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**Published in:** LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

We investigate how the semantics of a hybrid automaton deviates with respect to syntactic perturbations on the hybrid automaton. We consider syntactic perturbations of a hybrid automaton, wherein the syntactic representations of its elements, namely, initial sets, invariants, guards, and flows, in some logic are perturbed. Our main result establishes a continuity like property that states that small perturbations in the syntax lead to small perturbations in the semantics. More precisely, we show that for every real number epsilon>0 and natural number k, there is a real number delta>0 such that H^delta, the delta syntactic perturbation of a hybrid automaton H, is epsilon-simulation equivalent to H up to k transition steps. As a byproduct, we obtain a proof that a bounded safety verification tool such as dReach will eventually prove the safety of a safe hybrid automaton design (when only non-strict inequalities are used in all constraints) if dReach iteratively reduces the syntactic parameter delta that is used in checking approximate satisfiability. This has an immediate application in counter-example validation in a CEGAR framework, namely, when a counter-example is spurious, then we have a complete procedure for deducing the same.

Nima Roohi, Pavithra Prabhakar, and Mahesh Viswanathan. Relating Syntactic and Semantic Perturbations of Hybrid Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{roohi_et_al:LIPIcs.CONCUR.2018.26, author = {Roohi, Nima and Prabhakar, Pavithra and Viswanathan, Mahesh}, title = {{Relating Syntactic and Semantic Perturbations of Hybrid Automata}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {26:1--26:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-087-3}, ISSN = {1868-8969}, year = {2018}, volume = {118}, editor = {Schewe, Sven and Zhang, Lijun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.26}, URN = {urn:nbn:de:0030-drops-95644}, doi = {10.4230/LIPIcs.CONCUR.2018.26}, annote = {Keywords: Model Checking, Hybrid Automata, Approximation, Perturbation} }

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**Published in:** LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

A probabilistic finite automaton (PFA) A is said to be regular-approximable with respect to (x,y), if there is a regular language that contains all words accepted by A with probability at least x+y, but does not contain any word accepted with probability at most x. We show that the problem of determining if a PFA A is regular-approximable with respect to (x,y) is not recursively enumerable. We then show that many tractable sub-classes of PFAs identified in the literature - hierarchical PFAs, polynomially ambiguous PFAs, and eventually weakly ergodic PFAs - are regular-approximable with respect to all (x,y). Establishing the regular-approximability of a PFA has the nice consequence that its value can be effectively approximated, and the emptiness problem can be decided under the assumption of isolation.

Rohit Chadha, A. Prasad Sistla, and Mahesh Viswanathan. Approximating Probabilistic Automata by Regular Languages. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chadha_et_al:LIPIcs.CSL.2018.14, author = {Chadha, Rohit and Sistla, A. Prasad and Viswanathan, Mahesh}, title = {{Approximating Probabilistic Automata by Regular Languages}}, booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)}, pages = {14:1--14:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-088-0}, ISSN = {1868-8969}, year = {2018}, volume = {119}, editor = {Ghica, Dan R. and Jung, Achim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.14}, URN = {urn:nbn:de:0030-drops-96815}, doi = {10.4230/LIPIcs.CSL.2018.14}, annote = {Keywords: Probabilistic Finite Automata, Regular Languages, Ambiguity} }

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**Published in:** LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an exists^*forall^* quantifier prefix (over variables, functions and relations) making EQSMT conducive for modeling synthesis problems. Moreover, EQSMT allows reasoning using a combination of background theories provided that they have a decidable satisfiability problem for the exists^*forall^* FO-fragment (e.g., linear arithmetic). Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of exists^*forall^* formulae of each individual background theory, allowing us to use existing efficient SMT solvers supporting exists^*forall^* reasoning for these theories; hence our procedure can be seen as effectively quantified SMT (EQSMT) reasoning.

P. Madhusudan, Umang Mathur, Shambwaditya Saha, and Mahesh Viswanathan. A Decidable Fragment of Second Order Logic With Applications to Synthesis. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{madhusudan_et_al:LIPIcs.CSL.2018.31, author = {Madhusudan, P. and Mathur, Umang and Saha, Shambwaditya and Viswanathan, Mahesh}, title = {{A Decidable Fragment of Second Order Logic With Applications to Synthesis}}, booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)}, pages = {31:1--31:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-088-0}, ISSN = {1868-8969}, year = {2018}, volume = {119}, editor = {Ghica, Dan R. and Jung, Achim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.31}, URN = {urn:nbn:de:0030-drops-96987}, doi = {10.4230/LIPIcs.CSL.2018.31}, annote = {Keywords: second order logic, synthesis, decidable fragment} }

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**Published in:** LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

Given a Markov Decision Process (MDP) M, an LTL formula \varphi, and a threshold \theta \in [0,1], the verification question is to determine if there is a scheduler with respect to which the executions of M satisfying \varphi have probability greater than (or greater than or equal to) \theta. When \theta = 0, we call it the qualitative verification problem, and when \theta \in (0,1], we call it the quantitative verification problem. In this paper we study the precise complexity of these problems when the specification is constrained to be in different fragments of LTL.

Dileep Kini and Mahesh Viswanathan. Complexity of Model Checking MDPs against LTL Specifications. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kini_et_al:LIPIcs.FSTTCS.2017.35, author = {Kini, Dileep and Viswanathan, Mahesh}, title = {{Complexity of Model Checking MDPs against LTL Specifications}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {35:1--35:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-055-2}, ISSN = {1868-8969}, year = {2018}, volume = {93}, editor = {Lokam, Satya and Ramanujam, R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.35}, URN = {urn:nbn:de:0030-drops-83928}, doi = {10.4230/LIPIcs.FSTTCS.2017.35}, annote = {Keywords: Markov Decision Processes, Linear Temporal Logic, model checking, complexity} }

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**Published in:** LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

For concurrent probabilistic programs having process-level nondeterminism, it is often necessary to restrict the class of schedulers that resolve nondeterminism to obtain sound and precise model checking algorithms. In this paper, we introduce two classes of schedulers called view consistent and locally Markovian schedulers and consider the model checking problem of concurrent, probabilistic programs under these alternate semantics. Specifically, given a B\"{u}chi automaton $Spec$, a threshold $x$ in $[0,1]$, and a concurrent program $P$, the model checking problem asks if the measure of computations of $P$ that satisfy $Spec$ is at least $x$, under all view consistent (or locally Markovian) schedulers. We give precise complexity results for the model checking problem (for different classes of B\"{u}chi automata specifications) and contrast it with the complexity under the standard semantics that considers all schedulers.

Rohit Chadha, A. Prasad Sistla, and Mahesh Viswanathan. Model Checking Concurrent Programs with Nondeterminism and Randomization. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 364-375, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chadha_et_al:LIPIcs.FSTTCS.2010.364, author = {Chadha, Rohit and Sistla, A. Prasad and Viswanathan, Mahesh}, title = {{Model Checking Concurrent Programs with Nondeterminism and Randomization}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {364--375}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-23-1}, ISSN = {1868-8969}, year = {2010}, volume = {8}, editor = {Lodaya, Kamal and Mahajan, Meena}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.364}, URN = {urn:nbn:de:0030-drops-28788}, doi = {10.4230/LIPIcs.FSTTCS.2010.364}, annote = {Keywords: view consistent scheduler, locally Markovian scheduler, model-checking, probabilistic program} }