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

Following a recently considered generalization of linear equations to unordered data vectors, we perform a further generalization to ordered data vectors. These generalized equations naturally appear in the analysis of vector addition systems (or Petri nets) extended with ordered data. We show that nonnegative-integer solvability of linear equations is computationally equivalent (up to an exponential blowup) to the reachability problem for (plain) vector addition systems. This high complexity is surprising, and contrasts with NP-completeness for unordered data vectors. This also contrasts with our second result, namely polynomial time complexity of the solvability problem when the nonnegative-integer restriction on solutions is relaxed.

Piotr Hofman and Slawomir Lasota. Linear Equations with Ordered Data. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hofman_et_al:LIPIcs.CONCUR.2018.24, author = {Hofman, Piotr and Lasota, Slawomir}, title = {{Linear Equations with Ordered Data}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {24:1--24:17}, 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.2018.24}, URN = {urn:nbn:de:0030-drops-95624}, doi = {10.4230/LIPIcs.CONCUR.2018.24}, annote = {Keywords: Linear equations, Petri nets, Petri nets with data, vector addition systems, sets with atoms, orbit-finite sets} }

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

We investigate the languages recognized by well-structured transition systems (WSTS) with upward and downward compatibility. Our first result shows that, under very mild assumptions, every two disjoint WSTS languages are regular separable: There is a regular language containing one of them and being disjoint from the other. As a consequence, if a language as well as its complement are both recognized by WSTS, then they are necessarily regular. In particular, no subclass of WSTS languages beyond the regular languages is closed under complement. Our second result shows that for Petri nets, the complexity of the backwards coverability algorithm yields a bound on the size of the regular separator. We complement it by a lower bound construction.

Wojciech Czerwinski, Slawomir Lasota, Roland Meyer, Sebastian Muskalla, K. Narayan Kumar, and Prakash Saivasan. Regular Separability of Well-Structured Transition Systems. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2018.35, author = {Czerwinski, Wojciech and Lasota, Slawomir and Meyer, Roland and Muskalla, Sebastian and Narayan Kumar, K. and Saivasan, Prakash}, title = {{Regular Separability of Well-Structured Transition Systems}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {35:1--35:18}, 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.2018.35}, URN = {urn:nbn:de:0030-drops-95733}, doi = {10.4230/LIPIcs.CONCUR.2018.35}, annote = {Keywords: regular separability, wsts, coverability languages, Petri nets} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an integer sort. This subsumes analogous expressibility results previously known for finite and pushdown timed automata with untimed stack. As key technical tools, we use quantifier elimination for a fragment of hybrid linear arithmetic and for cyclic order atoms, and a reduction to register pushdown automata over cyclic order atoms.

Lorenzo Clemente and Slawomir Lasota. Binary Reachability of Timed Pushdown Automata via Quantifier Elimination and Cyclic Order Atoms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 118:1-118:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2018.118, author = {Clemente, Lorenzo and Lasota, Slawomir}, title = {{Binary Reachability of Timed Pushdown Automata via Quantifier Elimination and Cyclic Order Atoms}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {118:1--118:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.118}, URN = {urn:nbn:de:0030-drops-91228}, doi = {10.4230/LIPIcs.ICALP.2018.118}, annote = {Keywords: timed automata, reachability relation, timed pushdown automata, linear arithmetic} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model, we surprisingly show decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is disjoint from the other? We supplement this result by proving undecidability of the same problem already for languages of visibly one counter automata.

Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, and Charles Paperman. Regular Separability of Parikh Automata. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 117:1-117:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{clemente_et_al:LIPIcs.ICALP.2017.117, author = {Clemente, Lorenzo and Czerwinski, Wojciech and Lasota, Slawomir and Paperman, Charles}, title = {{Regular Separability of Parikh Automata}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {117:1--117:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.117}, URN = {urn:nbn:de:0030-drops-74971}, doi = {10.4230/LIPIcs.ICALP.2017.117}, annote = {Keywords: Regular separability problem, Parikh automata, integer vector addition systems, visible one counter automata, decidability, undecidability} }

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**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Given two families of sets F and G, the F-separability problem for G asks whether for two given sets U, V in G there exists a set S in F, such that U is included in S and V is disjoint with S. We consider two families of sets F: modular sets S which are subsets of N^d, defined as unions of equivalence classes modulo some natural number n in N, and unary sets, which extend modular sets by requiring equality below a threshold n, and equivalence modulo n above n. Our main result is decidability of modular- and unary-separability for the class G of reachability sets of Vector Addition Systems, Petri Nets, Vector Addition Systems with States, and for sections thereof.

Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, and Charles Paperman. Separability of Reachability Sets of Vector Addition Systems. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{clemente_et_al:LIPIcs.STACS.2017.24, author = {Clemente, Lorenzo and Czerwinski, Wojciech and Lasota, Slawomir and Paperman, Charles}, title = {{Separability of Reachability Sets of Vector Addition Systems}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {24:1--24:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.24}, URN = {urn:nbn:de:0030-drops-70091}, doi = {10.4230/LIPIcs.STACS.2017.24}, annote = {Keywords: separability, Petri nets, modular sets, unary sets, decidability} }

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**Published in:** LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definable by first-order interpretations in a fixed structure. Their signatures can be either finite or infinite but definable. The homomorphisms can be either arbitrary, or definable with parameters, or definable without parameters. For each of these variants, we determine its decidability status.

Bartek Klin, Slawomir Lasota, Joanna Ochremiak, and Szymon Torunczyk. Homomorphism Problems for First-Order Definable Structures. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{klin_et_al:LIPIcs.FSTTCS.2016.14, author = {Klin, Bartek and Lasota, Slawomir and Ochremiak, Joanna and Torunczyk, Szymon}, title = {{Homomorphism Problems for First-Order Definable Structures}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {14:1--14:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-027-9}, ISSN = {1868-8969}, year = {2016}, volume = {65}, editor = {Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.14}, URN = {urn:nbn:de:0030-drops-68498}, doi = {10.4230/LIPIcs.FSTTCS.2016.14}, annote = {Keywords: Sets with atoms, first-order interpretations, homomorphism problem} }

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**Published in:** LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.

Lorenzo Clemente and Slawomir Lasota. Reachability Analysis of First-order Definable Pushdown Systems. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 244-259, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{clemente_et_al:LIPIcs.CSL.2015.244, author = {Clemente, Lorenzo and Lasota, Slawomir}, title = {{Reachability Analysis of First-order Definable Pushdown Systems}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {244--259}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-90-3}, ISSN = {1868-8969}, year = {2015}, volume = {41}, editor = {Kreutzer, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.244}, URN = {urn:nbn:de:0030-drops-54185}, doi = {10.4230/LIPIcs.CSL.2015.244}, annote = {Keywords: automata theory, pushdown systems, sets with atoms, saturation technique} }

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**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

One-counter nets (OCN) are Petri nets with exactly one unbounded place.
They are equivalent to a subclass of one-counter automata with just a weak test for zero. Unlike many other semantic equivalences, strong and weak simulation preorder are decidable for OCN, but the computational complexity was an open problem. We show that both strong and weak simulation preorder on OCN are Pspace-complete.

Piotr Hofman, Slawomir Lasota, Richard Mayr, and Patrick Totzke. Simulation Over One-counter Nets is PSPACE-Complete. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 515-526, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{hofman_et_al:LIPIcs.FSTTCS.2013.515, author = {Hofman, Piotr and Lasota, Slawomir and Mayr, Richard and Totzke, Patrick}, title = {{Simulation Over One-counter Nets is PSPACE-Complete}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {515--526}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.515}, URN = {urn:nbn:de:0030-drops-43970}, doi = {10.4230/LIPIcs.FSTTCS.2013.515}, annote = {Keywords: Simulation preorder; one-counter nets; complexity} }

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

Bisimulation equivalence is decidable in polynomial time over normed graphs generated by a context-free grammar. We present a new algorithm, working in time $O(n^5)$, thus improving the previously known complexity $O(n^8 * polylog(n))$. It also improves the previously known complexity $O(n^6 * polylog(n))$ of the equality problem for simple grammars.

Wojciech Czerwinski and Slawomir Lasota. Fast equivalence-checking for normed context-free processes. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 260-271, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{czerwinski_et_al:LIPIcs.FSTTCS.2010.260, author = {Czerwinski, Wojciech and Lasota, Slawomir}, title = {{Fast equivalence-checking for normed context-free processes}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {260--271}, 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.2010.260}, URN = {urn:nbn:de:0030-drops-28690}, doi = {10.4230/LIPIcs.FSTTCS.2010.260}, annote = {Keywords: bisimulation, norm, context-free grammar, simple grammar} }

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