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Documents authored by Guttenberg, Roland

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.
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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.LICS.2026.53
PVASS Reachability Is Decidable

Authors: Roland Guttenberg, Eren Keskin, and Roland Meyer

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

Abstract
Reachability in pushdown vector addition systems with states (PVASS) is among the longest standing open problems in Theoretical Computer Science. We show that the problem is decidable in full generality. Our decision procedure is similar in spirit to the KLMST algorithm for VASS reachability, but works over objects that support an elaborate form of procedure summarization as known from pushdown reachability.
Cite as

Roland Guttenberg, Eren Keskin, and Roland Meyer. PVASS Reachability Is Decidable. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 53:1-53:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{guttenberg_et_al:LIPIcs.LICS.2026.53,
  author =	{Guttenberg, Roland and Keskin, Eren and Meyer, Roland},
  title =	{{PVASS Reachability Is Decidable}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{53:1--53:25},
  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.2026.53},
  URN =		{urn:nbn:de:0030-drops-268406},
  doi =		{10.4230/LIPIcs.LICS.2026.53},
  annote =	{Keywords: Pushdowns, Petri Nets, VASS, PVASS, Reachability, Decidability, Complexity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.158
Revisiting Finiteness of Matrix Monoids

Authors: Rida Ait El Manssour, Roland Guttenberg, Nathan Lhote, Mahsa Shirmohammadi, and James Ben Worrell

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
This paper concerns decision problems related to finite monoids of rational matrices. We show that determining finiteness of a given finitely presented monoid is in PSpace, improving the known coNExp^NP bound. We also show that the membership problem for finite matrix monoids is PSpace-complete, improving the known NExp-upper bound. Our two complexity results are corollaries of a new polynomial bit-size bound on matrix entries in finite monoids. This is obtained by reduction to the case of matrix groups, using the structure theory of noncommutative algebras and of matrix monoids. Our techniques also give us a polynomial-time algorithm for deciding whether a monoid of rational matrices is conjugate to a monoid of integer matrices.
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Rida Ait El Manssour, Roland Guttenberg, Nathan Lhote, Mahsa Shirmohammadi, and James Ben Worrell. Revisiting Finiteness of Matrix Monoids. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 158:1-158:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aitelmanssour_et_al:LIPIcs.ICALP.2026.158,
  author =	{Ait El Manssour, Rida and Guttenberg, Roland and Lhote, Nathan and Shirmohammadi, Mahsa and Worrell, James Ben},
  title =	{{Revisiting Finiteness of Matrix Monoids}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{158:1--158:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.158},
  URN =		{urn:nbn:de:0030-drops-265745},
  doi =		{10.4230/LIPIcs.ICALP.2026.158},
  annote =	{Keywords: Matrix Semigroups, Finiteness, Integrality, Bitsize Bound}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.177
Exploring VASS Parameterised by Geometric Dimension

Authors: Wojciech Czerwiński, Roland Guttenberg, Łukasz Orlikowski, Henry Sinclair-Banks, and Yangluo Zheng

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The geometric dimension g of a Vector Addition System with States (VASS) is the dimension of the vector space generated by cycles in the VASS; this parameter refines the standard dimension d, the number of counters. Recently, it was discovered that the fastest-known algorithm for solving the reachability problem for VASS has the same complexity in terms of g as in terms of d. This suggests that the geometric dimension may in fact be a more adequate parameter for measuring the complexity of VASS reachability problems. We initiate a more systematic study of the geometric dimension. We discuss differences between two parameters: the geometric dimension and the SCC dimension. Our main technical result states that classical results about the coverability and boundedness problems can be improved from dimension d to geometric dimension g. Namely, coverability is witnessed by runs of length n^{2^𝒪(g)} instead of n^{2^𝒪(d)}, and unboundedness can be witnessed by runs of length n^{2^𝒪(g log g)} instead of n^{2^𝒪(d log d)}, where n is the size of the instance. We also study integer reachability and simultaneous unboundedness in VASS parameterised by the geometric dimension.
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Wojciech Czerwiński, Roland Guttenberg, Łukasz Orlikowski, Henry Sinclair-Banks, and Yangluo Zheng. Exploring VASS Parameterised by Geometric Dimension. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 177:1-177:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{czerwinski_et_al:LIPIcs.ICALP.2026.177,
  author =	{Czerwi\'{n}ski, Wojciech and Guttenberg, Roland and Orlikowski, {\L}ukasz and Sinclair-Banks, Henry and Zheng, Yangluo},
  title =	{{Exploring VASS Parameterised by Geometric Dimension}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{177:1--177:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.177},
  URN =		{urn:nbn:de:0030-drops-265655},
  doi =		{10.4230/LIPIcs.ICALP.2026.177},
  annote =	{Keywords: vector addition systems, Petri nets, geometric dimensions, coverability problem, integer reachability problem, simultaneous unboundedness, reachability problem}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.1
The Expressive Power of Uniform Population Protocols with Logarithmic Space

