Simple matrix languages
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A characterization of L B as the smallest family of languages which contains the bounded context-free languages and which is closed under the operations of union and intersection is proved.Abstract:
Simple matrix languages and right-linear simple matrix languages are defined as subfamilies of matrix languages by putting restrictions on the form and length (degree) of the rewriting rules associated with matrix grammars. For each n ⩾ 1, let L ( n ) [ ℛ ( n ) ] be the class of simple matrix languages [right-linear simple matrix languages] of degree n, and let L = ⋃ n ⩾ 1 L ( n ) [ ℛ = ⋃ n ⩾ 1 ℛ ( n ) ] . It is shown that L ( 1 ) [ ℛ ( 1 ) ] coincides with the class of context-free languages [regular sets] and that L is a proper subset of the family of languages accepted by deterministic linear bounded automata. It is proved that L ( n ) [ ℛ ( n ) ] forms a hierarchy of classes of languages in L [ ℛ ] . The closure properties and decision problems associated with L ( n ) , L , ℛ ( n ) , and ℛ are thoroughly investigated. Let L B [ ℛ B ] be the bounded languages in L [ ℛ ] . It is shown that L B = ℛ B and that most of the positive closure and decision results which are true for bounded context-free languages are carried over in L B . A characterization of L B as the smallest family of languages which contains the bounded context-free languages and which is closed under the operations of union and intersection is proved.read more
Citations
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Journal ArticleDOI
Tree Transducers, L Systems, and Two-Way Machines
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Grammars with controlled derivations
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References
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Journal ArticleDOI
Finite automata and their decision problems
Michael O. Rabin,Dana Scott +1 more
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Journal ArticleDOI
On Context-Free Languages
TL;DR: In this report, certain properties of context-free (CF or type 2) Grammars are investigated, like that of Chomsky, and it is shown that this type of grammar is essentially stronger than type 2 grammars and has the advantage over type 1 grammARS that the phrase structure of a grammatical sentence is unique, once the derivation is given.