Space-bounded reducibility among combinatorial problems

  • Authors:
  • Neil D. Jones

  • Affiliations:
  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1975

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Abstract

Reducibility and completeness among combinatorial problems can be formulated in terms of space bounds, in some cases refining the polynomial time-reducibility of Cook and Karp. Two versions are defined, by means of Turing machines and by bounded-quantifier formulas. Following are the main results. (1) The problem ''Is there a path between specified nodes of a digraph?'' is shown to be complete for the sets acceptable in nondeterministic log(.) space; (2) The problem ''Given a finite function f: {1,...,n}-{1,...,n}, is there a k such that f^k(1)=n?'' is similarly complete for deterministic log(.) space; and (3) Each of the problems ''Is T(M)=o?'' and ''Is T(M) infinite?'' (for M a deterministic finite automaton) is shown to be complete for nondeterministic (deterministic) log n space in the case in which the alphabet of M is arbitrary (consists of one letter).