9 Search Results for "Zohar, Yoni"

Document
DOI: 10.4230/LIPIcs.ITP.2025.1
A Certified Proof Checker for Deep Neural Network Verification in Imandra

Authors: Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz

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

Abstract
Recent advances in the verification of deep neural networks (DNNs) have opened the way for a broader usage of DNN verification technology in many application areas, including safety-critical ones. However, DNN verifiers are themselves complex programs that have been shown to be susceptible to errors and numerical imprecision; this, in turn, has raised the question of trust in DNN verifiers. One prominent attempt to address this issue is enhancing DNN verifiers with the capability of producing certificates of their results that are subject to independent algorithmic checking. While formulations of Marabou certificate checking already exist on top of the state-of-the-art DNN verifier Marabou, they are implemented in C++, and that code itself raises the question of trust (e.g., in the precision of floating point calculations or guarantees for implementation soundness). Here, we present an alternative implementation of the Marabou certificate checking in Imandra - an industrial functional programming language and an interactive theorem prover (ITP) - that allows us to obtain full proof of certificate correctness. The significance of the result is two-fold. Firstly, it gives stronger independent guarantees for Marabou proofs. Secondly, it opens the way for the wider adoption of DNN verifiers in interactive theorem proving in the same way as many ITPs already incorporate SMT solvers.
Cite as

Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz. A Certified Proof Checker for Deep Neural Network Verification in Imandra. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{desmartin_et_al:LIPIcs.ITP.2025.1,
  author =	{Desmartin, Remi and Isac, Omri and Passmore, Grant and Komendantskaya, Ekaterina and Stark, Kathrin and Katz, Guy},
  title =	{{A Certified Proof Checker for Deep Neural Network Verification in Imandra}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{1:1--1:21},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-246000},
  doi =		{10.4230/LIPIcs.ITP.2025.1},
  annote =	{Keywords: Neural Network Verification, Farkas Lemma, Proof Certification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.26
Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL

Authors: Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli

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

Abstract
Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.
Cite as

Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli. Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lachnitt_et_al:LIPIcs.ITP.2025.26,
  author =	{Lachnitt, Hanna and Fleury, Mathias and Barbosa, Haniel and Jakpor, Jibiana and Andreotti, Bruno and Reynolds, Andrew and Schurr, Hans-J\"{o}rg and Barrett, Clark and Tinelli, Cesare},
  title =	{{Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{26:1--26:22},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-246243},
  doi =		{10.4230/LIPIcs.ITP.2025.26},
  annote =	{Keywords: interactive theorem proving, proof assistants, Isabelle/HOL, SMT, certification, proof certificates, proof reconstruction, proof automation}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2025.38
Sledgehammering Without ATPs (Short Paper)

Authors: Martin Desharnais and Jasmin Blanchette

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

Abstract
We describe an alternative architecture for "hammers," inspired by Magnushammer, in which proofs are found by the proof assistant’s built-in automation instead of by external automatic theorem provers (ATPs). We implemented this approach in Isabelle’s Sledgehammer and evaluated it. The new ATP-free approach nicely complements the traditional Sledgehammer. The two approaches in combination solve more goals than the traditional ATP-based approach alone.
Cite as

Martin Desharnais and Jasmin Blanchette. Sledgehammering Without ATPs (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 38:1-38:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{desharnais_et_al:LIPIcs.ITP.2025.38,
  author =	{Desharnais, Martin and Blanchette, Jasmin},
  title =	{{Sledgehammering Without ATPs}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{38:1--38:8},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-246366},
  doi =		{10.4230/LIPIcs.ITP.2025.38},
  annote =	{Keywords: Interactive theorem proving, proof assistants, proof automation}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.21
Practically Feasible Proof Logging for Pseudo-Boolean Optimization

