Dimension-Minimality and Primality of Counter Nets

Shaull Almagor, Guy Avni, Henry Sinclair-Banks, Asaf Yeshurun

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A k-Counter Net (k-CN) is a finite-state automaton equipped with k integer counters that are not allowed to become negative, but do not have explicit zero tests. This language-recognition model can be thought of as labelled vector addition systems with states, some of which are accepting. Certain decision problems for k-CNs become easier, or indeed decidable, when the dimension k is small. Yet, little is known about the effect that the dimension k has on the class of languages recognised by k-CNs. Specifically, it would be useful if we could simplify algorithmic reasoning by reducing the dimension of a given CN. To this end, we introduce the notion of dimension-primality for k-CN, whereby a k-CN is prime if it recognises a language that cannot be decomposed into a finite intersection of languages recognised by d-CNs, for some d<k. We show that primality is undecidable. We also study two related notions: dimension-minimality (where we seek a single language-equivalent d-CN of lower dimension) and language regularity. Additionally, we explore the trade-offs in expressiveness between dimension and non-determinism for CN.

Original languageEnglish
Title of host publicationFoundations of Software Science and Computation Structures - 27th International Conference, FoSSaCS 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Proceedings
EditorsNaoki Kobayashi, James Worrell
Pages229-249
Number of pages21
DOIs
StatePublished - 2024
Event27th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2024 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024 - Luxembourg City, Luxembourg
Duration: 6 Apr 202411 Apr 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14575 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2024 held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024
Country/TerritoryLuxembourg
CityLuxembourg City
Period6/04/2411/04/24

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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