Program equivalence and context-free grammars

  • Authors:

  • Barry K. Rosen

  • Affiliations:

  • -

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

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Abstract

Tree equivalence is a relation among polyadic recursion schemes. This relation is broad enough to be interesting: equivalent schemes may not be obviously equivalent and may still differ in computationally important ways. We show that this relation is also narrow enough to imply input-output equivalence. Is tree equivalence decidable? We assign context-free grammars to recursion schemes in such a way that schemes are tree equivalent iff their grammars generate the same language. Known results on LL(k) grammars then imply that tree equivalence is decidable for a class of schemes which includes the monadic recursion schemes without constants. Some important nonmonadic schemes are also included.