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The decidability of the reachability problem for vector addition systems (Preliminary Version)

Authors:

George S. Sacerdote,

Richard L. TenneyAuthors Info & Claims

STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

Pages 61 - 76

https://doi.org/10.1145/800105.803396

Published: 04 May 1977 Publication History

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Abstract

Let V be a finite set of integral vectors in Euclidian N-space, and let a be an integral point in the first orthant of N-space. The reachability set R(a,V) is the set of integral points b in the first orthant such that there is a polygonal path γ from a to b satisfying (i) all of γ lies in the first orthant, and (ii) the edges of γ are translates of the vectors in V. The reachability problem for the vector addition system (a,V) asks for an algorithm to decide which integral points b are in R(b,V). In this paper we give an algorithm to solve this problem.

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Leroux J(2024)Ackermannian Completion of SeparatorsFoundations of Software Science and Computation Structures10.1007/978-3-031-57228-9_1(3-10)Online publication date: 6-Apr-2024
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Baumann PD’Alessandro FGanardi MIbarra OMcQuillan ISchütze LZetzsche G(2023)Unboundedness Problems for Machines with Reversal-Bounded CountersFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_12(240-264)Online publication date: 21-Apr-2023
https://doi.org/10.1007/978-3-031-30829-1_12
Leroux J(2022)The Reachability Problem for Petri Nets is Not Primitive Recursive2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00121(1241-1252)Online publication date: Feb-2022
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Index Terms

The decidability of the reachability problem for vector addition systems (Preliminary Version)
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
2. Software and its engineering
  1. Software organization and properties
    1. Software system structures
      1. Software system models
        Petri nets

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STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

May 1977

318 pages

ISBN:9781450374095

DOI:10.1145/800105

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 May 1977

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STOC '77 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Leroux J(2024)Ackermannian Completion of SeparatorsFoundations of Software Science and Computation Structures10.1007/978-3-031-57228-9_1(3-10)Online publication date: 6-Apr-2024
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Baumann PD’Alessandro FGanardi MIbarra OMcQuillan ISchütze LZetzsche G(2023)Unboundedness Problems for Machines with Reversal-Bounded CountersFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_12(240-264)Online publication date: 21-Apr-2023
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Leroux J(2022)The Reachability Problem for Petri Nets is Not Primitive Recursive2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00121(1241-1252)Online publication date: Feb-2022
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Leroux J(2021)Flat Petri Nets (Invited Talk)Application and Theory of Petri Nets and Concurrency10.1007/978-3-030-76983-3_2(17-30)Online publication date: 16-Jun-2021
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Czerwiński WLasota SLazić RLeroux JMazowiecki FCharikar MCohen E(2019)The reachability problem for Petri nets is not elementaryProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316369(24-33)Online publication date: 23-Jun-2019
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Dong XFu YVaracca D(2019)Extensional Petri netFormal Aspects of Computing10.1007/s00165-018-0473-331:1(47-58)Online publication date: 12-Feb-2019
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Case ALutz JStull D(2018)Reachability problems for continuous chemical reaction networksNatural Computing: an international journal10.1007/s11047-017-9641-217:2(223-230)Online publication date: 1-Jun-2018
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Schmitz S(2016)The complexity of reachability in vector addition systemsACM SIGLOG News10.1145/2893582.28935853:1(4-21)Online publication date: 17-Feb-2016
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