On some classes of contextual grammars
01 Feb 2003-International Journal of Computer Mathematics (Taylor & Francis Group)-Vol. 80, Iss: 2, pp 151-164
TL;DR: A restricted version of depth-first contextual grammars, which depends on length of the inserting contexts, is considered, which gives a solution to the open problem P14 listed in [8].
Abstract: In this paper, we introduce some new variants of contextual grammars and investigate their generative power. We'consider a restricted version of depth-first contextual grammars, which depends on length of the inserting contexts. Using this variant, we give a solution to the open problem P14 listed in [8]. We also introduce random context contextual grammars and compare its generative power with the families IC , ICC , EC , ECC , TC . Time-varying contextual grammars are introduced which resemble time-varying grammars. We compare the generative power of this variant with the families of internal, external, total, matrix, and programmed contextual grammars.
Citations
More filters
Journal Article•
TL;DR: The hierarchy of language families of contextual languages which is obtained by the use of nilpotent, combinational, definite, regular suffix closed, and regular commutative languages as choice languages is determined.
Abstract: We discuss external contextual grammars with choice where the choice language belongs to a family of subregular languages. We determine the hierarchy of language families of contextual languages which is obtained by the use of nilpotent, combinational, definite, regular suffix closed, and regular commutative languages as choice languages.
9 citations
TL;DR: It is shown that the three basic non-context-free constructions in natural languages can be realized upon using all such variants, and that the membership problem for the family of absorbing right context contextual languages is decidable by a polynomial time algorithm.
Abstract: Contextual grammars were introduced by Marcus (Revue Roumaine de Mathematiques Pures et Appliquees 14:525–1534, 1969) based on the basic phenomenon in descriptive linguistics, that of acceptance of a word by a context or conversely. In this paper we present some results which are of interest for the potential application of contextual grammars to natural languages. We introduce some classes of internal contextual grammars, viz. maximum depth-first grammars, maximum lengthwise depth-first grammars, and absorbing right context grammars. The study of these classes is motivated by their potential linguistic relevance for natural languages. In particular, we analyze these variants with respect to the properties of mildly context-sensitive languages. With this aim, we first show that the three basic non-context-free constructions in natural languages can be realized upon using all such variants. Secondly, we state that the membership problem for the family of absorbing right context contextual languages is decidable by a polynomial time algorithm. Finally, we show that absorbing right context grammars produce semilinear languages only. Besides, we show that the non-marked duplication language can be generated by absorbing right context grammars, which is a unique feature not present in any other variant of contextual grammars.
5 citations
26 Jun 2006
TL;DR: It is shown that the three basic non-context-free constructions in natural languages can be realized upon using these variants and the family of languages generated by end-marked maximal depth-first grammars contains non-semilinear languages.
Abstract: In this paper, we present a few results which are of interest for the potential application of contextual grammars to natural languages We introduce two new classes of internal contextual grammars, called end-marked maximal depth-first and inner end-marked maximal depth-first contextual grammars We analyze the new variants with respect to the basic properties of the mildly context sensitive languages With this aim, we show that (i) the three basic non-context-free constructions in natural languages can be realized upon using these variants, (ii) the membership problem for these family of languages is decidable in polynomial time algorithm, (iii) the family of languages generated by end-marked maximal depth-first grammars contains non-semilinear languages We also solve the following open problem addressed in [3] and [1]: whether the families of languages generated by maximal depth-first and maximal local contextual grammars are semilinear or not?
2 citations
Cites background from "On some classes of contextual gramm..."
...Lengthwise depth-first grammars, are the restricted versions of depth-first grammars, introduced in [2], where at each derivation, the selector for the next derivation must contain the context u or v (introduced in the previous derivation) whichever is of maximal length....
[...]
Journal Article•
TL;DR: A new class of fully bracketed contextual grammars is introduced, called the semi-bracketed contextual Grammars, where the selectors can also be non-minimally Dyck covered language and the tree structure to the derived strings is still preserved in this variant.
Abstract: Bracketed and fully bracketed contextual grammars were introduced to bring the concept of a tree structure to the strings by associating a pair of parentheses to the adjoined contexts in the derivation. In this paper, we show that these grammars fail to generate all the basic non-context-free languages, thus cannot be a syntactical model for natural languages. To overcome this failure, we introduce a new class of fully bracketed contextual grammars, called the semi-bracketed contextual grammars, where the selectors can also be non-minimally Dyck covered language. We see that the tree structure to the derived strings is still preserved in this variant. when this new grammar is combined with the maximality feature, the generative power of these grammars is increased to the extend of covering the family of context-free languages and some basic non-context-free languages, thus possessing many properties of the so called `MCS formalism'.