Authors: Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Certifying solvers have long been standard for decision problems in Boolean satisfiability (SAT), allowing for proof logging and checking with very limited overhead, but developing similar tools for combinatorial optimization has remained a challenge. A recent promising approach covering a wide range of solving paradigms is pseudo-Boolean proof logging, but this has mostly consisted of proof-of-concept works far from delivering the performance required for real-world deployment. In this work, we present an efficient toolchain based on VeriPB and CakePB for formally verified pseudo-Boolean optimization. We implement proof logging for the full range of techniques in the state-of-the-art solvers RoundingSat and Sat4j, including core-guided search and linear programming integration with Farkas certificates and cut generation. Our experimental evaluation shows that proof logging and checking performance in this much more expressive paradigm is now quite close to the level of SAT solving, and hence is clearly practically feasible.
Cite as

Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals. Practically Feasible Proof Logging for Pseudo-Boolean Optimization. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 21:1-21:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koops_et_al:LIPIcs.CP.2025.21,
  author =	{Koops, Wietze and Le Berre, Daniel and Myreen, Magnus O. and Nordstr\"{o}m, Jakob and Oertel, Andy and Tan, Yong Kiam and Vinyals, Marc},
  title =	{{Practically Feasible Proof Logging for Pseudo-Boolean Optimization}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{21:1--21:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.21},
  URN =		{urn:nbn:de:0030-drops-238825},
  doi =		{10.4230/LIPIcs.CP.2025.21},
  annote =	{Keywords: proof logging, certifying algorithms, combinatorial optimization, certification, pseudo-Boolean solving, 0-1 integer linear programming}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.4
Bit-Precise Reasoning with Parametric Bit-Vectors

Authors: Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
The SMT-LIB theory of bit-vectors is restricted to bit-vectors of fixed width. However, several important applications can benefit from reasoning about bit-vectors of symbolic widths, i.e., parametric bit-vectors. Recent work has introduced an approach for solving formulas over parametric bit-vectors, via an eager translation to quantified integer arithmetic with uninterpreted functions. The approach was shown to be successful for several applications, including the bit-width independent verification of compiler optimizations, invertibility conditions, and rewrite rules. We extend and improve that approach in several aspects. Theoretically, we improve expressiveness by defining a new theory of parametric bit-vectors that supports more operators and allows reasoning about the bit-widths themselves. Algorithmically, we introduce a lazy algorithm that avoids the use of uninterpreted functions and quantified axioms for them. Empirically, we show a significant improvement by implementing and evaluating our approach, and comparing it experimentally to the previous one.
Cite as

Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli. Bit-Precise Reasoning with Parametric Bit-Vectors. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berger_et_al:LIPIcs.SAT.2025.4,
  author =	{Berger, Zvika and Zohar, Yoni and Niemetz, Aina and Preiner, Mathias and Reynolds, Andrew and Barrett, Clark and Tinelli, Cesare},
  title =	{{Bit-Precise Reasoning with Parametric Bit-Vectors}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.4},
  URN =		{urn:nbn:de:0030-drops-237385},
  doi =		{10.4230/LIPIcs.SAT.2025.4},
  annote =	{Keywords: Satisfiability Modulo Theories, Bit-precise Reasoning, Parametric Bit-vectors}
}
Document
DOI: 10.4230/OASIcs.FMBC.2025.3
Formal Verification in Solidity and Move: Insights from a Comparative Analysis

Authors: Massimo Bartoletti, Silvia Crafa, and Enrico Lipparini

Published in: OASIcs, Volume 129, 6th International Workshop on Formal Methods for Blockchains (FMBC 2025)

Abstract
Formal verification plays a crucial role in making smart contracts safer, being able to find bugs or to guarantee their absence, as well as checking whether the business logic is correctly implemented. For Solidity, even though there already exist several mature verification tools, the semantical quirks of the language can make verification quite hard in practice. Move, on the other hand, has been designed with security and verification in mind, and it has been accompanied since its early stages by a formal verification tool, the Move Prover. In this paper, we investigate through a comparative analysis: 1) how the different designs of the two contract languages impact verification, and 2) what is the state-of-the-art of verification tools for the two languages, and how do they compare on three paradigmatic use cases. Our investigation is supported by an open dataset of verification tasks performed in Certora and in the Aptos Move Prover.
Cite as

