},
  title =	{{Useful Call-by-Value: A Semantic Interpretation via Quantitative Types}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{47:1--47:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.47},
  URN =		{urn:nbn:de:0030-drops-254721},
  doi =		{10.4230/LIPIcs.CSL.2026.47},
  annote =	{Keywords: Lambda calculus, Evaluation strategies, Call-by-Value, Useful Evaluation, Intersection types, Quantitative models}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.99
AC⁰[p]-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard

Authors: Jiaqi Lu, Rahul Santhanam, and Iddo Tzameret

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study whether lower bounds against constant-depth algebraic circuits computing the Permanent over finite fields (Limaye-Srinivasan-Tavenas [J. ACM, 2025] and Forbes [CCC'24]) are hard to prove in certain proof systems. We focus on a DNF formula that expresses that such lower bounds are hard for constant-depth algebraic proofs. Using an adaptation of the diagonalization framework of Santhanam and Tzameret (SIAM J. Comput., 2025), we show unconditionally that this family of DNF formulas does not admit polynomial-size propositional AC⁰[p]-Frege proofs, infinitely often. This rules out the possibility that the DNF family is easy, and establishes that its status is either that of a hard tautology for AC⁰[p]-Frege or else unprovable (i.e., not a tautology). While it remains open whether the DNFs in question are tautologies, we provide evidence in this direction. In particular, under the plausible assumption that certain (weak) properties of multilinear algebra - specifically, those involving tensor rank - do not admit short constant-depth algebraic proofs, the DNFs are tautologies. We also observe that several weaker variants of the DNF formula are provably tautologies, and we show that the question of whether the DNFs are tautologies connects to conjectures of Razborov (ICALP'96) and Krajíček (J. Symb. Log., 2004). Additionally, our result has the following special features: ii) Existential depth amplification: the DNF formula considered is parameterised by a constant depth d bounding the depth of the algebraic proofs. We show that there exists some fixed depth d such that if there are no small depth-d algebraic proofs of certain circuit lower bounds for the Permanent, then there are no such small algebraic proofs in any constant depth. iii) Necessity: We show that our result is a necessary step towards establishing lower bounds against constant-depth algebraic proofs, and more generally against any sufficiently strong proof system. In particular, showing there are no short proofs for our DNF formulas, obtained by replacing "constant-depth algebraic circuits" with any "reasonable" algebraic circuit class C, is necessary in order to prove any super-polynomial lower bounds against algebraic proofs operating with circuits from C.
Cite as

Jiaqi Lu, Rahul Santhanam, and Iddo Tzameret. AC⁰[p]-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 99:1-99:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lu_et_al:LIPIcs.ITCS.2026.99,
  author =	{Lu, Jiaqi and Santhanam, Rahul and Tzameret, Iddo},
  title =	{{AC⁰\lbrackp\rbrack-Frege Cannot Efficiently Prove That Constant-Depth Algebraic Circuit Lower Bounds Are Hard}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{99:1--99:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.99},
  URN =		{urn:nbn:de:0030-drops-253865},
  doi =		{10.4230/LIPIcs.ITCS.2026.99},
  annote =	{Keywords: Complexity, Lower bounds, Proof complexity, AC⁰\lbrackp\rbrack-Frege, Diagonalisation, Algebraic complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2025.2
Unboundedness Problems for Formal Languages (Invited Talk)

Authors: Georg Zetzsche

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Informally, unboundedness problems are decision problems that ask about the existence of infinitely many words (satisfying certain properties) in a formal language. For example: Is a given language infinite? Or: Does a given language have super-polynomial growth? These came into focus in recent years because of their connections to downward closure computation and separability problems. Although unboundedness problems may seem difficult at first, it turns out that there are techniques that are at the same time conceptually very simple, but also apply to a surprisingly wide variety of language classes. The talk will survey recent results (and techniques) concerning unboundedness problems.
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Georg Zetzsche. Unboundedness Problems for Formal Languages (Invited Talk). In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zetzsche:LIPIcs.FSTTCS.2025.2,
  author =	{Zetzsche, Georg},
  title =	{{Unboundedness Problems for Formal Languages}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.2},
  URN =		{urn:nbn:de:0030-drops-250810},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.2},
  annote =	{Keywords: Decidability, formal languages, unifying frameworks, downward closure, separability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.8
Parameterized Verification of Timed Networks with Clock Invariants