Authors: Philipp Czerner, Vincent Fischer, and Roland Guttenberg

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n)∩𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly those predicates, whose unary encoding lies in NSPACE(f(n) log n).
Cite as

Philipp Czerner, Vincent Fischer, and Roland Guttenberg. The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czerner_et_al:LIPIcs.SAND.2025.1,
  author =	{Czerner, Philipp and Fischer, Vincent and Guttenberg, Roland},
  title =	{{The Expressive Power of Uniform Population Protocols with Logarithmic Space}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.1},
  URN =		{urn:nbn:de:0030-drops-230540},
  doi =		{10.4230/LIPIcs.SAND.2025.1},
  annote =	{Keywords: Population Protocols, Uniform, Expressive Power}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.44
Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space

Authors: Philipp Czerner, Vincent Fischer, and Roland Guttenberg

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n) ∩ 𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly NSPACE(f(n) log n).
Cite as

Philipp Czerner, Vincent Fischer, and Roland Guttenberg. Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 44:1-44:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czerner_et_al:LIPIcs.DISC.2024.44,
  author =	{Czerner, Philipp and Fischer, Vincent and Guttenberg, Roland},
  title =	{{Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{44:1--44:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.44},
  URN =		{urn:nbn:de:0030-drops-212726},
  doi =		{10.4230/LIPIcs.DISC.2024.44},
  annote =	{Keywords: Population Protocols, Uniform, Expressive Power}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.141
Flattability of Priority Vector Addition Systems

Authors: Roland Guttenberg

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS is reachable from a given initial configuration. One of the main approaches to solve the problem on practical instances is called flattening, intuitively removing nested loops. This technique is known to terminate for semilinear VAS due to [Jérôme Leroux, 2013]. In this paper, we prove that also for VAS with nested zero tests, called Priority VAS, flattening does in fact terminate for all semilinear reachability relations. Furthermore, we prove that Priority VAS admit semilinear inductive invariants. Both of these results are obtained by defining a well-quasi-order on runs of Priority VAS which has good pumping properties.
Cite as

Roland Guttenberg. Flattability of Priority Vector Addition Systems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 141:1-141:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guttenberg:LIPIcs.ICALP.2024.141,
  author =	{Guttenberg, Roland},
  title =	{{Flattability of Priority Vector Addition Systems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{141:1--141:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.141},
  URN =		{urn:nbn:de:0030-drops-202848},
  doi =		{10.4230/LIPIcs.ICALP.2024.141},
  annote =	{Keywords: Priority Vector Addition Systems, Semilinear, Inductive Invariants, Geometry, Flattability, Almost Semilinear, Transformer Relation}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.156
Verification of Population Protocols with Unordered Data

Authors: Steffen van Bergerem, Roland Guttenberg, Sandra Kiefer, Corto Mascle, Nicolas Waldburger, and Chana Weil-Kennedy

