Document

**Published in:** LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

In this paper we propose two new subclasses of Petri nets with resets, for which the reachability and coverability problems become tractable. Namely, we add an acyclicity condition that only applies to the consumptions and productions, not the resets. The first class is acyclic Petri nets with resets, and we show that coverability is PSPACE-complete for them. This contrasts the known Ackermann-hardness for coverability in (not necessarily acyclic) Petri nets with resets. We prove that the reachability problem remains undecidable for acyclic Petri nets with resets. The second class concerns workflow nets, a practically motivated and natural subclass of Petri nets. Here, we show that both coverability and reachability in acyclic workflow nets with resets are PSPACE-complete. Without the acyclicity condition, reachability and coverability in workflow nets with resets are known to be equally hard as for Petri nets with resets, that being Ackermann-hard and undecidable, respectively.

Dmitry Chistikov, Wojciech Czerwiński, Piotr Hofman, Filip Mazowiecki, and Henry Sinclair-Banks. Acyclic Petri and Workflow Nets with Resets. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chistikov_et_al:LIPIcs.FSTTCS.2023.16, author = {Chistikov, Dmitry and Czerwi\'{n}ski, Wojciech and Hofman, Piotr and Mazowiecki, Filip and Sinclair-Banks, Henry}, title = {{Acyclic Petri and Workflow Nets with Resets}}, booktitle = {43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)}, pages = {16:1--16:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-304-1}, ISSN = {1868-8969}, year = {2023}, volume = {284}, editor = {Bouyer, Patricia and Srinivasan, Srikanth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.16}, URN = {urn:nbn:de:0030-drops-193892}, doi = {10.4230/LIPIcs.FSTTCS.2023.16}, annote = {Keywords: Petri nets, Workflow Nets, Resets, Acyclic, Reachability, Coverability} }

Document

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

Vector addition systems with states (VASS) are a popular model for concurrent systems. However, many decision problems have prohibitively high complexity. Therefore, it is sometimes useful to consider overapproximating semantics in which these problems can be decided more efficiently.
We study an overapproximation, called monus semantics, that slightly relaxes the semantics of decrements: A key property of a vector addition systems is that in order to decrement a counter, this counter must have a positive value. In contrast, our semantics allows decrements of zero-valued counters: If such a transition is executed, the counter just remains zero.
It turns out that if only a subset of transitions is used with monus semantics (and the others with classical semantics), then reachability is undecidable. However, we show that if monus semantics is used throughout, reachability remains decidable. In particular, we show that reachability for VASS with monus semantics is as hard as that of classical VASS (i.e. Ackermann-hard), while the zero-reachability and coverability are easier (i.e. EXPSPACE-complete and NP-complete, respectively). We provide a comprehensive account of the complexity of the general reachability problem, reachability of zero configurations, and coverability under monus semantics. We study these problems in general VASS, two-dimensional VASS, and one-dimensional VASS, with unary and binary counter updates.

Pascal Baumann, Khushraj Madnani, Filip Mazowiecki, and Georg Zetzsche. Monus Semantics in Vector Addition Systems with States. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baumann_et_al:LIPIcs.CONCUR.2023.10, author = {Baumann, Pascal and Madnani, Khushraj and Mazowiecki, Filip and Zetzsche, Georg}, title = {{Monus Semantics in Vector Addition Systems with States}}, booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)}, pages = {10:1--10:18}, 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.2023.10}, URN = {urn:nbn:de:0030-drops-190047}, doi = {10.4230/LIPIcs.CONCUR.2023.10}, annote = {Keywords: Vector addition systems, Overapproximation, Reachability, Coverability} }

