Synchronous boolean finite dynamical systems on directed graphs over XOR functions

Mitsunori Ogihara, Kei Uchizawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we investigate the complexity of a number of computational problems defined on a synchronous boolean finite dynamical system, where update functions are chosen from a template set of exclusive-or and its negation. We first show that the reachability and path-intersection problems are solvable in logarithmic space-uniform AC1 if the objects execute permutations, while the reachability problem is known to be in P and the path-intersection problem to be in UP in general. We also explore the case where the reachability or intersection are tested on a subset of objects, and show that this hardens complexity of the problems: both problems become NP-complete, and even Πp2-complete if we further require universality of the intersection. We next consider the exact cycle length problem, that is, determining whether there exists an initial configuration that yields a cycle in the configuration space having exactly a given length, and show that this problem is NP-complete. Lastly, we consider the t-predecessor and t-Garden of Eden problem, and prove that these are solvable in polynomial time even if the value of t is also given in binary as part of instance, and the two problems are in logarithmic space-uniform NC2 if the value of t is given in unary as part of instance.

Original languageEnglish (US)
Title of host publication45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
EditorsJavier Esparza, Daniel Kral�, Daniel Kral�
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771597
DOIs
StatePublished - Aug 1 2020
Event45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 - Prague, Czech Republic
Duration: Aug 25 2020Aug 26 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume170
ISSN (Print)1868-8969

Conference

Conference45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
CountryCzech Republic
CityPrague
Period8/25/208/26/20

Keywords

  • Computational complexity
  • Dynamical systems
  • Garden of Eden
  • Predecessor
  • Reachability

ASJC Scopus subject areas

  • Software

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