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Invited Talk

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Context-bounded analysis of concurrent programs is a technique to compute a sequence of under-approximations of all behaviors of the program. For a fixed bound k, a context bounded analysis considers only those runs in which a single process is interrupted at most k times. As k grows, we capture more and more behaviors of the program. Practically, context-bounding has been very effective as a bug-finding tool: many bugs can be found even with small bounds. Theoretically, context-bounded analysis is decidable for a large number of programming models for which verification problems are undecidable. In this paper, we survey some recent work in context-bounded analysis of multithreaded programs.
In particular, we show a general decidability result. We study context-bounded reachability in a language-theoretic setup. We fix a class of languages (satisfying some mild conditions) from which each thread is chosen. We show context-bounded safety and termination verification problems are decidable iff emptiness is decidable for the underlying class of languages and context-bounded boundedness is decidable iff finiteness is decidable for the underlying class.

Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Context-Bounded Analysis of Concurrent Programs (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.3, author = {Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg}, title = {{Context-Bounded Analysis of Concurrent Programs}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {3:1--3:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.3}, URN = {urn:nbn:de:0030-drops-180559}, doi = {10.4230/LIPIcs.ICALP.2023.3}, annote = {Keywords: Context-bounded analysis, Multi-threaded programs, Decidability} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

In the language-theoretic approach to refinement verification, we check that the language of traces of an implementation all belong to the language of a specification. We consider the refinement verification problem for asynchronous programs against specifications given by a Dyck language. We show that this problem is EXPSPACE-complete - the same complexity as that of language emptiness and for refinement verification against a regular specification. Our algorithm uses several technical ingredients. First, we show that checking if the coverability language of a succinctly described vector addition system with states (VASS) is contained in a Dyck language is EXPSPACE-complete. Second, in the more technical part of the proof, we define an ordering on words and show a downward closure construction that allows replacing the (context-free) language of each task in an asynchronous program by a regular language. Unlike downward closure operations usually considered in infinite-state verification, our ordering is not a well-quasi-ordering, and we have to construct the regular language ab initio. Once the tasks can be replaced, we show a reduction to an appropriate VASS and use our first ingredient. In addition to the inherent theoretical interest, refinement verification with Dyck specifications captures common practical resource usage patterns based on reference counting, for which few algorithmic techniques were known.

Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. Checking Refinement of Asynchronous Programs Against Context-Free Specifications. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2023.110, author = {Baumann, Pascal and Ganardi, Moses and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg}, title = {{Checking Refinement of Asynchronous Programs Against Context-Free Specifications}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {110:1--110:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.110}, URN = {urn:nbn:de:0030-drops-181622}, doi = {10.4230/LIPIcs.ICALP.2023.110}, annote = {Keywords: Asynchronous programs, VASS, Dyck languages, Language inclusion, Refinement verification} }

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**Published in:** LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

We study first-order logic (FO) over the structure consisting of finite words over some alphabet A, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is well-understood: If every word is available as a constant, then even the Σ₁ (i.e., existential) fragment is undecidable, already for binary alphabets A.
However, up to now, little is known about the expressiveness of the quantifier alternation fragments: For example, the undecidability proof for the existential fragment relies on Diophantine equations and only shows that recursively enumerable languages over a singleton alphabet (and some auxiliary predicates) are definable.
We show that if |A| ≥ 3, then a relation is definable in the existential fragment over A with constants if and only if it is recursively enumerable. This implies characterizations for all fragments Σ_i: If |A| ≥ 3, then a relation is definable in Σ_i if and only if it belongs to the i-th level of the arithmetical hierarchy. In addition, our result yields an analogous complete description of the Σ_i-fragments for i ≥ 2 of the pure logic, where the words of A^* are not available as constants.

