Technical Report CS0044

Title: Theory Of W-languages; Part I: Characterizations Of W-context Free Languages
Authors: Rina S.Cohen and Arie Y.Gold
Abstract: An w-language is a set consisting of w-type strings over some alphabet. This paper introduces the basic notions concerning generation of w-languages by means of w-grammars and their recognition by w-machines of various types. Attention is then focused on W-CFL's, the w-languages generated by w-context free grammars. Two main characterizations of the family of W-CFL' s are ob tained: a) An w-language is an w-CFL if and only if n W' t can be represented as .u UiVi' where for each i = l, •••n, Ui and 1-i Vi are context free languages. This result gener4lizes McNaughton's characterization of w-regular languages [Mc]. b) w-CFL' s are precisely the w-languages recognized by w-pushdown automata by designated state sets (and also by "emptying" the pushdown store infinitely many times). A few other characterizations and normal forms for the w-CFL's are given and several decidability results, e.g. the solvability of the emptiness problem, are established.
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