Principal AFL

  • Authors:

  • Seymour Ginsburg;Sheila Greibach

  • Affiliations:

  • -;-

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1970

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Abstract

A (full) principal AFL is a (full) AFL generated by a single language, i.e., it is thesmallest (full) AFL containing the given language. In the present paper, a study is made of such AFL. First, an AFA (abstract family of acceptors) characterization of (full) principal AFL is given. From this result, many well-known families of AFL can be shown to be (full) principal AFL. Next, two representation theorems for each language in a (full) principal AFL are given. The first involves the generator and one application each of concatenation, star, intersection with a regular set, inverse homomorphism, and a special type of homomorphism. The second involves an a-transducer, the generator, and one application of concatenation and star. Finally, it is shown that if @?"1 and @?"2 are (full) principal AFL, then so are (a) the smallest (full) AFL containing {L"1@?L"2/L"1 in @?"1, L"2 in @?"2 and (b) the family obtained by substituting @e-free languages of @?"2 into languages of @?"1.