Matrix Grammars with a Leftmost Restriction
نویسنده
چکیده
Matrix grammars introduced by Nbrah~tm (1965) have proved to be a very fruitful generalization of context-free grammars: simple in principle, easy to deal with and yet very powerful [cf. Brainerd (1968), Ibarra (1970) and Siromoney (1969)]. They fall into the category of grammars with restricted use of productions, and possess the same generative capacity as programmed grammars, periodically time-variant grammars and grammars with a regular control language [cf. Salomaa (1970)]. In this paper, we consider matrix grammars, where the core productions in the matrices have the context-free form X--~ P, X being a nonterminal. It is known [cf. Rosenkrantz (1969) and Salomaa (1970)] that if the core productions are also A-free, i.e., the right side P is always distinct from the empty word A, then the family of languages generated by such matrix grammars is properly included in the family of context-sensitive languages. On the other hand, if a is allowed on the right side and, furthermore, an appearancechecking interpretation in the application of productions is considered, then the family of generated languages coincides with the family of recursively enumerable languages [Rosenkrantz (1969) and Salomaa (1970)]. (In this interpretation, a production X--~ P may be applied by (i) noticing that X does not occur in the word under scan, and (ii) moving on to the next production.) It is an open problem how large the family of generated languages will be if A is allowed on the right side of productions but the appearancechecking interpretation is not considered. For instance, it is not known whether nonregular languages over one letter belong to this family [cf. Salomaa (1970) and (1970a)].
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ورودعنوان ژورنال:
- Information and Control
دوره 20 شماره
صفحات -
تاریخ انتشار 1972