Massimo Bartoletti, Silvia Crafa, and Enrico Lipparini. Formal Verification in Solidity and Move: Insights from a Comparative Analysis. In 6th International Workshop on Formal Methods for Blockchains (FMBC 2025). Open Access Series in Informatics (OASIcs), Volume 129, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bartoletti_et_al:OASIcs.FMBC.2025.3,
  author =	{Bartoletti, Massimo and Crafa, Silvia and Lipparini, Enrico},
  title =	{{Formal Verification in Solidity and Move: Insights from a Comparative Analysis}},
  booktitle =	{6th International Workshop on Formal Methods for Blockchains (FMBC 2025)},
  pages =	{3:1--3:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-371-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{129},
  editor =	{Marmsoler, Diego and Xu, Meng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2025.3},
  URN =		{urn:nbn:de:0030-drops-230302},
  doi =		{10.4230/OASIcs.FMBC.2025.3},
  annote =	{Keywords: Smart contracts, Solidity, Move, Verification, Blockchain}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.37
On the Existential Theory of the Reals Enriched with Integer Powers of a Computable Number

Authors: Jorge Gallego-Hernández and Alessio Mansutti

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
This paper investigates ∃ℝ(ξ^ℤ), that is the extension of the existential theory of the reals by an additional unary predicate ξ^ℤ for the integer powers of a fixed computable real number ξ > 0. If all we have access to is a Turing machine computing ξ, it is not possible to decide whether an input formula from this theory is satisfiable. However, we show an algorithm to decide this problem when - ξ is known to be transcendental, or - ξ is a root of some given integer polynomial (that is, ξ is algebraic). In other words, knowing the algebraicity of ξ suffices to circumvent undecidability. Furthermore, we establish complexity results under the proviso that ξ enjoys what we call a polynomial root barrier. Using this notion, we show that the satisfiability problem of ∃ℝ(ξ^ℤ) is - in ExpSpace if ξ is an algebraic number, and - in 3Exp if ξ is a logarithm of an algebraic number, Euler’s e, or the number π, among others. To establish our results, we first observe that the satisfiability problem of ∃ℝ(ξ^ℤ) reduces in exponential time to the problem of solving quantifier-free instances of the theory of the reals where variables range over ξ^ℤ. We then prove that these instances have a small witness property: only finitely many integer powers of ξ must be considered to find whether a formula is satisfiable. Our complexity results are shown by relying on well-established machinery from Diophantine approximation and transcendental number theory, such as bounds for the transcendence measure of numbers. As a by-product of our results, we are able to remove the appeal to Schanuel’s conjecture from the proof of decidability of the entropic risk threshold problem for stochastic games with rational probabilities, rewards and threshold [Baier et al., MFCS, 2023]: when the base of the entropic risk is e and the aversion factor is a fixed algebraic number, the problem is (unconditionally) in Exp.
Cite as

Jorge Gallego-Hernández and Alessio Mansutti. On the Existential Theory of the Reals Enriched with Integer Powers of a Computable Number. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gallegohernandez_et_al:LIPIcs.STACS.2025.37,
  author =	{Gallego-Hern\'{a}ndez, Jorge and Mansutti, Alessio},
  title =	{{On the Existential Theory of the Reals Enriched with Integer Powers of a Computable Number}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.37},
  URN =		{urn:nbn:de:0030-drops-228635},
  doi =		{10.4230/LIPIcs.STACS.2025.37},
  annote =	{Keywords: Theory of the reals with exponentiation, decision procedures, computability}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAT.2024.2
Scalable Proof Production and Checking in SMT (Invited Talk)