Document

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

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

Seminal results establish that the coverability problem for Vector Addition Systems with States (VASS) is in EXPSPACE (Rackoff, '78) and is EXPSPACE-hard already under unary encodings (Lipton, '76). More precisely, Rosier and Yen later utilise Rackoff’s bounding technique to show that if coverability holds then there is a run of length at most n^{2^𝒪(d log d)}, where d is the dimension and n is the size of the given unary VASS. Earlier, Lipton showed that there exist instances of coverability in d-dimensional unary VASS that are only witnessed by runs of length at least n^{2^Ω(d)}. Our first result closes this gap. We improve the upper bound by removing the twice-exponentiated log(d) factor, thus matching Lipton’s lower bound. This closes the corresponding gap for the exact space required to decide coverability. This also yields a deterministic n^{2^𝒪(d)}-time algorithm for coverability. Our second result is a matching lower bound, that there does not exist a deterministic n^{2^o(d)}-time algorithm, conditioned upon the Exponential Time Hypothesis.
When analysing coverability, a standard proof technique is to consider VASS with bounded counters. Bounded VASS make for an interesting and popular model due to strong connections with timed automata. Withal, we study a natural setting where the counter bound is linear in the size of the VASS. Here the trivial exhaustive search algorithm runs in 𝒪(n^{d+1})-time. We give evidence to this being near-optimal. We prove that in dimension one this trivial algorithm is conditionally optimal, by showing that n^{2-o(1)}-time is required under the k-cycle hypothesis. In general fixed dimension d, we show that n^{d-2-o(1)}-time is required under the 3-uniform hyperclique hypothesis.

Marvin Künnemann, Filip Mazowiecki, Lia Schütze, Henry Sinclair-Banks, and Karol Węgrzycki. Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 131:1-131:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kunnemann_et_al:LIPIcs.ICALP.2023.131, author = {K\"{u}nnemann, Marvin and Mazowiecki, Filip and Sch\"{u}tze, Lia and Sinclair-Banks, Henry and W\k{e}grzycki, Karol}, title = {{Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {131:1--131:20}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.131}, URN = {urn:nbn:de:0030-drops-181834}, doi = {10.4230/LIPIcs.ICALP.2023.131}, annote = {Keywords: Vector Addition System, Coverability, Reachability, Fine-Grained Complexity, Exponential Time Hypothesis, k-Cycle Hypothesis, Hyperclique Hypothesis} }

Document

**Published in:** LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

We study the class of rational recursive sequences (ratrec) over the rational numbers. A ratrec sequence is defined via a system of sequences using mutually recursive equations of depth 1, where the next values are computed as rational functions of the previous values. An alternative class is that of simple ratrec sequences, where one uses a single recursive equation, however of depth k: the next value is defined as a rational function of k previous values.
We conjecture that the classes ratrec and simple ratrec coincide. The main contribution of this paper is a proof of a variant of this conjecture where the initial conditions are treated symbolically, using a formal variable per sequence, while the sequences themselves consist of rational functions over those variables. While the initial conjecture does not follow from this variant, we hope that the introduced algebraic techniques may eventually be helpful in resolving the problem.
The class ratrec strictly generalises a well-known class of polynomial recursive sequences (polyrec). These are defined like ratrec, but using polynomial functions instead of rational ones. One can observe that if our conjecture is true and effective, then we can improve the complexities of the zeroness and the equivalence problems for polyrec sequences. Currently, the only known upper bound is Ackermanian, which follows from results on polynomial automata. We complement this observation by proving a PSPACE lower bound for both problems for polyrec. Our lower bound construction also implies that the Skolem problem is PSPACE-hard for the polyrec class.

Lorenzo Clemente, Maria Donten-Bury, Filip Mazowiecki, and Michał Pilipczuk. On Rational Recursive Sequences. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{clemente_et_al:LIPIcs.STACS.2023.24, author = {Clemente, Lorenzo and Donten-Bury, Maria and Mazowiecki, Filip and Pilipczuk, Micha{\l}}, title = {{On Rational Recursive Sequences}}, booktitle = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)}, pages = {24:1--24:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-266-2}, ISSN = {1868-8969}, year = {2023}, volume = {254}, editor = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.24}, URN = {urn:nbn:de:0030-drops-176763}, doi = {10.4230/LIPIcs.STACS.2023.24}, annote = {Keywords: recursive sequences, polynomial automata, zeroness problem, equivalence problem} }

Document

**Published in:** LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so through the lenses of parameterized dynamic data structures: we assume that the automaton is fixed and its size is the parameter, while the input word is revealed as in a stream, one symbol at a time following the natural order on positions. The goal is to design a dynamic data structure that can be efficiently updated upon revealing the next symbol, while maintaining the answer to the query on whether the word consisting of symbols revealed so far is accepted by the automaton. We provide complexity bounds for this dynamic acceptance problem for timed automata that process symbols interleaved with time spans. The main contribution is a dynamic data structure that maintains acceptance of a fixed one-clock timed automaton 𝒜 with amortized update time 2^{𝒪(|𝒜|)} per input symbol.