Authors: Étienne André, Swen Jacobs, Shyam Lal Karra, and Ocan Sankur

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via location guards that enable a transition only if there is another process in a certain location. We solve for the first time the case with unrestricted clock invariants, and establish that the parameterized model checking problem (PMCP) over finite local traces can be reduced to the corresponding model checking problem on a single TA. Moreover, we prove that the PMCP for networks that communicate via lossy broadcast can be reduced to the PMCP for DTNs. Finally, we show that for networks with k-wise synchronization, and therefore also for timed Petri nets, location reachability can be reduced to location reachability in DTNs. As a consequence we can answer positively the open problem from Abdulla et al. (2018) whether the universal safety problem for timed Petri nets with multiple clocks is decidable.
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Étienne André, Swen Jacobs, Shyam Lal Karra, and Ocan Sankur. Parameterized Verification of Timed Networks with Clock Invariants. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andre_et_al:LIPIcs.FSTTCS.2025.8,
  author =	{Andr\'{e}, \'{E}tienne and Jacobs, Swen and Karra, Shyam Lal and Sankur, Ocan},
  title =	{{Parameterized Verification of Timed Networks with Clock Invariants}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.8},
  URN =		{urn:nbn:de:0030-drops-250878},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.8},
  annote =	{Keywords: Networks of Timed Automata, Parameterized Verification, Timed Petri Nets}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.16
Finiteness of Symbolic Derivatives in Lean

Authors: Ekaterina Zhuchko, Hendrik Maarand, Margus Veanes, and Gabriel Ebner

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Brzozowski proved that the set of derivatives of any regular expression is finite modulo associativity, idempotence and, notably, commutativity of the union operator. We extend this result to the case of symbolic location based derivatives, for which we prove finiteness of the state space by quotienting only by associativity, deduplication and idempotence (ADI); the fact that we don't use commutativity allows for this result to carry over to the derivative based backtracking (PCRE) match semantics, where the union operator is noncommutative. Furthermore, we consider regular expressions extended with lookarounds, intersection, and negation. We also show that our method for proving finiteness allows us to include certain simplification rules in the derivative operation while preserving finiteness. The finiteness proof is constructive: given an expression R, we construct a finite set that is an overapproximation (modulo ADI) of the set of derivatives of R. We reuse some of the infrastructure provided in previous formalization efforts for regular expressions in Lean 4, showing the flexibility and reusability of the framework.
Cite as

Ekaterina Zhuchko, Hendrik Maarand, Margus Veanes, and Gabriel Ebner. Finiteness of Symbolic Derivatives in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhuchko_et_al:LIPIcs.ITP.2025.16,
  author =	{Zhuchko, Ekaterina and Maarand, Hendrik and Veanes, Margus and Ebner, Gabriel},
  title =	{{Finiteness of Symbolic Derivatives in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.16},
  URN =		{urn:nbn:de:0030-drops-246144},
  doi =		{10.4230/LIPIcs.ITP.2025.16},
  annote =	{Keywords: Lean, regular languages, lookarounds, derivatives, finiteness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.51
Word Structures and Their Automatic Presentations

