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Tracy, Traces, and Transducers: Computable Counterexamples and Explanations for HyperLTL Model-Checking (2404.18280v2)

Published 28 Apr 2024 in cs.LO and cs.FL

Abstract: HyperLTL model-checking enables the automated verification of information-flow properties for security-critical systems. However, it only provides a binary answer. Here, we introduce two paradigms to compute counterexamples and explanations for HyperLTL model-checking, thereby considerably increasing its usefulness. Both paradigms are based on the maxim ``counterexamples/explanations are Skolem functions for the existentially quantified trace variables''. Our first paradigm is complete (everything can be explained), but restricted to ultimately periodic system traces. The second paradigm works with (Turing machine) computable Skolem functions and is therefore much more general, but also shown incomplete (not everything can computably be explained). Finally, we prove that it is decidable whether a given finite transition system and a formula have computable Skolem functions witnessing that the system satisfies the formula. Our algorithm also computes transducers implementing computable Skolem functions, if they exist.

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References (31)
  1. Counterexample generation for discrete-time Markov models: An introductory survey. In Marco Bernardo, Ferruccio Damiani, Reiner Hähnle, Einar Broch Johnsen, and Ina Schaefer, editors, SFM 2014, volume 8483 of LNCS, pages 65–121. Springer, 2014.
  2. The basic concepts and constructions of general topology. In L. S. Arkhangel’skiǐ, A. V.and Pontryagin, editor, General Topology I: Basic Concepts and Constructions Dimension Theory, pages 1–90. Springer, 1990.
  3. Explainable artificial intelligence (XAI): concepts, taxonomies, opportunities and challenges toward responsible AI. Inf. Fusion, 58:82–115, 2020.
  4. Hierarchical information and the synthesis of distributed strategies. Acta Informatica, 55(8):669–701, 2018.
  5. Prophecy variables for hyperproperty verification. In CSF 2022, pages 471–485. IEEE, 2022.
  6. Bounded model checking. Adv. Comput., 58:117–148, 2003.
  7. Counterexample-guided abstraction refinement. In E. Allen Emerson and A. Prasad Sistla, editors, CAV, volume 1855 of LNCS, pages 154–169. Springer, 2000.
  8. Tree-like counterexamples in model checking. In LICS 2002, pages 19–29. IEEE Computer Society, 2002.
  9. Temporal logics for hyperproperties. In Martín Abadi and Steve Kremer, editors, POST 2014, volume 8414 of LNCS, pages 265–284. Springer, 2014.
  10. Hyperproperties. J. Comput. Secur., 18(6):1157–1210, 2010.
  11. Explaining hyperproperty violations. In Sharon Shoham and Yakir Vizel, editors, CAV 2022, Part I, volume 13371 of LNCS, pages 407–429. Springer, 2022.
  12. Regular expressions for PCTL counterexamples. In QEST 2008, pages 179–188. IEEE Computer Society, 2008.
  13. Synthesizing computable functions from rational specifications over infinite words. Int. J. Found. Comput. Sci., 35(01n02):179–214, 2024.
  14. Synthesis from hyperproperties. Acta Informatica, 57(1-2):137–163, 2020.
  15. Algorithms for Model Checking HyperLTL and HyperCTL∗. In Daniel Kroening and Corina S. Pasareanu, editors, CAV 2015, Part I, volume 9206 of LNCS, pages 30–48. Springer, 2015.
  16. Bounded synthesis. Int. J. Softw. Tools Technol. Transf., 15(5-6):519–539, 2013.
  17. The First-Order Logic of Hyperproperties. In STACS 2017, volume 66 of LIPIcs, pages 30:1–30:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
  18. Automata, Logics, and Infinite Games: A Guide to Current Research, volume 2500 of LNCS. Springer, 2002.
  19. Proof-like counter-examples. In Hubert Garavel and John Hatcliff, editors, TACAS 2003, volume 2619 of LNCS, pages 160–175. Springer, 2003.
  20. Counterexamples in probabilistic model checking. In Orna Grumberg and Michael Huth, editors, TACAS 2007, volume 4424 of LNCS, pages 72–86. Springer, 2007.
  21. Degrees of lookahead in regular infinite games. Log. Methods Comput. Sci., 8(3), 2012.
  22. Visual analysis of hyperproperties for understanding model checking results. IEEE Trans. Vis. Comput. Graph., 28(1):357–367, 2022.
  23. Finite delay solutions for sequential conditions. In ICALP 1972, pages 45–60, 1972.
  24. How much lookahead is needed to win infinite games? Log. Methods Comput. Sci., 12(3), 2016.
  25. Prompt delay. In Akash Lal, S. Akshay, Saket Saurabh, and Sandeep Sen, editors, FSTTCS 2016, volume 65 of LIPIcs, pages 43:1–43:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016.
  26. Robert P. Kurshan. Verification technology transfer. In Orna Grumberg and Helmut Veith, editors, 25 Years of Model Checking - History, Achievements, Perspectives, volume 5000 of LNCS, pages 46–64. Springer, 2008.
  27. The keys to decidable HyperLTL satisfiability: Small models or very simple formulas. In Maribel Fernández and Anca Muscholl, editors, CSL 2020, volume 152 of LIPIcs, pages 29:1–29:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
  28. Amir Pnueli. The temporal logic of programs. In FOCS 1977, pages 46–57. IEEE, Oct 1977.
  29. Distributed reactive systems are hard to synthesize. In FOCS 1990, Volume II, pages 746–757. IEEE Computer Society, 1990.
  30. Markus N. Rabe. A temporal logic approach to information-flow control. PhD thesis, Saarland University, 2016.
  31. A game-based framework for CTL counterexamples and 3-valued abstraction-refinement. ACM Trans. Comput. Log., 9(1):1, 2007.
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