Document

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

We study constraint automata, which are finite-state automata over infinite alphabets consisting of tuples of words. A constraint automaton can compare the words of the consecutive tuples using Boolean combinations of the relations prefix, suffix, infix and equality.
First, we show that the reachability problem of such automata is PSpace-complete. Second, we study automata over infinite sequences with Büchi conditions. We show that the problem: given a constraint automaton, is there a bound B and a sequence of tuples of words of length bounded by B, which is accepted by the automaton, is also PSpace-complete. These results contribute towards solving the long-standing open problem of the decidability of the emptiness problem for constraint automata, in which the words can have arbitrary lengths.

Jakub Michaliszyn, Jan Otop, and Piotr Wieczorek. Reachability and Bounded Emptiness Problems of Constraint Automata with Prefix, Suffix and Infix. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{michaliszyn_et_al:LIPIcs.CONCUR.2023.3, author = {Michaliszyn, Jakub and Otop, Jan and Wieczorek, Piotr}, title = {{Reachability and Bounded Emptiness Problems of Constraint Automata with Prefix, Suffix and Infix}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {3:1--3:16}, 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.2023.3}, URN = {urn:nbn:de:0030-drops-189971}, doi = {10.4230/LIPIcs.CONCUR.2023.3}, annote = {Keywords: constraint automata, emptiness problem} }

Document

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

We study the problem of active learning deterministic visibly pushdown automata. We show that in the classical L^*-setting, efficient active learning algorithms are not possible. To overcome this difficulty, we propose the accessible stack setting, where the algorithm has the read and write access to the stack. In this setting, we show that active learning can be done in polynomial time in the size of the target automaton and the counterexamples provided by the teacher. As counterexamples of exponential size are inevitable, we consider an algorithm working with words in a compressed representation via (visibly) Straight-Line Programs. Employing compression allows us to obtain an algorithm where the teacher and the learner work in time polynomial in the size of the target automaton alone.

Jakub Michaliszyn and Jan Otop. Learning Deterministic Visibly Pushdown Automata Under Accessible Stack. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 74:1-74:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{michaliszyn_et_al:LIPIcs.MFCS.2022.74, author = {Michaliszyn, Jakub and Otop, Jan}, title = {{Learning Deterministic Visibly Pushdown Automata Under Accessible Stack}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {74:1--74:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.74}, URN = {urn:nbn:de:0030-drops-168729}, doi = {10.4230/LIPIcs.MFCS.2022.74}, annote = {Keywords: visibly pushdown automata, automata inference, minimization} }

Document

**Published in:** LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2020.23, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {23:1--23:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-160-3}, ISSN = {1868-8969}, year = {2020}, volume = {171}, editor = {Konnov, Igor and Kov\'{a}cs, Laura}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.23}, URN = {urn:nbn:de:0030-drops-128359}, doi = {10.4230/LIPIcs.CONCUR.2020.23}, annote = {Keywords: vector addition systems, mean-payoff, multidimension, probabilistic semantics} }

Document

**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the passive learning case, we show that limit-average automata are not PAC-learnable as samples must be of exponential-size to provide (with good probability) enough details to learn an automaton. We also show that the problem of finding an automaton that fits a given sample is NP-complete. In the active learning case, we show that limit-average automata can be learned almost-exactly, i.e., we can learn in polynomial time an automaton that is consistent with the target automaton on almost all words. On the other hand, we show that the problem of learning an automaton that approximates the target automaton (with perhaps fewer states) is NP-complete. The abovementioned results are shown for the uniform distribution on words. We briefly discuss learning over different distributions.

