Intractability of decision problems for finite-memory automata

Hiroshi Sakamoto, Daisuke Ikeda

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


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
Issue number2
Publication statusPublished - Jan 28 2000

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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