License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.8
URN: urn:nbn:de:0030-drops-81078
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8107/
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Kawachi, Akinori ; Ogihara, Mitsunori ; Uchizawa, Kei

Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems

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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.

BibTeX - Entry

@InProceedings{kawachi_et_al:LIPIcs:2017:8107,
  author =	{Akinori Kawachi and Mitsunori Ogihara and Kei Uchizawa},
  title =	{{Generalized Predecessor Existence Problems for Boolean Finite Dynamical Systems}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8107},
  URN =		{urn:nbn:de:0030-drops-81078},
  doi =		{10.4230/LIPIcs.MFCS.2017.8},
  annote =	{Keywords: Computational complexity, dynamical systems, Garden of Eden, predecessor}
}

Keywords: Computational complexity, dynamical systems, Garden of Eden, predecessor
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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