Alejandro Grez, Filip Mazowiecki, Michał Pilipczuk, Gabriele Puppis, and Cristian Riveros. Dynamic Data Structures for Timed Automata Acceptance. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{grez_et_al:LIPIcs.IPEC.2021.20, author = {Grez, Alejandro and Mazowiecki, Filip and Pilipczuk, Micha{\l} and Puppis, Gabriele and Riveros, Cristian}, title = {{Dynamic Data Structures for Timed Automata Acceptance}}, booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)}, pages = {20:1--20:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-216-7}, ISSN = {1868-8969}, year = {2021}, volume = {214}, editor = {Golovach, Petr A. and Zehavi, Meirav}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.20}, URN = {urn:nbn:de:0030-drops-154037}, doi = {10.4230/LIPIcs.IPEC.2021.20}, annote = {Keywords: timed automata, data stream, dynamic data structure} }

Document

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

The reachability problem is a central decision problem in verification of vector addition systems with states (VASS). In spite of recent progress, the complexity of the reachability problem remains unsettled, and it is closely related to the lengths of shortest VASS runs that witness reachability.
We obtain three main results for VASS of fixed dimension. For the first two, we assume that the integers in the input are given in unary, and that the control graph of the given VASS is flat (i.e., without nested cycles). We obtain a family of VASS in dimension 3 whose shortest runs are exponential, and we show that the reachability problem is NP-hard in dimension 7. These results resolve negatively questions that had been posed by the works of Blondin et al. in LICS 2015 and Englert et al. in LICS 2016, and contribute a first construction that distinguishes 3-dimensional flat VASS from 2-dimensional ones. Our third result, by means of a novel family of products of integer fractions, shows that 4-dimensional VASS can have doubly exponentially long shortest runs. The smallest dimension for which this was previously known is 14.

Wojciech Czerwiński, Sławomir Lasota, Ranko Lazić, Jérôme Leroux, and Filip Mazowiecki. Reachability in Fixed Dimension Vector Addition Systems with States. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 48:1-48:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2020.48, author = {Czerwi\'{n}ski, Wojciech and Lasota, S{\l}awomir and Lazi\'{c}, Ranko and Leroux, J\'{e}r\^{o}me and Mazowiecki, Filip}, title = {{Reachability in Fixed Dimension Vector Addition Systems with States}}, booktitle = {31st International Conference on Concurrency Theory (CONCUR 2020)}, pages = {48:1--48:21}, 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.2020.48}, URN = {urn:nbn:de:0030-drops-128605}, doi = {10.4230/LIPIcs.CONCUR.2020.48}, annote = {Keywords: reachability problem, vector addition systems, Petri nets} }

Document

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

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

We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is b_n = n!. Our main result is that the sequence u_n = nⁿ is not polynomial recursive.

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, and Géraud Sénizergues. On Polynomial Recursive Sequences. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 117:1-117:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cadilhac_et_al:LIPIcs.ICALP.2020.117, author = {Cadilhac, Micha\"{e}l and Mazowiecki, Filip and Paperman, Charles and Pilipczuk, Micha{\l} and S\'{e}nizergues, G\'{e}raud}, title = {{On Polynomial Recursive Sequences}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {117:1--117:17}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.117}, URN = {urn:nbn:de:0030-drops-125240}, doi = {10.4230/LIPIcs.ICALP.2020.117}, annote = {Keywords: recursive sequences, expressive power, weighted automata, higher-order pushdown automata} }

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**Published in:** LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers.

