The Solvability of the Derivability Problem for One-Normal Systems

  • Authors:

  • Stephen A. Cook

  • Affiliations:

  • Harvard University, Cambridge, Massachusetts

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1966

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Abstract

A one-normal system is a Post production system on a finite alphabet {s1, s2, · · ·, s&sgr;} with productions siP → PEij, where i ranges over a subset of {1, 2, · · ·, &sgr;} and, for fixed i, j takes on the values 1, 2, · · ·, ni. The following derivability problem is shown to be solvable for each such system: Given two words P and Q, decide whether Q can be derived from P by successive applications of the production rules. The result was proved by Hao Wang for the monogenic case (i.e., when each ni = 1).