Intractability of decision problems for finite-memory automata

Hiroshi Sakamoto, Daisuke Ikeda

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

This paper deals with finite-memory automata, introduced in Kaminski and Francez (Theoret. Comput. Sci. 134 (1994) 329-363). With a restricted memory structure that consists of a finite number of registers, a finite-memory automaton can store arbitrary input symbols. Thus, the language accepted by a finite-memory automaton is defined over a potentially infinite alphabet. The following decision problems are studied for a general finite-memory automata A as well as for deterministic ones: the membership problem, i.e., given an A and a string w, to decide whether w is accepted by A, and the non-emptiness problem, i.e., given an A, to decide whether the language accepted by A is non-empty. The membership problem is P-complete, provided a given automaton is deterministic, and each of the other problems is NP-complete. Thus, we conclude that the decision problems considered are intractable.

Original languageEnglish
Pages (from-to)297-308
Number of pages12
JournalTheoretical Computer Science
Volume231
Issue number2
DOIs
Publication statusPublished - Jan 28 2000

Fingerprint

Decision problem
Automata
Data storage equipment
Computational complexity
NP-complete problem
Strings
Arbitrary
Language

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Intractability of decision problems for finite-memory automata. / Sakamoto, Hiroshi; Ikeda, Daisuke.

In: Theoretical Computer Science, Vol. 231, No. 2, 28.01.2000, p. 297-308.

Research output: Contribution to journalArticle

@article{cf7e87bdd5dc4a37a9e01489e1ccbc65,
title = "Intractability of decision problems for finite-memory automata",
abstract = "This paper deals with finite-memory automata, introduced in Kaminski and Francez (Theoret. Comput. Sci. 134 (1994) 329-363). With a restricted memory structure that consists of a finite number of registers, a finite-memory automaton can store arbitrary input symbols. Thus, the language accepted by a finite-memory automaton is defined over a potentially infinite alphabet. The following decision problems are studied for a general finite-memory automata A as well as for deterministic ones: the membership problem, i.e., given an A and a string w, to decide whether w is accepted by A, and the non-emptiness problem, i.e., given an A, to decide whether the language accepted by A is non-empty. The membership problem is P-complete, provided a given automaton is deterministic, and each of the other problems is NP-complete. Thus, we conclude that the decision problems considered are intractable.",
author = "Hiroshi Sakamoto and Daisuke Ikeda",
year = "2000",
month = "1",
day = "28",
doi = "10.1016/S0304-3975(99)00105-X",
language = "English",
volume = "231",
pages = "297--308",
journal = "Theoretical Computer Science",
issn = "0304-3975",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Intractability of decision problems for finite-memory automata

AU - Sakamoto, Hiroshi

AU - Ikeda, Daisuke

PY - 2000/1/28

Y1 - 2000/1/28

N2 - This paper deals with finite-memory automata, introduced in Kaminski and Francez (Theoret. Comput. Sci. 134 (1994) 329-363). With a restricted memory structure that consists of a finite number of registers, a finite-memory automaton can store arbitrary input symbols. Thus, the language accepted by a finite-memory automaton is defined over a potentially infinite alphabet. The following decision problems are studied for a general finite-memory automata A as well as for deterministic ones: the membership problem, i.e., given an A and a string w, to decide whether w is accepted by A, and the non-emptiness problem, i.e., given an A, to decide whether the language accepted by A is non-empty. The membership problem is P-complete, provided a given automaton is deterministic, and each of the other problems is NP-complete. Thus, we conclude that the decision problems considered are intractable.

AB - This paper deals with finite-memory automata, introduced in Kaminski and Francez (Theoret. Comput. Sci. 134 (1994) 329-363). With a restricted memory structure that consists of a finite number of registers, a finite-memory automaton can store arbitrary input symbols. Thus, the language accepted by a finite-memory automaton is defined over a potentially infinite alphabet. The following decision problems are studied for a general finite-memory automata A as well as for deterministic ones: the membership problem, i.e., given an A and a string w, to decide whether w is accepted by A, and the non-emptiness problem, i.e., given an A, to decide whether the language accepted by A is non-empty. The membership problem is P-complete, provided a given automaton is deterministic, and each of the other problems is NP-complete. Thus, we conclude that the decision problems considered are intractable.

UR - http://www.scopus.com/inward/record.url?scp=0042465982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042465982&partnerID=8YFLogxK

U2 - 10.1016/S0304-3975(99)00105-X

DO - 10.1016/S0304-3975(99)00105-X

M3 - Article

AN - SCOPUS:0042465982

VL - 231

SP - 297

EP - 308

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 2

ER -