Jakub Michaliszyn and Jan Otop. Approximate Learning of Limit-Average Automata. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{michaliszyn_et_al:LIPIcs.CONCUR.2019.17, author = {Michaliszyn, Jakub and Otop, Jan}, title = {{Approximate Learning of Limit-Average Automata}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {17:1--17:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.17}, URN = {urn:nbn:de:0030-drops-109198}, doi = {10.4230/LIPIcs.CONCUR.2019.17}, annote = {Keywords: weighted automata, learning, expected value} }

Document

**Published in:** LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Long-Run Average Behavior of Vector Addition Systems with States. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2019.27, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Long-Run Average Behavior of Vector Addition Systems with States}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {27:1--27:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-121-4}, ISSN = {1868-8969}, year = {2019}, volume = {140}, editor = {Fokkink, Wan and van Glabbeek, Rob}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.27}, URN = {urn:nbn:de:0030-drops-109293}, doi = {10.4230/LIPIcs.CONCUR.2019.27}, annote = {Keywords: vector addition systems, mean-payoff, Diophantine inequalities} }

Document

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

We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We consider the probabilistic questions of computing the expected value and the cumulative distribution for such random variables.
The exact answers to the probabilistic questions for non-deterministic automata can be irrational and are uncomputable in general. To overcome this limitation, we propose an approximation algorithm for the probabilistic questions, which works in exponential time in the automaton and polynomial time in the Markov chain. We apply this result to show that non-deterministic automata can be effectively determinised with respect to the standard deviation metric.

Jakub Michaliszyn and Jan Otop. Non-deterministic Weighted Automata on Random Words. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{michaliszyn_et_al:LIPIcs.CONCUR.2018.10, author = {Michaliszyn, Jakub and Otop, Jan}, title = {{Non-deterministic Weighted Automata on Random Words}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {10:1--10:16}, 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.2018.10}, URN = {urn:nbn:de:0030-drops-95481}, doi = {10.4230/LIPIcs.CONCUR.2018.10}, annote = {Keywords: quantitative verification, weighted automata, expected value} }

Document

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

We study the average stack cost of Buechi pushdown automata (Buechi PDA). We associate a non-negative price with each stack symbol and define the cost of a stack as the sum of costs of all its elements. We introduce and study the average stack cost problem (ASC), which asks whether there exists an accepting run of a given Buechi PDA such that the long-run average of stack costs is below some given threshold. The ASC problem generalises mean-payoff objective and can be use to express quantitative properties of pushdown systems. In particular, we can compute the average response time using the ASC problem. We show that the ASC problem can be solved in polynomial time.

Jakub Michaliszyn and Jan Otop. Average Stack Cost of Büchi Pushdown Automata. 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. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{michaliszyn_et_al:LIPIcs.FSTTCS.2017.42, author = {Michaliszyn, Jakub and Otop, Jan}, title = {{Average Stack Cost of B\"{u}chi Pushdown Automata}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {42:1--42:13}, 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.2017.42}, URN = {urn:nbn:de:0030-drops-83971}, doi = {10.4230/LIPIcs.FSTTCS.2017.42}, annote = {Keywords: pushdown automata, average stack cost, weighted pushdown systems} }

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

Querying graph databases has recently received much attention. We propose a new approach to this problem, which balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of minimal (e.g. shortest) and maximal (e.g. most valuable) paths satisfying given criteria. To express complex properties in a modular way, we introduce labelling-generating ontologies. The resulting formalism is computationally attractive - queries can be answered in non-deterministic
logarithmic space in the size of the database.

Jakub Michaliszyn, Jan Otop, and Piotr Wieczorek. Querying Best Paths in Graph Databases. 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. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{michaliszyn_et_al:LIPIcs.FSTTCS.2017.43, author = {Michaliszyn, Jakub and Otop, Jan and Wieczorek, Piotr}, title = {{Querying Best Paths in Graph Databases}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {43:1--43:15}, 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.2017.43}, URN = {urn:nbn:de:0030-drops-83989}, doi = {10.4230/LIPIcs.FSTTCS.2017.43}, annote = {Keywords: graph databases, queries, aggregation} }

