TY - GEN

T1 - Generalized predecessor existence problems for boolean finite dynamical systems

AU - Kawachi, Akinori

AU - Ogihara, Mitsunori

AU - Uchizawa, Kei

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

KW - Computational complexity

KW - Dynamical systems

KW - Garden of Eden

KW - Predecessor

UR - http://www.scopus.com/inward/record.url?scp=85038443054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038443054&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2017.8

DO - 10.4230/LIPIcs.MFCS.2017.8

M3 - Conference contribution

AN - SCOPUS:85038443054

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

A2 - Larsen, Kim G.

A2 - Raskin, Jean-Francois

A2 - Bodlaender, Hans L.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

Y2 - 21 August 2017 through 25 August 2017

ER -