Authors: Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study automatic presentations of the structures (ℕ; S), (ℕ; E_S), (ℕ; ≤), and their expansions by a unary predicate U. Here S is the successor function, E_S is the undirected version of S, and ≤ is the natural order. We call these structures word structures. Our goal is three-fold. First, we study the isomorphism problem for automatic word structures by focusing on the following three problems. The first problem asks to design an algorithm that, given an automatic structure A, decides if A is isomorphic to (ℕ; S). The second asks to design an algorithm that, given two automatic presentations of (ℕ; S, U₁) and (ℕ; S, U₂), where U₁ and U₂ are unary predicates, decides if these structures are isomorphic. The third problem investigates if there is an algorithm that, given two automatic presentations of (ℕ; ≤, U₁) and (ℕ; ≤, U₂), decides whether U₁ ∩ U₂ ≠ ∅. We show that these problems are undecidable. Next, we study intrinsic regularity of the function S in the structure Path_ω = (ℕ; E_S). We build an automatic presentation of Path_ω in which S is not regular. This implies that S is not intrinsically regular in Path_ω. For U ⊆ ℕ, let d_U be the function that computes the distances between the consecutive elements of U. We build automatic presentations of (ℕ; ≤, U) where d_U can realise logarithmic, radical, intermediate, and exponential functions.
Cite as

Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge. Word Structures and Their Automatic Presentations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gong_et_al:LIPIcs.MFCS.2025.51,
  author =	{Gong, Xiaoyang and Khoussainov, Bakh and Zhuge, Yuyang},
  title =	{{Word Structures and Their Automatic Presentations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-241581},
  doi =		{10.4230/LIPIcs.MFCS.2025.51},
  annote =	{Keywords: Automatic structures, the isomorphism problem, decidability, undecidability, regular relations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.88
Color Refinement for Relational Structures

Authors: Benjamin Scheidt and Nicole Schweikardt

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Color Refinement, also known as Naive Vertex Classification, is a classical method to distinguish graphs by iteratively computing a coloring of their vertices. While it is traditionally used as an imperfect way to test for isomorphism, the algorithm has permeated many other, seemingly unrelated, areas of computer science. The method is algorithmically simple, and it has a well-understood distinguishing power: it has been logically characterized by Immerman and Lander (1990) and Cai, Fürer, Immerman (1992), who showed that it distinguishes precisely those graphs that can be distinguished by a sentence of first-order logic with counting quantifiers and only two variables. A combinatorial characterization was given by Dvořák (2010), who showed that it distinguishes precisely those graphs that differ in the number of homomorphisms from some tree. In this paper, we introduce Relational Color Refinement (RCR, for short), a generalization of the Color Refinement method from graphs to arbitrary relational structures, whose distinguishing power admits the equivalent combinatorial and logical characterizations as Color Refinement has on graphs: we show that RCR distinguishes precisely those structures that differ in the number of homomorphisms from an acyclic connected relational structure. Further, we show that RCR distinguishes precisely those structures that are distinguished by a sentence of the guarded fragment of first-order logic with counting quantifiers. Additionally, we show that for every fixed finite relational signature, RCR can be implemented to run on structures of that signature in time O(N⋅log N), where N denotes the number of tuples present in the structure.
Cite as

Benjamin Scheidt and Nicole Schweikardt. Color Refinement for Relational Structures. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 88:1-88:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{scheidt_et_al:LIPIcs.MFCS.2025.88,
  author =	{Scheidt, Benjamin and Schweikardt, Nicole},
  title =	{{Color Refinement for Relational Structures}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{88:1--88:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.88},
  URN =		{urn:nbn:de:0030-drops-241958},
  doi =		{10.4230/LIPIcs.MFCS.2025.88},
  annote =	{Keywords: color refinement, counting logics, homomorphism counts, homomorphism indistinguishability, guarded logics, pebble games, relational structures, alpha-acyclicity, join-trees}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.38
The Complexity of Separability for Semilinear Sets and Parikh Automata

