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Documents authored by Puch, Antoni

Document
DOI: 10.4230/LIPIcs.LICS.2026.19
Reachability in VASS Extended with Integer Counters

Authors: Clotilde Bizière, Wojciech Czerwiński, Roland Guttenberg, Jérôme Leroux, Vincent Michielini, Łukasz Orlikowski, Antoni Puch, and Henry Sinclair-Banks

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
We consider a variant of VASS extended with integer counters, denoted VASS+ℤ. These are automata equipped with ℕ- and ℤ-counters; the ℕ-counters are required to remain nonnegative and the ℤ-counters do not have this restriction. We study the complexity of the reachability problem for VASS+ℤ when the number of ℕ-counters is fixed. We show that reachability is NP-complete in 1-VASS+ℤ (i.e. when there is only one ℕ-counter) regardless of unary or binary encoding. For d ≥ 2, using a KLMST-based algorithm, we prove that reachability in d-VASS+ℤ lies in the complexity class ℱ_{d+2}. Our upper bound improves on the naively obtained Ackermannian complexity by simulating the ℤ-counters with ℕ-counters. To complement our upper bounds, we show that extending VASS with integer counters significantly lowers the number of ℕ-counters needed to exhibit hardness. We prove that reachability in unary 2-VASS+ℤ is PSpace-hard; without ℤ-counters this lower bound is only known in dimension 5. We also prove that reachability in unary 3-VASS+ℤ is Tower-hard. Without ℤ-counters, reachability in 3-VASS has elementary complexity and Tower-hardness is only known in dimension 8.
Cite as

Clotilde Bizière, Wojciech Czerwiński, Roland Guttenberg, Jérôme Leroux, Vincent Michielini, Łukasz Orlikowski, Antoni Puch, and Henry Sinclair-Banks. Reachability in VASS Extended with Integer Counters. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 19:1-19:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{biziere_et_al:LIPIcs.LICS.2026.19,
  author =	{Bizi\`{e}re, Clotilde and Czerwi\'{n}ski, Wojciech and Guttenberg, Roland and Leroux, J\'{e}r\^{o}me and Michielini, Vincent and Orlikowski, {\L}ukasz and Puch, Antoni and Sinclair-Banks, Henry},
  title =	{{Reachability in VASS Extended with Integer Counters}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{19:1--19:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.19},
  URN =		{urn:nbn:de:0030-drops-268061},
  doi =		{10.4230/LIPIcs.LICS.2026.19},
  annote =	{Keywords: vector addition systems, Petri nets, counter automata, reachability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.67
Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata

Authors: Filip Mazowiecki, Antoni Puch, and Daniel Smertnig

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are interested in understanding their expressiveness power. Over the field of rationals and 1-letter alphabets, it is known that the two classes coincide; they are equivalent to linear recurrence sequences (LRS) whose exponential bases are roots of rationals. We develop a tool we call Pumping Sequence Families, which, by exploiting the simple single-letter behaviour of the models, yields two pumping-like results over arbitrary fields with unrestricted alphabets, one for each class. As a corollary of these results, we present examples proving that the two classes become incomparable over the field of rationals with unrestricted alphabets. We complement the results by analysing the zeroness and equivalence problems. For weighted automata (even unrestricted) these problems are well understood: there are polynomial time, and even NC² algorithms. For copyless cost register automata we show that the two problems are PSpace-complete, where the difficulty is to show the lower bound.
Cite as

Filip Mazowiecki, Antoni Puch, and Daniel Smertnig. Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 67:1-67:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2026.67,
  author =	{Mazowiecki, Filip and Puch, Antoni and Smertnig, Daniel},
  title =	{{Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{67:1--67:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.67},
  URN =		{urn:nbn:de:0030-drops-255568},
  doi =		{10.4230/LIPIcs.STACS.2026.67},
  annote =	{Keywords: weighted automata, cost register automata, ambiguity, linear recurrence sequences, equivalence problem}
}
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