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The hierarchy of families of language generated by multiset controlled grammar.
Source publication
This study focusses on defining a new variant of regulated grammars called multiset controlled grammars as well as investigating their computational power. In general, a multiset controlled grammar is a grammar equipped with an arithmetic expression over multisets terminals where to every production in the grammar a multiset is assigned, which repr...
Context in source publication
Context 1
... showed that multiset controlled grammars are more powerful than the traditional Chomsky grammar and have at least the lower bound of computational power as additive valence grammars as well as they also can generate the languages that are included in family of languages of matrix. A comprehensive picture of the hierarchy of languages generated by multiset controlled grammars is portrayed in Figure 1. Yet, some of the interesting questions are still remaining unanswered such: ...
Citations
... It is believed that the first regulated grammar, which is a matrix grammar, was introduced by Abraham in 1965 with the idea such in a derivation step, a sequence of productions are applied together [3]. Since then, a plenty of regulated grammars have been introduced and investigated in several papers such as [1][2][3][4][5][6][7][8][9][10][11][12][13], where each has a different control mechanism, and provides useful structures to handle a variety of issues in formal languages, programming languages, DNA computing, security, bioinformatics and many other areas. ...
... In this paper, we continue our research on multiset controlled grammars (see [4]); we investigate the closure properties of the family of languages generated by multiset controlled grammars. The study of closure properties is one of a crucial investigation in formal language theory since it provides a meaningful merit in both theory and practice of grammars. ...
... First, we give some basic notations and knowledge concerning to the theory of formal languages in which include grammars with regulated rewriting and set-theoretic operations on languages that will be used throughout the study. Then, we recall the definitions of multiset controlled grammars defined in [4] together with results on their generative power. Then, we demonstrate that for multiset controlled grammars one can construct equivalent normal forms, which will be used in study of the closure properties. ...
Multisets are very powerful and yet simple control mechanisms in regulated rewriting systems. In this paper, we review back the main results on the generative power of multiset controlled grammars introduced in recent research. It was proven that multiset controlled grammars are at least as powerful as additive valence grammars and at most as powerful as matrix grammars. In this paper, we mainly investigate the closure properties of multiset controlled grammars. We show that the family of languages generated by multiset controlled grammars is closed under operations union, concatenation, kleene-star, homomorphism and mirror image. © 2017 Institute of Advanced Engineering and Science. All rights reserved.