Corentin Barloy, Nathanaël Fijalkow, Nathan Lhote, and Filip Mazowiecki. A Robust Class of Linear Recurrence Sequences. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barloy_et_al:LIPIcs.CSL.2020.9, author = {Barloy, Corentin and Fijalkow, Nathana\"{e}l and Lhote, Nathan and Mazowiecki, Filip}, title = {{A Robust Class of Linear Recurrence Sequences}}, booktitle = {28th EACSL Annual Conference on Computer Science Logic (CSL 2020)}, pages = {9:1--9:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-132-0}, ISSN = {1868-8969}, year = {2020}, volume = {152}, editor = {Fern\'{a}ndez, Maribel 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.CSL.2020.9}, URN = {urn:nbn:de:0030-drops-116521}, doi = {10.4230/LIPIcs.CSL.2020.9}, annote = {Keywords: linear recurrence sequences, weighted automata, cost-register automata} }

Document

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

In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the input. This model gained a lot of attention in 2012 when Haase et al. showed its connections with timed automata. Later in 2013 Fearnley and Jurdziński proved that the reachability problem in this model is PSPACE-complete even in dimension 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is 2 or larger.

Filip Mazowiecki and Michał Pilipczuk. Reachability for Bounded Branching VASS. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mazowiecki_et_al:LIPIcs.CONCUR.2019.28, author = {Mazowiecki, Filip and Pilipczuk, Micha{\l}}, title = {{Reachability for Bounded Branching VASS}}, booktitle = {30th International Conference on Concurrency Theory (CONCUR 2019)}, pages = {28:1--28:13}, 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.2019.28}, URN = {urn:nbn:de:0030-drops-109303}, doi = {10.4230/LIPIcs.CONCUR.2019.28}, annote = {Keywords: Branching VASS, counter machines, reachability problem, bobrvass} }

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

We study the reachability problem for affine Z-VASS, which are integer vector addition systems with states in which transitions perform affine transformations on the counters. This problem is easily seen to be undecidable in general, and we therefore restrict ourselves to affine Z-VASS with the finite-monoid property (afmp-Z-VASS). The latter have the property that the monoid generated by the matrices appearing in their affine transformations is finite. The class of afmp-Z-VASS encompasses classical operations of counter machines such as resets, permutations, transfers and copies. We show that reachability in an afmp-Z-VASS reduces to reachability in a Z-VASS whose control-states grow polynomially in the size of the matrix monoid. Our construction shows that reachability relations of afmp-Z-VASS are semilinear, and in particular enables us to show that reachability in Z-VASS with transfers and Z-VASS with copies is PSPACE-complete.

Michael Blondin, Christoph Haase, and Filip Mazowiecki. Affine Extensions of Integer Vector Addition Systems with States. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{blondin_et_al:LIPIcs.CONCUR.2018.14, author = {Blondin, Michael and Haase, Christoph and Mazowiecki, Filip}, title = {{Affine Extensions of Integer Vector Addition Systems with States}}, booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)}, pages = {14:1--14:17}, 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.2018.14}, URN = {urn:nbn:de:0030-drops-95520}, doi = {10.4230/LIPIcs.CONCUR.2018.14}, annote = {Keywords: Vector addition systems, affine transformations, reachability, semilinear sets, computational complexity} }

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

The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous.

Laure Daviaud, Marcin Jurdzinski, Ranko Lazic, Filip Mazowiecki, Guillermo A. Pérez, and James Worrell. When is Containment Decidable for Probabilistic Automata?. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 121:1-121:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{daviaud_et_al:LIPIcs.ICALP.2018.121, author = {Daviaud, Laure and Jurdzinski, Marcin and Lazic, Ranko and Mazowiecki, Filip and P\'{e}rez, Guillermo A. and Worrell, James}, title = {{When is Containment Decidable for Probabilistic Automata?}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {121:1--121:14}, 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.2018.121}, URN = {urn:nbn:de:0030-drops-91251}, doi = {10.4230/LIPIcs.ICALP.2018.121}, annote = {Keywords: Probabilistic automata, Containment, Emptiness, Ambiguity} }

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**Published in:** LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

We present three pumping lemmas for three classes of functions definable by fragments of weighted automata over the min-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus semiring.

