Codifiable languages and the Parikh (original) (raw)
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Codifiable languages and the Parikh matrix mapping
We introduce a couple of families of codi able languages and investigate properties of these families as well as interrelationships between di erent families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codi able context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is de ned.
Codi able Languages and the Parikh Matrix Mapping 1
2015
Abstract: We introduce a couple of families of codiable languages and investigate properties of these families as well as interrelationships between dierent families. We also develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codiable context-free language. Finally, an attributed grammar that computes the values of the Parikh matrix mapping is dened.
On a classification of context-free languages
Kybernetika (Praha), 1967
The set E of strings is said to be definable (strongly definable) if there is a context-free grammar G such that E is the set of all terminal strings generated from the initial symbol (from all non terminal symbols) of G. The classification of definable and strongly definable sets in dependence on minimal number of nonterminal symbols needed for their generation is given.
On some representations of context-free languages
2020
Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown automata (for recognition). The purpose of this study is to describe some unconventional methods of description of context-free languages, namely a representation with the help of finite digraphs and with automata - generators of context-free languages. We will mainly focus on the mathematical models of these representations.
Comparisons of Parikh's condition to other conditions for context-free languages
Theoretical Computer Science, 1998
In this paper we first compare Parikh's condition to various pumping conditions ~ Bar-Hillel's pumping lemma, Ogden's condition and Bader-Moura's condition; secondly, to interchange condition; and finally, to Sokolowski's and Grant"s conditions. In order to carry out these comparisons we present some properties of Parikh's languages. The main result is the orthogonality of the previously mentioned conditions and Parikh's condition. 0 1998-Elsevier Science B.V. All rights reserved
Journal of the ACM, 1966
In this report, certain properties of context-free (CF or type 2) grammars are investigated, like that of Chomsky. In particular, questions regarding structure, possible ambiguity and relationship to finite automata are considered. The following results are presented: The language generated by a context-free grammmar is linear in a sense that is defined precisely. The requirement of unambiguity—that every sentence has a unique phrase structure—weakens the grammar in the sense that there exists a CF language that cannot be generated unambiguously by a CF grammar. The result that not every CF language is a finite automaton (FA) language is improved in the following way. There exists a CF language L such that for any L′ ⊆ L , if L′ is FA, an L″ ⊆ L can be found such that L″ is also FA, L′ ⊆ L″ and L″ contains infinitely many sentences not in L′ . A type of grammar is defined that is intermediate between type 1 and type 2 grammars. It is shown that this type of grammar is essentially st...
C-grammars and tree-codifications
Journal of Computer and System Sciences, 1977
The paper introduces two new concepts, namely C-grammar and tree-codification, based on the theory of formal languages, by means of which we try to exhibit a new aspect of general coding theory. Both linear algebraic coding and convolutional coding are presented here as a particular case of tree-codification. The main result of the paper gathers the two new concepts mentioned above. Thus, Theorem 10 establishes that to each tree-codification corresponds a C-grammar in which that tree-codification can be achieved, and vice versa. Some examples are given justifying both the concepts and the assertion that any algebraic coding (linear or convolutional) can be looked upon as a treecodification.