Contextual Grammars Research Articles

Contextual array grammars and array P systems

Contextual array grammars, with selectors not having empty cells, are considered. A P system model, called contextual array P system, that makes use of array objects and contextual array rules, is introduced and its generative power for the description of picture arrays is examined. A main result of the paper is that there is a proper infinite hierarchy with respect to the classes of languages described by contextual array P systems. Such a hierarchy holds as well in the case when the selector is also endowed with the #?sensing ability.

Necessary conditions for subclasses of random context languages

Random context grammars belong to the class of context-free grammars with regulated rewriting. Their productions depend on context that may be randomly distributed in a sentential form. Context is classified as either permitting or forbidding, where permitting context enables the application of a production and forbidding context inhibits it. We have proven a pumping lemma for random permitting context languages and a shrinking lemma for random forbidding context languages. We now present new necessary conditions for both these classes of languages and illustrate them with examples. We also present and illustrate a new necessary condition for context-free languages.

On the Trade-off Between Ambiguity and Complexity in Contextual Languages

Contextual grammars are introduced by Solomon Marcus in 1969 based on the fundamental concept of descriptive linguistics of insertion of strings in given contexts. Internal contextual grammars are introduced by Paun and Nguyen in 1980. For contextual grammars several descriptional complexity measures and levels of ambiguity have been defined. In this paper, we analyze the trade-off between ambiguity and complexity of languages generated by internal contextual grammars. The notion of a pseudo inherently ambiguous language with respect to two complexity measures is introduced and investigated. These languages can be generated by unambiguous grammars which are minimal with respect to one measure and ambiguous if they are minimal with respect to the other measure. An open problem from [15] is solved in this framework.

Left Random Context ET0L Grammars

Consider ET0L grammars. Modify them such that a set of permitting symbols and a set of forbidding symbols are attached to each of their rules, just like in random context grammars. A rule like this can rewrite a symbol if each of its permitting symbols occurs to the left of the symbol to be rewritten in the current sentential form while each of its forbidding symbols does not occur there. ET0L grammars modified in this way are referred to as left random context ET0L grammars, and they represent the principal subject of the investigation in this paper. We prove that these grammars characterize the family of recursively enumerable languages, and without erasing rules, they characterize the family of context-sensitive languages. We also introduce a variety of special cases of these grammars and establish their generative power. In the conclusion, we put all the achieved results into the context of formal language theory as a whole and formulate several open questions.

On external contextual grammars with subregular selection languages

In this paper, we study the power of external contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families Fn which are obtained by restriction to n states or nonterminals or productions or symbols to accept or to generate regular languages, we obtain four infinite hierarchies of the corresponding families of languages generated by external contextual grammars with selection languages in Fn. Moreover, we give some results on the power of external contextual grammars with regular commutative, regular circular, definite, suffix-free, ordered, combinational, nilpotent, and union-free selection languages.

Nonterminal complexity of one-sided random context grammars

In the present paper, we study the nonterminal complexity of one-sided random context grammars. More specifically, we prove that every recursively enumerable language can be generated by a one-sided random context grammar with no more than ten nonterminals. An analogical result holds for thirteen nonterminals in terms of these grammars with the set of left random context rules coinciding with the set of right random context rules. Furthermore, we introduce the notion of a right random context nonterminal, defined as a nonterminal that appears on the left-hand side of a right random context rule. We demonstrate how to convert any one-sided random context grammar G to an equivalent one-sided random context grammar H with two right random context nonterminals. An analogical conversion is given in terms of (1) propagating one-sided random context grammars and (2) left random context nonterminals. In the conclusion, two open problems are stated.

On Subregular Selection Languages in Internal Contextual Grammars.

In this paper, we study the power of internal contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families ${\cal F}_n$ which are obtained by restriction to $n$ states, nonterminals, productions, or symbols to accept or to generate a regular language, we obtain four infinite hierarchies of the corresponding families of languages generated by internal contextual grammars with selection languages in ${\cal F}_n$. Moreover, we present some results on the power of internal contextual grammars with finite, monoidal, nilpotent, combinational, definite, ordered, regular commutative, regular circular, regular suffix-closed, and union-free selection languages.

D-Primitive Words and Contextual Grammars

nite alphabet having at least two letters. In this paper, we prove the language D(1) of all non-overlapping (d-primitive) words, which is a proper subset of Q, cannot be generated by Marcus contextual grammars both in the external mode and in the internal mode.

Assessment of Grammatical Competence Based on Authentic Texts

This study illustrates how alternative assessment could be made observing both recognition and production skills of the participants who were English language students at the ELT department, University of Cukurova. In an English Contextual Grammar course, news articles were used as lesson material during the first term of the 2009-2010 academic year, and a midterm and a progress test were administered following a rather unconventional set of procedures. The study displays such procedures aiming to show how an effective and truly learner-centered approach to assessment of grammatical competence can be embraced yielding an alternative type to the conventional assessment methods in the field of English language teaching (ELT) through the use of target language news articles; it also reflects students’ perceptions about the alternative method presented in this study.

