Noncommutative algebras, context-free grammars and algebraic Hilbert series
نویسندگان
چکیده
منابع مشابه
An Algebraic Approach to Multiple Context-Free Grammars
We define an algebraic structure, Paired Complete Idempotent Semirings (pcis), which are appropriate for defining a denotational semantics for multiple context-free grammars of dimension 2 (2-mcfg). We demonstrate that homomorphisms of this structure will induce wellbehaved morphisms of the grammar, and generalize the syntactic concept lattice from context-free grammars to the 2-mcfg case. We s...
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We present theoretical foundations, and a practical implementation, that makes the method of Algebraic Dynamic Programming available for Multiple ContextFree Grammars. This allows to formulate optimization problems, where the search space can be described by such grammars, in a concise manner and solutions may be obtained efficiently. This improves on the previous state of the art which require...
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The question arises from time to time what the relation is between dependency grammars (DG’s) and phrase-structure grammars. A classic paper by Gaifman [1] would appear to have laid the issue to rest, by proving that dependency grammars are a special case of context-free grammars (CFG’s). Gaifman proves that dependency grammars are equivalent to a proper subset of phrasestructure grammars, thos...
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Pregroup grammars were introduced by Lambek [20] as a new formalism of type-logical grammars. They are weakly equivalent to context-free grammars [8]. The proof in one direction uses the fact that context-free languages are closed under homomorphism and inverse homomorphism. Here we present a direct construction of a context-free grammar and a push-down automaton, equivalent to a given pregroup...
متن کاملModularized Context-Free Grammars
Given two context-free grammars (CFGs), G 1 and G 2 , the language generated by the union of the grammars is not the union of the languages generated by each grammar: L(G 1 G 2) 6 = L(G 1) L(G 2). In order to account for mod-ularity of grammars, another way of deening the meaning of grammars is needed. This paper adapts results from the semantics of logic programming languages to CFGs. We discu...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2020
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.06.005