Some problems of finite representability

Altman, Edward I.; Banerji, Ranan B.

doi:10.1016/s0019-9958(65)90196-8

Cited by 20 publications

(10 citation statements)

References 2 publications

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“…Grammar with finite index (the index of a grammar is the maximal number of nonterminals simultaneously appearing in its complete derivations (considering the most economical derivations for each string)) were first considered by Brainerd [7]. Nonterminal-bounded grammars (a grammar a nonterminal-bounded if the total number of nonterminals in every sentential form does not exceed an upper bound) were introduced by Altman and Banerji in [3][4][5]. A "weak" variant of nonterminal-bounded grammars (only the complete derivations are required to be bounded) were defined by Moriya [44].…”

Section: Capacity-bounded Grammarsmentioning

confidence: 99%

“…If we notice the definitions of derivation-bounded [32] or nonterminal-bounded grammars [3][4][5] only nonterminal strings are allowed as left-hand sides of production rules. Here, an interesting question is emerged, what kind of languages can be generated if we derestrict this condition, i.e., allow any string in the left-hand side of the rules?…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

See 1 more Smart Citation

Grammars Controlled by Petri Nets

Dassow¹,

Mavlankulov²,

Othman³

et al. 2012

Petri Nets - Manufacturing and Computer Science

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Section: Capacity-bounded Grammarsmentioning

confidence: 99%

Section: Conclusion and Future Researchmentioning

confidence: 99%

Grammars Controlled by Petri Nets

Dassow¹,

Mavlankulov²,

Othman³

et al. 2012

Petri Nets - Manufacturing and Computer Science

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“…:Pf -+ p* be a homomorphism such that~(P) is the parent of P for each By induction on the lengths of derivations the following generalizations of (1) and (2) is closed under regular substitution.…”

Section: Now For Eachmentioning

confidence: 99%

Abstract families of context-free grammars

Workman¹

1981

International Journal of Computer Mathematics

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“…We omit the proof, which has appeared in the literature for the cases of leftmost derivations [1] and arbitrary derivations [3].…”

Section: Lemma 4 Let G Be a Grammar And Let R Be A Regular Subset Ofmentioning

confidence: 99%

Control sets on grammars using depth-first derivations

Luker

1979

Math. Systems Theory

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Abstract. Control sets on grammars are extended to depth-first derivations. It is proved that a context-free language is generated by the depth-first derivations of an arbitrary context-free grammar controlled by an arbitrary regular set. This result is sharpened to obtain a new characterization of the family of derivation-bounded languages: a language L is derivation bounded if and only if it is generated by the depth-first derivations of a context-free grammar G controlled by a regular subset R of the Szilard language of G. The left-derivation-bounded languages are characterized analogously using leftmost derivations. It is proved that a grammar G is nonterminal bounded if and only if the Szilard language defined using only the depth-first derivations of G is regular. Finally, it is proved that if a family of languages C is a trio, a semi-AFL, an AFL, or an AFL closed under k-free substitution, then the family of languages generated using arbitrary context-free grammars controlled by members of C is full, is closed under reversal, and has the closure properties assumed of C.

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Some problems of finite representability

Cited by 20 publications

References 2 publications

Grammars Controlled by Petri Nets

Grammars Controlled by Petri Nets

Abstract families of context-free grammars

Control sets on grammars using depth-first derivations

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