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Population protocols are a well-studied model of distributed computation in which a group of anonymous finite-state agents communicates via pairwise interactions. Together they decide whether their initial configuration, i. e., the initial distribution of agents in the states, satisfies a property. As an extension in order to express properties of multisets over an infinite data domain, Blondin and Ladouceur (ICALP'23) introduced population protocols with unordered data (PPUD). In PPUD, each agent carries a fixed data value, and the interactions between agents depend on whether their data are equal or not. Blondin and Ladouceur also identified the interesting subclass of immediate observation PPUD (IOPPUD), where in every transition one of the two agents remains passive and does not move, and they characterised its expressive power. We study the decidability and complexity of formally verifying these protocols. The main verification problem for population protocols is well-specification, that is, checking whether the given PPUD computes some function. We show that well-specification is undecidable in general. By contrast, for IOPPUD, we exhibit a large yet natural class of problems, which includes well-specification among other classic problems, and establish that these problems are in ExpSpace. We also provide a lower complexity bound, namely coNExpTime-hardness.
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Steffen van Bergerem, Roland Guttenberg, Sandra Kiefer, Corto Mascle, Nicolas Waldburger, and Chana Weil-Kennedy. Verification of Population Protocols with Unordered Data. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 156:1-156:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{vanbergerem_et_al:LIPIcs.ICALP.2024.156,
  author =	{van Bergerem, Steffen and Guttenberg, Roland and Kiefer, Sandra and Mascle, Corto and Waldburger, Nicolas and Weil-Kennedy, Chana},
  title =	{{Verification of Population Protocols with Unordered Data}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{156:1--156:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.156},
  URN =		{urn:nbn:de:0030-drops-202993},
  doi =		{10.4230/LIPIcs.ICALP.2024.156},
  annote =	{Keywords: Population protocols, Parameterized verification, Distributed computing, Well-specification}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.6
Geometry of Reachability Sets of Vector Addition Systems

Authors: Roland Guttenberg, Mikhail Raskin, and Javier Esparza

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

Abstract
Vector Addition Systems (VAS), aka Petri nets, are a popular model of concurrency. The reachability set of a VAS is the set of configurations reachable from the initial configuration. Leroux has studied the geometric properties of VAS reachability sets, and used them to derive decision procedures for important analysis problems. In this paper we continue the geometric study of reachability sets. We show that every reachability set admits a finite decomposition into disjoint almost hybridlinear sets enjoying nice geometric properties. Further, we prove that the decomposition of the reachability set of a given VAS is effectively computable. As a corollary, we derive a new proof of Hauschildt’s 1990 result showing the decidability of the question whether the reachability set of a given VAS is semilinear. As a second corollary, we prove that the complement of a reachability set, if it is infinite, always contains an infinite linear set.
Cite as

Roland Guttenberg, Mikhail Raskin, and Javier Esparza. Geometry of Reachability Sets of Vector Addition Systems. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{guttenberg_et_al:LIPIcs.CONCUR.2023.6,
  author =	{Guttenberg, Roland and Raskin, Mikhail and Esparza, Javier},
  title =	{{Geometry of Reachability Sets of Vector Addition Systems}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{6:1--6:16},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-190005},
  doi =		{10.4230/LIPIcs.CONCUR.2023.6},
  annote =	{Keywords: Vector Addition System, Petri net, Reachability Set, Almost hybridlinear, Partition, Geometry}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.11
Fast and Succinct Population Protocols for Presburger Arithmetic

Authors: Philipp Czerner, Roland Guttenberg, Martin Helfrich, and Javier Esparza

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
In their 2006 seminal paper in Distributed Computing, Angluin et al. present a construction that, given any Presburger predicate as input, outputs a leaderless population protocol that decides the predicate. The protocol for a predicate of size m (when expressed as a Boolean combination of threshold and remainder predicates with coefficients in binary) runs in 𝒪(m ⋅ n² log n) expected number of interactions, which is almost optimal in n, the number of interacting agents. However, the number of states of the protocol is exponential in m. This is a problem for natural computing applications, where a state corresponds to a chemical species and it is difficult to implement protocols with many states. Blondin et al. described in STACS 2020 another construction that produces protocols with a polynomial number of states, but exponential expected number of interactions. We present a construction that produces protocols with 𝒪(m) states that run in expected 𝒪(m⁷ ⋅ n²) interactions, optimal in n, for all inputs of size Ω(m). For this, we introduce population computers, a carefully crafted generalization of population protocols easier to program, and show that our computers for Presburger predicates can be translated into fast and succinct population protocols.
Cite as

Philipp Czerner, Roland Guttenberg, Martin Helfrich, and Javier Esparza. Fast and Succinct Population Protocols for Presburger Arithmetic. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{czerner_et_al:LIPIcs.SAND.2022.11,
  author =	{Czerner, Philipp and Guttenberg, Roland and Helfrich, Martin and Esparza, Javier},
  title =	{{Fast and Succinct Population Protocols for Presburger Arithmetic}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.11},
  URN =		{urn:nbn:de:0030-drops-159535},
  doi =		{10.4230/LIPIcs.SAND.2022.11},
  annote =	{Keywords: population protocols, fast, succinct, population computers}
}
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