Conjunctive grammars with restricted disjunction

Okhotin, Alexander; Reitwieβner, Christian

doi:10.1016/j.tcs.2010.03.015

Cited by 16 publications

(5 citation statements)

References 6 publications

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“…Theorem C. Every language described by a conjunctive grammar can be described by a conjunctive grammar in odd normal form. (Okhotin and Reitwießner, 2010) Proof of Theorem 1. The "if" part is easier.…”

Section: Equivalence Of Conjunctive Grammars and Conjunctive Categorial Grammarsmentioning

confidence: 97%

“…Rules of the latter kind are allowed only if S is never referenced in any rules. Theorem C (Okhotin and Reitwießner [2010]). Every language without the empty string described by a conjunctive grammar can be described by a conjunctive grammar in the odd normal form.…”

Section: Equivalence Of Conjunctive Grammars and Conjunctive Categori...mentioning

confidence: 97%

“…One particular difficulty is that the normal form theorems for conjunctive grammars are weaker than those for the contextfree grammars: in particular, no analogue of the Greibach normal form is known for conjunctive grammars. For this reason, the simulation of conjunctive grammars by the proposed conjunctive categorial grammars relies on a different normal form by Okhotin and Reitwießner (2010). This leads to a representation of the whole class of conjunctive grammars, in contrast to the result by Kuznetsov (2013), which is valid only for grammars in Greibach normal form.…”

Section: Introductionmentioning

confidence: 99%

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Conjunctive Categorial Grammars

Kuznetsov

Okhotin

2017

Proceedings of the 15th Meeting on the Mathematics of Language

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Basic categorial grammars are enriched with a conjunction operation, and it is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that is, context-free grammars enhanced with conjunction. It is also shown that categorial grammars with conjunction can be naturally embedded into the Lambek calculus with conjunction and disjunction operations. This further implies that a certain NP-complete set can be defined in the Lambek calculus with conjunction.

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Section: Equivalence Of Conjunctive Grammars and Conjunctive Categorial Grammarsmentioning

confidence: 97%

Section: Equivalence Of Conjunctive Grammars and Conjunctive Categori...mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Conjunctive Categorial Grammars

Kuznetsov

Okhotin

2017

Proceedings of the 15th Meeting on the Mathematics of Language

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“…For conjunctive grammars, there is a normal form known as the odd normal form [18], in which all nonterminal symbols, except maybe the initial symbol, define only strings of odd length. In the following generalization of that normal form to the case of grammars with contexts, each nonterminal symbol defines strings of the form u v , where the length of v is odd and the length of its context u is even.…”

Section: The Even-odd Normal Formmentioning

confidence: 99%

“…However, already for conjunctive grammars, no analogue of the Greibach normal form is known, and the construction of a hardest language relies on a more complicated odd normal form, established by Okhotin and Reitwießner [18], with all rules of the form…”

Section: Introductionmentioning

confidence: 99%

The hardest language for grammars with context operators

Mrykhin¹,

Okhotin²

2020

Preprint

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In 1973, Greibach ("The hardest context-free language", SIAM J. Comp., 1973) constructed a context-free language L 0 with the property that every context-free language can be reduced to L 0 by a homomorphism, thus representing it as an inverse homomorphic image h −1 (L 0 ). In this paper, a similar characterization is established for a family of grammars equipped with operators for referring to the left context of any substring, recently defined by Barash and Okhotin ("An extension of context-free grammars with one-sided context specifications", Inform. Comput., 2014). An essential step of the argument is a new normal form for grammars with context operators, in which every nonterminal symbol defines only strings of odd length in left contexts of even length: the even-odd normal form.

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The Hardest Language for Conjunctive Grammars

Okhotin

2016

Computer Science – Theory and Applications

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Conjunctive grammars with restricted disjunction

Cited by 16 publications

References 6 publications

Conjunctive Categorial Grammars

Conjunctive Categorial Grammars

The hardest language for grammars with context operators

The Hardest Language for Conjunctive Grammars

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