Authors: Elias Rojas Collins, Chris Köcher, and Georg Zetzsche

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In a separability problem, we are given two sets K and L from a class 𝒞, and we want to decide whether there exists a set S from a class 𝒮 such that K ⊆ S and S ∩ L = ∅. In this case, we speak of separability of sets in 𝒞 by sets in 𝒮. We study two types of separability problems. First, we consider separability of semilinear sets (i.e. subsets of ℕ^d for some d) by sets definable by quantifier-free monadic Presburger formulas (or equivalently, the recognizable subsets of ℕ^d). Here, a formula is monadic if each atom uses at most one variable. Second, we consider separability of languages of Parikh automata by regular languages. A Parikh automaton is a machine with access to counters that can only be incremented, and have to meet a semilinear constraint at the end of the run. Both of these separability problems are known to be decidable with elementary complexity. Our main results are that both problems are coNP-complete. In the case of semilinear sets, coNP-completeness holds regardless of whether the input sets are specified by existential Presburger formulas, quantifier-free formulas, or semilinear representations. Our results imply that recognizable separability of rational subsets of Σ* × ℕ^d (shown decidable by Choffrut and Grigorieff) is coNP-complete as well. Another application is that regularity of deterministic Parikh automata (where the target set is specified using a quantifier-free Presburger formula) is coNP-complete as well.
Cite as

Elias Rojas Collins, Chris Köcher, and Georg Zetzsche. The Complexity of Separability for Semilinear Sets and Parikh Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{collins_et_al:LIPIcs.MFCS.2025.38,
  author =	{Collins, Elias Rojas and K\"{o}cher, Chris and Zetzsche, Georg},
  title =	{{The Complexity of Separability for Semilinear Sets and Parikh Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.38},
  URN =		{urn:nbn:de:0030-drops-241457},
  doi =		{10.4230/LIPIcs.MFCS.2025.38},
  annote =	{Keywords: Vector Addition System, Separability, Regular Language}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.31
Games with ω-Automatic Preference Relations

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.
Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruyere_et_al:LIPIcs.MFCS.2025.31,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{Games with \omega-Automatic Preference Relations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-241381},
  doi =		{10.4230/LIPIcs.MFCS.2025.31},
  annote =	{Keywords: Games played on graphs, Nash equilibrium, \omega-automatic relations, \omega-recognizable relations, constrained Nash equilibria existence problem}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.17
Just Verification of Mutual Exclusion Algorithms

Authors: Rob van Glabbeek, Bas Luttik, and Myrthe S. C. Spronck

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We verify the correctness of a variety of mutual exclusion algorithms through model checking. We look at algorithms where communication is via shared read/write registers, where those registers can be atomic or non-atomic. For the verification of liveness properties, it is necessary to assume a completeness criterion to eliminate spurious counterexamples. We use justness as completeness criterion. Justness depends on a concurrency relation; we consider several such relations, modelling different assumptions on the working of the shared registers. We present executions demonstrating the violation of correctness properties by several algorithms, and in some cases suggest improvements.
Cite as

Rob van Glabbeek, Bas Luttik, and Myrthe S. C. Spronck. Just Verification of Mutual Exclusion Algorithms. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanglabbeek_et_al:LIPIcs.CONCUR.2025.17,
  author =	{van Glabbeek, Rob and Luttik, Bas and Spronck, Myrthe S. C.},
  title =	{{Just Verification of Mutual Exclusion Algorithms}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{17:1--17:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.17},
  URN =		{urn:nbn:de:0030-drops-239670},
  doi =		{10.4230/LIPIcs.CONCUR.2025.17},
  annote =	{Keywords: Mutual exclusion, safe registers, regular registers, overlapping reads and writes, atomicity, safety, liveness, starvation freedom, justness, model checking, mCRL2}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.31
Compositional Reasoning for Parametric Probabilistic Automata

