The theory of languages (original) (raw)
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Oxford Handbooks Online, 2005
This article introduces the preliminaries of classical formal language theory. It outlines the main classes of grammars as language-generating devices and automata as language-recognizing devices. It offers a number of definitions and examples and presents the basic results. It classifies grammar according to several criteria. The most widespread one is the form of their productions. This article presents a systematic study of the common properties of language families has led to the theory of abstract families of languages. It shows that a context-free grammar generates not only a set of strings, but a set of trees too: each one of the trees is associated with a string and illustrates the way this string is derived in the grammar.
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.
2016
These lecture notes present some basic notions and results on Automata Theory, Formal Languages Theory, Computability Theory, and Parsing Theory. I prepared these notes for a course on Automata, Languages, and Translators which I am teaching at the University of Roma Tor Vergata. More material on these topics and on parsing techniques for context-free languages can be found in standard textbooks such as [1, 8, 9]. The reader is encouraged to look at those books. A theorem denoted by the triple k.m.n is in Chapter k and Section m, and within that section it is identified by the number n. Analogous numbering system is used for algorithms, corollaries, definitions, examples, exercises, figures, and remarks. We use 'iff' to mean 'if and only if'. Many thanks to my colleagues of the Department of Informatics, Systems, and Production of the University of Roma Tor Vergata. I am also grateful to my students and co-workers and, in particular, to
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...
Symmetry
A binary grammar is a relational grammar with two nonterminal alphabets, two terminal alphabets, a set of pairs of productions and the pair of the initial nonterminals that generates the binary relation, i.e., the set of pairs of strings over the terminal alphabets. This paper investigates the binary context-free grammars as mutually controlled grammars: two context-free grammars generate strings imposing restrictions on selecting production rules to be applied in derivations. The paper shows that binary context-free grammars can generate matrix languages whereas binary regular and linear grammars have the same power as Chomskyan regular and linear grammars.
On permutative grammars generating context-free languages
BIT, 1985
A grammar is said to be permutative if it has permutation productions of the form AB --, BA in addition to context-free productions. Szilard languages and label languages are studied as examples of languages generable by permutative grammars. Particularly, sufficient conditions for a permutative grammar to generate a context-free language are studied.