Family Of Context-free Languages Research Articles

Computational Power of Static Watson-Crick Context-free Grammars

Sticker system is a computer model which is coded with single and double-stranded molecules of DNA; meanwhile, Watson-Crick automata is the automata counterpart of the sticker system representing the biological properties of DNA. Both are the modelings of DNA molecules in DNA computing which use the feature of Watson-Crick complementarity. Formerly, Watson-Crick grammars which are classified into three classes have been introduced [1]. In this research, a grammar counterpart of sticker systems that uses the rule as in context-free grammar is introduced, known as a static Watson-Crick context-free grammar. The research finding on the computational power of these grammar shows that the family of context-free languages is strictly included in the family of static Watson-Crick context-free languages; the static Watson-Crick context-free grammars can generate non context-free languages; the family of Watson-Crick context-free languages is included in the family of static Watson-Crick context-free languages which are presented in terms of their hierarchy.

On Succinct Description of Certain Context-Free Languages by Ins-Del and Matrix Ins-Del Systems

In this paper, we introduce some basic measures for insertion-deletion system and matrix insertion-deletion system. These measures are based on the number of variables, the number of productions and the number of symbols in a grammar. We show that with respect to these measures, both the systems are more succinct over context-free grammars in representing certain families of context-free languages.

Controlled finite automata

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.

Generalized one-sided forbidding grammars

In generalized one-sided forbidding grammars (GOFGs), each context-free rule has associated a finite set of forbidding strings, and the set of rules is divided into the sets of left and right forbidding rules. A left forbidding rule can rewrite a nonterminal if each of its forbidding strings is absent to the left of the rewritten symbol. A right forbidding rule is applied analogically. Apart from this, they work like any generalized forbidding grammar. This paper proves the following three results. (1) GOFGs where each forbidding string consists of at most two symbols characterize the family of recursively enumerable languages. (2) GOFGs where the rules in one of the two sets of rules contain only ordinary context-free rules without any forbidding strings characterize the family of context-free languages. (3) GOFGs with the set of left forbidding rules coinciding with the set of right forbidding rules characterize the family of context-free languages.

One-sided forbidding grammars and selective substitution grammars

In one-sided forbidding grammars, the set of rules is divided into the set of left forbidding rules and the set of right forbidding rules. A left forbidding rule can rewrite a non-terminal if each of its forbidding symbols is absent to the left of the rewritten symbol in the current sentential form, while a right forbidding rule is applied analogically except that this absence is verified to the right. Apart from this, they work like ordinary forbidding grammars. As its main result, this paper proves that one-sided forbidding grammars are equivalent to selective substitution grammars. This equivalence is established in terms of grammars with and without erasing rules. Furthermore, this paper proves that one-sided forbidding grammars in which the set of left forbidding rules coincides with the set of right forbidding rules characterize the family of context-free languages. In the conclusion, the significance of the achieved results is discussed.

CONTEXT-FREE GRAMMARS WITH LINKED NONTERMINALS

We introduce a new type of finite copying parallel rewriting system, i. e., grammars with linked nonterminals, which extend the generative capacity of context-free grammars. They can be thought of as having sentential forms where some instances of a nonterminal may be linked. The context-free-like productions replace a nonterminal together with its connected instances. New links are only established between symbols of the derived subforms. A natural limitation is to bound the degree of synchronous rewriting. We present an infinite degree hierarchy of separated language families with the property that degree one characterizes the family of regular and degree two the family of context-free languages. Furthermore, the hierarchy is a refinement of the known hierarchy of finite copying rewriting systems. Several closure properties known from equivalent systems are summarized.

EXTENDED FINITE AUTOMATA AND WORD PROBLEMS

This paper considers extended finite automata over monoids, in the sense of Dassow and Mitrana. We show that the family of languages accepted by extended finite automata over a monoid K is controlled by the word problem of K in a precisely stated manner. We also point out a critical error in the proof of the main result in the paper by Dassow and Mitrana. However as one consequence of our approach, by analyzing a certain word problem, we obtain a complete proof of this result, namely that the family of languages accepted by extended finite automata over the free group of rank two is exactly the family of context-free languages. We further deduce that along with the free group of rank two, the only finitely generated groups with this property are precisely the groups that have a nonabelian free subgroup of finite index.

Context-Sensitive String Languages and Recognizable Picture Languages

The theorem stating that the family of frontiers of recognizable tree languages is exactly the family of context-free languages (see J. Mezei and J. B. Wright, 1967, Inform. and Comput. 11 , 3–29), is a basic result in the theory of formal languages. In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of context-sensitive languages

Context free closed families of languages

We study context free closed families of languages, that is families L verifying the equation CF o L = L where CF denotes the family of context free languages and o is the substitution operation. Call a family L a context free AFL if it is both context free closed and a rational cone. The families CF and RE (of recursively enumerable languages) have this property. We show that the class of context free AFL's is properly contained into that of full AFL's. Moreover the context free AFL generated by a family L, is given by the formula L Δ = CF o LΓ where LΓ denotes the rational cone generated by L. Using this result we establish the remarkable inclusion (L o M)Δ ⊃ LΔ o MΔ holding for all families L and M as well as the equality LΔ = CF o LΓ LΓ being the full AFL generated by L.