Filip Mazowiecki and Cristian Riveros. Pumping Lemmas for Weighted Automata. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2018.50, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Pumping Lemmas for Weighted Automata}}, booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, pages = {50:1--50:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-062-0}, ISSN = {1868-8969}, year = {2018}, volume = {96}, editor = {Niedermeier, Rolf 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.2018.50}, URN = {urn:nbn:de:0030-drops-84984}, doi = {10.4230/LIPIcs.STACS.2018.50}, annote = {Keywords: Weighted automata, regular functions over words, pumping lemmas} }

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

Whether the reachability problem for branching vector addition systems, or equivalently the provability problem for multiplicative exponential linear logic, is decidable has been a long-standing open question. The one-dimensional case is a generalisation of the extensively studied one-counter nets, and it was recently established polynomial-time complete provided counter updates are given in unary. Our main contribution is to determine the complexity when the encoding is binary: polynomial-space complete.

Diego Figueira, Ranko Lazic, Jérôme Leroux, Filip Mazowiecki, and Grégoire Sutre. Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 119:1-119:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{figueira_et_al:LIPIcs.ICALP.2017.119, author = {Figueira, Diego and Lazic, Ranko and Leroux, J\'{e}r\^{o}me and Mazowiecki, Filip and Sutre, Gr\'{e}goire}, title = {{Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {119:1--119:14}, 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.2017.119}, URN = {urn:nbn:de:0030-drops-74374}, doi = {10.4230/LIPIcs.ICALP.2017.119}, annote = {Keywords: branching vector addition systems, reachability problem} }

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**Published in:** LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study structural properties, expressiveness, and closure properties of copyless CRA. We show that copyless CRA are strictly less expressive than weighted automata and are not closed under reverse operation. To find a better class we impose restrictions on copyless CRA, which ends successfully with a new robust computational model that is closed under reverse and other extensions.

Filip Mazowiecki and Cristian Riveros. Copyless Cost-Register Automata: Structure, Expressiveness, and Closure Properties. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 53:1-53:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2016.53, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Copyless Cost-Register Automata: Structure, Expressiveness, and Closure Properties}}, booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)}, pages = {53:1--53:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-001-9}, ISSN = {1868-8969}, year = {2016}, volume = {47}, editor = {Ollinger, Nicolas and Vollmer, Heribert}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.53}, URN = {urn:nbn:de:0030-drops-57547}, doi = {10.4230/LIPIcs.STACS.2016.53}, annote = {Keywords: Cost Register Automata, Weighted Automata, Semirings} }

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

It is highly desirable for a computational model to have a logic characterization like in the seminal work from Buchi that connects MSO with finite automata. For example, weighted automata are the quantitative extension of finite automata for computing functions over words and they can be naturally characterized by a subframent of weighted logic introduced by Droste and Gastin. Recently, cost register automata (CRA) were introduced by Alur et al. as an alternative model for weighted automata. In hope of finding decidable subclasses of weighted automata, they proposed to restrict their model with the so-called copyless restriction. Unfortunately, copyless CRA do not enjoy good closure properties and, therefore, a logical characterization of this class seems to be unlikely.
In this paper, we introduce a new logic called maximal partition logic (MPL) for studying the expressiveness of copyless CRA. In contrast from the previous approaches (i.e. weighted logics), MPL is based on a new set of "regular" quantifiers that partition a word into maximal subwords, compute the output of a subformula over each subword separately, and then aggregate these outputs with a semiring operation. We study the expressiveness of MPL and compare it with weighted logics. Furthermore, we show that MPL is equally expressive to a natural subclass of copyless CRA. This shows the first logical characterization of copyless CRA and it gives a better understanding of the copyless restriction in weighted automata.

Filip Mazowiecki and Cristian Riveros. Maximal Partition Logic: Towards a Logical Characterization of Copyless Cost Register Automata. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 144-159, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{mazowiecki_et_al:LIPIcs.CSL.2015.144, author = {Mazowiecki, Filip and Riveros, Cristian}, title = {{Maximal Partition Logic: Towards a Logical Characterization of Copyless Cost Register Automata}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {144--159}, 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.2015.144}, URN = {urn:nbn:de:0030-drops-54127}, doi = {10.4230/LIPIcs.CSL.2015.144}, annote = {Keywords: MSO, Finite Automata, Cost Register Automata, Weighted Automata, Weighted Logics, Semirings} }