One-sided random context grammars

The notion of a one-sided random context grammar is defined as a context-free-based regulated grammar, in which a set of permitting symbols and a set of forbidding symbols are attached to every rule, and its set of rules is divided into the set of left random context rules and the set of right random context rules. A left random context rule can rewrite a nonterminal if each of its permitting symbols occurs to the left of the rewritten symbol in the current sentential form while each of its forbidding symbols does not occur there. A right random context rule is applied analogically except that the symbols are examined to the right of the rewritten symbol. The paper demonstrates that without erasing rules, one-sided random context grammars characterize the family of context-sensitive languages, and with erasing rules, these grammars characterize the family of recursively enumerable languages. In fact, these characterization results hold even if the set of left random context rules coincides with the set of right random context rules. Several special cases of these grammars are considered, and their generative power is established. In its conclusion, some important open problems are suggested to study in the future.

Scattered Context Grammars Generating Sentences Followed by Derivation Trees

Propagating scattered context grammars are used to generate sentences of languages defined by scatterd context grammars followed by the strings corresponding to the derivation trees. It is proved that for every language defined by a scattered context grammar, there exists a propagating scattered context grammar whose language consists of original language sentences followed by strings representing their derivation trees.

Cooperating Distributed Grammar Systems with Random Context Grammars as Components

In this paper, we discuss cooperating distributed grammar systems where components are (variants of) random context grammars. We give an overview of known results and open problems, and prove some further results.

Scattered context grammars generate any recursively enumerable language with two nonterminals

By showing that two nonterminals are sufficient, we present the optimal lower bound on the number of nonterminals of scattered context grammars being able to generate any recursively enumerable language.

Bounded Number of Parallel Productions in Scattered Context Grammars with Three Nonterminals

Scattered context grammars with three nonterminals are known to be computationally complete. So far, however, it was an open problem whether the number of parallel productions can be bounded along with three nonterminals. In this paper, we prove that every recursively enumerable language is generated by a scattered context grammar with three nonterminals and five parallel productions, each of which simultaneously rewrites no more than nine nonterminals.

Descriptional Complexity of Three-Nonterminal Scattered Context Grammars: An Improvement

Recently, it has been shown that every recursively enumerable language can be generated by a scattered context grammar with no more than three nonterminals. However, in that construction, the maximal number of nonterminals simultaneously rewritten during a derivation step depends on many factors, such as the cardinality of the alphabet of the generated language and the structure of the generated language itself. This paper improves the result by showing that the maximal number of nonterminals simultaneously rewritten during any derivation step can be limited by a small constant regardless of other factors.

On Insertion Grammars with Maximum Parallel Derivation

In this paper we investigate insertion grammars and explore their capacity to generate words parallelly by introducing parallel derivation (where more than one rule can be applied to the string in parallel) and maximum parallel derivation (where as many rules as possible are applied to the string in parallel). We compare the generative power of these grammars with context sensitive and context free grammars and with different variants of contextual grammars. We apply these grammars to syllabification in Romanian and provide arguments that they can also be used in a cognitive perspective.

An infinite hierarchy of language families generated by scattered context grammars with n-limited derivations

This paper introduces scattered context grammars without erasing productions, in which an application of a production always occurs within the first n nonterminals of the current sentential form. It demonstrates that this restriction gives rise to an infinite hierarchy of language families each of which is properly included in the family of context-sensitive languages. In addition, it proves analogous results for unordered scattered context grammars. Some consequences of these results are derived and open problems formulated.

Scattered context grammars that erase nonterminals in a generalized k-limited way

A scattered context grammar erases nonterminals in a generalized k-limited way in a successful derivation, where k is a positive integer, if in every sentential form of a derivation, each of its substrings consisting of nonterminals from which the grammar derives empty strings is of length k or less. This paper demonstrates that if a scattered context grammar generates its sentences in this way, it can be converted to a scattered context grammar without erasing productions; in general, however, this is not possible.

On the descriptional complexity of scattered context grammars

This paper proves that every recursively enumerable language is generated by a scattered context grammar with no more than four nonterminals and three non-context-free productions. In its conclusion, it gives an overview of the results and open problems concerning scattered context grammars and languages.

Leftmost derivations of propagating scattered context grammars: a new proof

Automata, Logic and Semantics In 1973, V. Virkkunen proved that propagating scattered context grammars which use leftmost derivations are as powerful as context-sensitive grammars. This paper brings a significantly simplified proof of this result.