Pascal Baumann, Moses Ganardi, Ramanathan S. Thinniyam, and Georg Zetzsche. Existential Definability over the Subword Ordering. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baumann_et_al:LIPIcs.STACS.2022.7, author = {Baumann, Pascal and Ganardi, Moses and Thinniyam, Ramanathan S. and Zetzsche, Georg}, title = {{Existential Definability over the Subword Ordering}}, booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, pages = {7:1--7:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-222-8}, ISSN = {1868-8969}, year = {2022}, volume = {219}, editor = {Berenbrink, Petra and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.7}, URN = {urn:nbn:de:0030-drops-158178}, doi = {10.4230/LIPIcs.STACS.2022.7}, annote = {Keywords: subword, subsequence, definability, expressiveness, first order logic, existential fragment, quantifier alternation} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Dynamic networks of concurrent pushdown systems (DCPS) are a theoretical model for multi-threaded recursive programs with shared global state and dynamical creation of threads. The (global) state reachability problem for DCPS is undecidable in general, but Atig et al. (2009) showed that it becomes decidable, and is in 2EXPSPACE, when each thread is restricted to a fixed number of context switches. The best known lower bound for the problem is EXPSPACE-hard and this lower bound follows already when each thread is a finite-state machine and runs atomically to completion (i.e., does not switch contexts). In this paper, we close the gap by showing that state reachability is 2EXPSPACE-hard already with only one context switch. Interestingly, state reachability analysis is in EXPSPACE both for pushdown threads without context switches as well as for finite-state threads with arbitrary context switches. Thus, recursive threads together with a single context switch provide an exponential advantage.
Our proof techniques are of independent interest for 2EXPSPACE-hardness results. We introduce transducer-defined Petri nets, a succinct representation for Petri nets, and show coverability is 2EXPSPACE-hard for this model. To show 2EXPSPACE-hardness, we present a modified version of Lipton’s simulation of counter machines by Petri nets, where the net programs can make explicit recursive procedure calls up to a bounded depth.

Pascal Baumann, Rupak Majumdar, Ramanathan S. Thinniyam, and Georg Zetzsche. The Complexity of Bounded Context Switching with Dynamic Thread Creation. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 111:1-111:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2020.111, author = {Baumann, Pascal and Majumdar, Rupak and Thinniyam, Ramanathan S. and Zetzsche, Georg}, title = {{The Complexity of Bounded Context Switching with Dynamic Thread Creation}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {111:1--111:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.111}, URN = {urn:nbn:de:0030-drops-125187}, doi = {10.4230/LIPIcs.ICALP.2020.111}, annote = {Keywords: Dynamic thread creation, Bounded context switching, Asynchronous Programs, Safety verification, State reachability, Petri nets, Complexity, Succinctness, Counter Programs} }

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**Published in:** LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

The problem of regular separability asks, given two languages K and L, whether there exists a regular language S that includes K and is disjoint from L. This problem becomes interesting when the input languages K and L are drawn from language classes beyond the regular languages. For such classes, a mild and useful assumption is that they are full trios, i.e. closed under rational transductions.
All the results on regular separability for full trios obtained so far exhibited a noteworthy correspondence with the intersection emptiness problem: In each case, regular separability is decidable if and only if intersection emptiness is decidable. This raises the question whether for full trios, regular separability can be reduced to intersection emptiness or vice-versa.
We present counterexamples showing that neither of the two problems can be reduced to the other. More specifically, we describe full trios C_1, D_1, C_2, D_2 such that (i) intersection emptiness is decidable for C_1 and D_1, but regular separability is undecidable for C_1 and D_1 and (ii) regular separability is decidable for C_2 and D_2, but intersection emptiness is undecidable for C_2 and D_2.

Ramanathan S. Thinniyam and Georg Zetzsche. Regular Separability and Intersection Emptiness Are Independent Problems. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{thinniyam_et_al:LIPIcs.FSTTCS.2019.51, author = {Thinniyam, Ramanathan S. and Zetzsche, Georg}, title = {{Regular Separability and Intersection Emptiness Are Independent Problems}}, booktitle = {39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)}, pages = {51:1--51:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-131-3}, ISSN = {1868-8969}, year = {2019}, volume = {150}, editor = {Chattopadhyay, Arkadev and Gastin, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.51}, URN = {urn:nbn:de:0030-drops-116138}, doi = {10.4230/LIPIcs.FSTTCS.2019.51}, annote = {Keywords: Regular separability, intersection emptiness, decidability} }

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