### 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 language | English |
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Pages (from-to) | 297-308 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 231 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 28 2000 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*231*(2), 297-308. https://doi.org/10.1016/S0304-3975(99)00105-X

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 231, no. 2, pp. 297-308. https://doi.org/10.1016/S0304-3975(99)00105-X

}

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.

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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 -