Document

**Published in:** LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Nested weighted automata (NWA) present a robust and convenient automata-theoretic formalism for quantitative specifications.
Previous works have considered NWA that processed input words only in the forward direction. It is natural to allow the automata to process input words backwards as well, for example, to measure the maximal or average time between a response and the preceding request. We therefore introduce and study bidirectional NWA that can process input
words in both directions. First, we show that bidirectional NWA can express interesting quantitative properties that are not expressible by forward-only NWA. Second, for the fundamental decision problems of emptiness and universality, we establish decidability and complexity results for the new framework which match the best-known results for the special case of forward-only NWA. Thus, for NWA, the increased expressiveness of bidirectionality is achieved at no additional computational complexity. This is in stark contrast to the unweighted case, where bidirectional finite automata are no more expressive but exponentially more succinct than their forward-only counterparts.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Bidirectional Nested Weighted Automata. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chatterjee_et_al:LIPIcs.CONCUR.2017.5, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Bidirectional Nested Weighted Automata}}, booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)}, pages = {5:1--5:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-048-4}, ISSN = {1868-8969}, year = {2017}, volume = {85}, editor = {Meyer, Roland and Nestmann, Uwe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.5}, URN = {urn:nbn:de:0030-drops-77763}, doi = {10.4230/LIPIcs.CONCUR.2017.5}, annote = {Keywords: weighted automata, nested weighted automata, complexity, bidirectional} }

Document

**Published in:** LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.

Krishnendu Chatterjee, Thomas A. Henzinger, and Jan Otop. Nested Weighted Limit-Average Automata of Bounded Width. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2016.24, author = {Chatterjee, Krishnendu and Henzinger, Thomas A. and Otop, Jan}, title = {{Nested Weighted Limit-Average Automata of Bounded Width}}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, pages = {24:1--24:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-016-3}, ISSN = {1868-8969}, year = {2016}, volume = {58}, editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.24}, URN = {urn:nbn:de:0030-drops-64397}, doi = {10.4230/LIPIcs.MFCS.2016.24}, annote = {Keywords: weighted automata, nested weighted automata, complexity, mean-payoff} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity - a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation
using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using set-similarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.

Thomas A. Henzinger, Jan Otop, and Roopsha Samanta. Lipschitz Robustness of Finite-state Transducers. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 431-443, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{henzinger_et_al:LIPIcs.FSTTCS.2014.431, author = {Henzinger, Thomas A. and Otop, Jan and Samanta, Roopsha}, title = {{Lipschitz Robustness of Finite-state Transducers}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {431--443}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.431}, URN = {urn:nbn:de:0030-drops-48614}, doi = {10.4230/LIPIcs.FSTTCS.2014.431}, annote = {Keywords: Robustness, Transducers, Weighted Automata} }

Document

**Published in:** LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

We show that modal logic over universally first-order definable classes of transitive frames is decidable. More precisely, let K be an arbitrary class of transitive Kripke frames definable by a universal first-order sentence. We show that the global and finite global satisfiability problems of modal logic over K are decidable in NP, regardless of choice of K. We also show that the local satisfiability and the finite local satisfiability problems of modal logic over K are decidable in NExpTime.

Jakub Michaliszyn and Jan Otop. Elementary Modal Logics over Transitive Structures. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 563-577, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{michaliszyn_et_al:LIPIcs.CSL.2013.563, author = {Michaliszyn, Jakub and Otop, Jan}, title = {{Elementary Modal Logics over Transitive Structures}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {563--577}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.563}, URN = {urn:nbn:de:0030-drops-42195}, doi = {10.4230/LIPIcs.CSL.2013.563}, annote = {Keywords: Modal logic, Transitive frames, Elementary modal logics, Decidability} }

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**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

We consider the satisfiability problem for modal logic over classes of structures definable by universal first-order formulas with three variables. We exhibit a simple formula for which the problem is undecidable. This improves an earlier result in which nine variables were used. We also show that for classes defined by three-variable, universal Horn formulas the problem is decidable. This subsumes decidability results for many natural modal logics, including T, B, K4, S4, S5.

Emanuel Kieronski, Jakub Michaliszyn, and Jan Otop. Modal Logics Definable by Universal Three-Variable Formulas. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 264-275, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{kieronski_et_al:LIPIcs.FSTTCS.2011.264, author = {Kieronski, Emanuel and Michaliszyn, Jakub and Otop, Jan}, title = {{Modal Logics Definable by Universal Three-Variable Formulas}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {264--275}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.264}, URN = {urn:nbn:de:0030-drops-33495}, doi = {10.4230/LIPIcs.FSTTCS.2011.264}, annote = {Keywords: modal logic, decidability} }

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