The &ohgr;-sequence equivalence problem for DOL systems is decidable

  • Authors:
  • Karel Culik, II;Tero Harju

  • Affiliations:
  • -;-

  • Venue:
  • STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
  • Year:
  • 1981

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Abstract

The following problem is shown to be decidable. Given are homomorphisms h1 and h2 from &Sgr;* to &Sgr;* and strings &sgr;1 and &sgr;2 over &Sgr; such that hni(&sgr;i) is a proper prefix of hn+1i (&sgr;i) for i &equil; 1, 2 and all n ≥ 0, i.e. for i &equil; 1, 2, hi generates from &sgr;i an infinite string &agr;i with prefixes hni(&sgr;i) for all n ≥ 0. Test whether &agr;1 &equil; &agr;2. From this result easily follows the decidability of limit language equivalence (&ohgr;-equivalence) for DOL systems.