Authors: Cesare Tinelli

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

Abstract
Solvers for Satisfiability Modulo Theories (SMT) have become crucial components in safety- or mission-critical formal methods applications, in particular model checking, verification, and security analysis. Since state-of-the-art SMT solvers are large and complex systems, they are prohibitively difficult to prove correct. Hence, proof production is essential as a way to demonstrate instead the correctness of their responses, making those responses amenable to independent verification. Historically, the main challenges for proof production in SMT have been solver performance and proof coverage, often leading to the disabling of many sophisticated solving techniques when running in proof-production mode, or to coarse-grained, and harder to check, proofs. The first part of this talk presents a flexible proof-production architecture designed to handle the complexity of versatile, industrial-strength SMT solvers, and discusses how it has been leveraged to produce detailed proofs, even for sophisticated reasoning components. The architecture, implemented in the state-of-the-art SMT solver cvc5, allows proofs to be produced modularly, as needed, and with various safeguards for correctness. The architecture supports the generation of textual proof certificates in different formats, for offline proof checking by external tools, as well as a rich API, which is useful for online integration of the SMT solver into other reasoning tools such as, for instance, skeptical proof assistants. Extensive experimental evaluations with both SMT-LIB benchmarks and benchmarks provided by industrial partners have shown that the new architecture results in greater proof coverage than previous approaches, imposes a small runtime overhead, and supports fine-grained proofs in the great majority of cases. The second part of the talk gives an overview of a new generic language for expressing SMT proof certificates that builds on almost two decades of work and experience in proof generation and checking in SMT and combines the benefits of several previous efforts on the topic. While developed to express cvc5’s proof certificates, the language is meant to be useful to other SMT solvers as well. It is in fact a logical framework, based on the syntax and semantics of the upcoming Version 3 of the SMT-LIB standard, that can be customized, as in the case of cvc5, with the specific proof system used by the solver through the definition of new symbols, binders and proof rules. In addition, it features an intuitive syntax for representing natural-deduction-style proofs and the ability to integrate other proof formats (such as, for instance, those currently used by SAT solvers) via the use of oracles. The talk discusses an initial evaluation of the proof language, obtained with a companion checker for it and an instantiation to cvc5’s proof system. The evaluation shows the viability of high-performance, fine-grained proof production and checking for SMT. The talk concludes with a brief overview of future work and new potential applications enabled by scalable proof certificate production and checking.
Cite as

Cesare Tinelli. Scalable Proof Production and Checking in SMT (Invited Talk). In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{tinelli:LIPIcs.SAT.2024.2,
  author =	{Tinelli, Cesare},
  title =	{{Scalable Proof Production and Checking in SMT}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{2:1--2:2},
  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.2024.2},
  URN =		{urn:nbn:de:0030-drops-205241},
  doi =		{10.4230/LIPIcs.SAT.2024.2},
  annote =	{Keywords: Satisfiability Modulo Theories, Proof generation and certification}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.26
DNN Verification, Reachability, and the Exponential Function Problem

Authors: Omri Isac, Yoni Zohar, Clark Barrett, and Guy Katz

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: (i) the decidability of verifying DNNs with a particular set of piecewise-smooth activation functions, including Sigmoid and tanh, is equivalent to a well-known, open problem formulated by Tarski; and (ii) the DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network’s activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools.
Cite as

Omri Isac, Yoni Zohar, Clark Barrett, and Guy Katz. DNN Verification, Reachability, and the Exponential Function Problem. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{isac_et_al:LIPIcs.CONCUR.2023.26,
  author =	{Isac, Omri and Zohar, Yoni and Barrett, Clark and Katz, Guy},
  title =	{{DNN Verification, Reachability, and the Exponential Function Problem}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.26},
  URN =		{urn:nbn:de:0030-drops-190205},
  doi =		{10.4230/LIPIcs.CONCUR.2023.26},
  annote =	{Keywords: Formal Verification, Computability Theory, Deep Neural Networks}
}
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