Syntactic operators on full semiAFLs

  • Authors:
  • Sheila A. Greibach

  • Affiliations:
  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1972

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Abstract

The class of syntactic operators is defined. If a full AFL @? is not closed undera syntactic operator @?, then repeated application of @? to @? produces an infinite hierarchy of full AFLs and the closure of @? under @? is not full principal. If @?"1 and @?"2 are incomparable full AFLs, then the least full AFL containing @?"1 and @?"2 is not closed under any syntactic operator. If L is any generator of a full AFL @? closed under any syntactic operator, then all of @? may be expressed as finite state translations of L (without applying concatenation or star). It is shown that substitution, insertion, intercalation and homomorphic replication are all syntactic operators.