1 citations
Cites background from "On some classes of contextual gramm..."
...Later on, many variants of contextual grammars were introduced and we refer to [5],[9],[10],[20] for some of them....
[...]
01 Jan 2004
TL;DR: The decade of the 1950s has witnessed great steps forward in the systematic investigation of natural languages by means of mathematical tools as mentioned in this paper, with the publication of Chomsky's pioneering book [5] in 1957, the generative approach emerged, while, at the same time, research done within the Russian school of Mathematics gave a new start in the development of analytical mathematical models of language.
Abstract: The decade of the 1950s has witnessed great steps forward in the systematic investigation of natural languages by means of mathematical tools. With the publication of Chomsky’s pioneering book [5] in 1957, the generative approach emerged, while, at the same time, research done within the Russian school of Mathematics gave a new start in the development of analytical mathematical models of language.
1 citations
References
More filters
01 Apr 1997
TL;DR: This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field.
Abstract: The theory of formal languages is the oldest and most fundamental area of theoretical computer science. It has served as a basis of formal modeling from the early stages of programming languages to the recent beginnings of DNA computing. This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field. Best specialists of various subareas, altogether 50 in number, are among the authors. The maturity of the field makes it possible to include a historical perspective in many presentations. The individual chapters can be studied independently, both as a text and as a source of reference. The Handbook is an invaluable aid for advanced students and specialists in theoretical computer science and related areas in mathematics, linguistics, and biology.
1,915 citations
Book•
01 Jan 1997
TL;DR: 1. Origin and Motivation, Formal Language Theory Prerequisites, and A Generalization: n-Contextual Grammars.
Abstract: 1. Origin and Motivation. 2. Formal Language Theory Prerequisites. 3. Contexts (Adjoining) Everywhere. 4. Basic Classes of Contextual Grammars. 5. Generative Capacity. 6. Language Theoretic Properties. 7. Linguistically Relevant Properties. 8. Grammars with Restricted Selection. 9. Grammars with Minimal/Maximal Use of Selectors. 10. Variants of Contextual Grammars. 11. Two-Level Contextual Grammars. 12. Regulated Contextual Grammars. 13. A Generalization: n-Contextual Grammars. 14. A Dual Model: Insertion Grammars. 15. Further Topics. 16. Open Problems and Research Topics. Bibliography. Subject Index.
179 citations
TL;DR: It is shown that all the three basic non-context-free constructions in natural languages, that is, multiple agreements, crossed agreements, and duplication, can be realized using this type of grammars and that these languages are parsable in polynomial time.
25 citations
"On some classes of contextual gramm..." refers background in this paper
...Depth-first contextual grammars were introduced in [5], and a restrictive variant of this class of contextual grammars was investigated in [7]....
[...]
Journal Article•
TL;DR: It is proved that each recursively enumerable language L can be written in the form L — cutd(L' fl R), where L' is a language generated by a one-sided internal contextual grammar witli context-free choice, R is a regular language, and cutd is the operation which removes the prefix bounded by the special symbol d.
Abstract: In this paper we prove that each recursively enumerable language L can be written in the form L — cutd(L' fl R), where L' is a language generated by a one-sided internal contextual grammar witli context-free choice, R is a regular language, and cutd is the operation which removes the prefix bounded by the special symbol d, which appears exactly once in the strings for which cutd is defined. However, the context-free choice sets are always deterministic linear languages of a very simple form. Similar representations can be obtained using one-sided contextual grammars with finite choice and with erased or with erasing contexts. K e y w o r d s . Formal languages, contextual grammars, recursively enumerable languages.
9 citations
"On some classes of contextual gramm..." refers methods in this paper
...A characterization of recursively enumerable languages using one-sided internal contextual grammars with context-free choice is given in [3]....
[...]
Book•
01 May 1994
TL;DR: Two normal form theorems for contextual grammars with regular choice are given, one concerning the (dyna mic) use of productions in derivations when a contextual grammar is executed in the external mode and the other concerned the (static) relationships between the productions.
Abstract: Two normal form theorems for contextual grammars with regular choice are given. The first one concerns the (dyna mic) use of productions in derivations when a contextual grammar is executed in the external mode. The second one concerns the (static) relationships between the productions and so it applies to both the external and the internal execution of contextual gram mars. Using the first normal form, a new (more elegant) proof of the linearity of the external languages of contextual grammars with regular choice is given.
6 citations