Generalized predecessor existence problems for boolean finite dynamical systems

Akinori Kawachi, Mitsunori Ogihara, Kei Uchizawa

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

1 Scopus citations

Abstract

A Boolean Finite Synchronous Dynamical System (BFDS, for short) consists of a finite number of objects that each maintains a boolean state, where after individually receiving state assignments, the objects update their state with respect to object-specific time-independent boolean functions synchronously in discrete time steps. The present paper studies the computational complexity of determining, given a boolean finite synchronous dynamical system, a configuration, which is a boolean vector representing the states of the objects, and a positive integer t, whether there exists another configuration from which the given configuration can be reached in t steps. It was previously shown that this problem, which we call the t-Predecessor Problem, is NP-complete even for t = 1 if the update function of an object is either the conjunction of arbitrary fan-in or the disjunction of arbitrary fan-in. This paper studies the computational complexity of the t-Predecessor Problem for a variety of sets of permissible update functions as well as for polynomially bounded t. It also studies the t-Garden-Of-Eden Problem, a variant of the t-Predecessor Problem that asks whether a configuration has a t-predecessor, which itself has no predecessor. The paper obtains complexity theoretical characterizations of all but one of these problems.

Original languageEnglish (US)
Title of host publication42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
EditorsKim G. Larsen, Jean-Francois Raskin, Hans L. Bodlaender
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770460
DOIs
StatePublished - Nov 1 2017
Event42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 - Aalborg, Denmark
Duration: Aug 21 2017Aug 25 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume83
ISSN (Print)1868-8969

Other

Other42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
CountryDenmark
CityAalborg
Period8/21/178/25/17

Keywords

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

ASJC Scopus subject areas

  • Software

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  • Cite this

    Kawachi, A., Ogihara, M., & Uchizawa, K. (2017). Generalized predecessor existence problems for boolean finite dynamical systems. In K. G. Larsen, J-F. Raskin, & H. L. Bodlaender (Eds.), 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 83). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2017.8