Authors: Hannah Mertens, Tim Quatmann, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions over a finite set of parameters. We lift an existing framework for PA to the pPA setting, incorporating asymmetric, circular, and interleaving proof rules. Our approach enables the verification of a broad spectrum of multi-objective queries for pPA, encompassing probabilistic properties and (parametric) expected total rewards. Additionally, we introduce a rule for reasoning about monotonicity in composed pPAs.
Cite as

Hannah Mertens, Tim Quatmann, and Joost-Pieter Katoen. Compositional Reasoning for Parametric Probabilistic Automata. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mertens_et_al:LIPIcs.CONCUR.2025.31,
  author =	{Mertens, Hannah and Quatmann, Tim and Katoen, Joost-Pieter},
  title =	{{Compositional Reasoning for Parametric Probabilistic Automata}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.31},
  URN =		{urn:nbn:de:0030-drops-239810},
  doi =		{10.4230/LIPIcs.CONCUR.2025.31},
  annote =	{Keywords: Verification, Probabilistic systems, Assume-guarantee reasoning, Parametric Probabilistic Automata, Parameter synthesis}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.32
Resolving Nondeterminism by Chance

Authors: Soumyajit Paul, David Purser, Sven Schewe, Qiyi Tang, Patrick Totzke, and Di-De Yen

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some accepting run, then the constructed run is also accepting. Motivated by checking qualitative properties in probabilistic verification, we consider the setting where the resolver strategy can randomise and only needs to succeed with lower-bounded probability. We study the expressiveness of such stochastically-resolvable automata as well as consider the decision questions of whether a given automaton has this property. In particular, we show that it is undecidable to check if a given NFA is λ-stochastically resolvable. This problem is decidable for finitely-ambiguous automata. We also present complexity upper and lower bounds for several well-studied classes of automata for which this problem remains decidable.
Cite as

Soumyajit Paul, David Purser, Sven Schewe, Qiyi Tang, Patrick Totzke, and Di-De Yen. Resolving Nondeterminism by Chance. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{paul_et_al:LIPIcs.CONCUR.2025.32,
  author =	{Paul, Soumyajit and Purser, David and Schewe, Sven and Tang, Qiyi and Totzke, Patrick and Yen, Di-De},
  title =	{{Resolving Nondeterminism by Chance}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.32},
  URN =		{urn:nbn:de:0030-drops-239822},
  doi =		{10.4230/LIPIcs.CONCUR.2025.32},
  annote =	{Keywords: History-determinism, finite automata, probabilistic automata}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.36
Explainability is a Game for Probabilistic Bisimilarity Distances

Authors: Emily Vlasman, Anto Nanah Ji, James Worrell, and Franck van Breugel

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We revisit a game from the literature that characterizes the probabilistic bisimilarity distances of a labelled Markov chain. We illustrate how an optimal policy of the game can explain these distances. Like the games that characterize bisimilarity and probabilistic bisimilarity, the game is played on pairs of states and matches transitions of those states. To obtain more convincing and interpretable explanations than those provided by generic optimal policies, we restrict to optimal policies that delay reaching observably inequivalent state pairs for as long as possible (called 1-maximal) while quickly reaching equivalent ones (called 0-minimal). We present iterative algorithms that compute 1-maximal and 0-minimal policies and prove an exponential lower bound for the number of iterations of the algorithm that computes 1-maximal policies.
Cite as

Emily Vlasman, Anto Nanah Ji, James Worrell, and Franck van Breugel. Explainability is a Game for Probabilistic Bisimilarity Distances. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vlasman_et_al:LIPIcs.CONCUR.2025.36,
  author =	{Vlasman, Emily and Nanah Ji, Anto and Worrell, James and van Breugel, Franck},
  title =	{{Explainability is a Game for Probabilistic Bisimilarity Distances}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.36},
  URN =		{urn:nbn:de:0030-drops-239861},
  doi =		{10.4230/LIPIcs.CONCUR.2025.36},
  annote =	{Keywords: probabilistic bisimilarity distance, labelled Markov chain, game, policy, explainability}
}
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