Automata and languages generalized to ω-continuous semirings

We generalize the following two language- and automata-theoretic results to ω-continuous semirings. • (i) The family of languages accepted by finite automata is the smallest class containing all finite languages and closed under union, product and star (Kleene's Theorem). • (ii) The family of languages accepted by pushdown automata is the family ofcontext-free languages.

On the equivalence problem of compositions of morphisms and inverse morphisms on context-free languages

It is shown that the equivalence problem of H −1 H on the family of context-free languages is decidable, where H is the family of morphisms and H −1 is the family of inverse morphisms.

Formes de langages et de grammaires

This paper is devoted to the study of context-free languages over infinite alphabets. This work can be viewed as a new attempt to study families of grammars, replacing the usual "grammar forms" and giving a new point of view on these questions. A language over an infinite alphabet or I-language appears as being a model for a family of usual languages; an interpretation is an homomorphism from the infinite alphabet to any finite alphabet. Using this notion of interpretation we can associate to each family of I-languages an image, called its shadow, which is a family of usual languages. The closure properties of families, generalizing to infinite alphabets the family of context-free languages, lead to define rational transductions between infinite alphabets or I-transductions, and then, families of I-languages closed under I-transductions, or I-cones. We study here relations between the closure properties of a family of I-languages and these of its shadow. As a result, we obtain that any union closed rational cone of context-free languages, principal or not, is the shadow of a principal I-cone. This work leads to new results about the classical theory of context-free languages. For instance, we prove that any principal rational cone of context-free languages can be generated by a context-free language, whose grammar has only 6 variables. This work also leads to more general considerations about the adequacy of some generating devices to the generated languages. It appears that the context-free grammars are fair, in a sense that we define, for generating context-free languages but that non-expansive context-free grammars are not for generating non-expansive context-free languages. This point of view raises a number of questions.

On String Pattern Matching: A New Model with a Polynomial Time Algorithm

A polynomial time algorithm is presented for string pattern matching. Earley’s parsing algorithm is adapted for context-free patterns and is extended to allow the augmentation of the immediate assignment operation of SNOBOL4 and a powerful descriptive operator not previously implemented, set complement. Canonical pattern definition systems are defined to describe patterns for which our algorithm will perform pattern matching. The languages generated by such systems are called extended context-free languages, and are shown to properly contain the family of context-free languages and all families of k-intersection languages which have been shown to establish an infinite hierarchy between the family of context-free languages and the family of context-sensitive languages. It is also shown that for an alphabet of one character, the immediate assignment operator cannot be expressed in terms of the complement operator. Some results on the closure properties and unsolvable problems for this new family are also sh...

On equivalence of grammars through transformation trees

One approach to solving the equivalence problem for certain families of context free languages is through the use of ‘transformation trees’. We explore this approach in general. The methods developed provide a clear and complete proof of the decidability of the equivalence problem for ‘simple’ languages. It is shown how to decide the equivalence problem for two deterministic context free languages, one of which is simple.

Context-dependent L forms

The notions of an EIL form and its interpretations are introduced. The resulting families of L systems and languages are studied from a number of different points of view. Some of the main results are: the family of context-free languages is generated by an EIL form (contrary to the earlier results concerning context-free L forms) and, as regards reducibility in the amount of context, EIL forms lie between IL and EIL systems.

On the generative capacity of context-free matrix forms

This paper deals with the concepts of a matrix form and strict interpretation. By a matrix form we mean a context-free matrix grammar. Via an interpretation mechanism it generates a family of structurally related grammars and these generate a family of languages. We study here the properties of matrix forms as generators for the families of regular, linear and context-free languages. It is for instance shown that an arbitrary matrix form with only one nonterminal symbol does not generate the family of context-free languages if it contains a matrix with at least two productions.

On non context-free grammar forms

A grammar formF defines via a so-calledinterpretation mechanism, a family of languages (F). In this paper we establish that for many grammar formsF, (the family of context-free languages) implies (F)= RE (the family of recursively enumerable sets). We conjecture that this is also true in general. Because of this, it seems necessary to use restricted interpretations for non context-free grammar forms, a form giving then rise to a family We compare the obvious alternatives for restricting interpretations and focus attention on two promising alternatives, Q (F) and st(F) and their combination Q, st(F). Using st-interpretations, surprising families can be generated and strong normal form results can be obtained. Closure results and decidability results are also given. UnderQ, st-interpretation, it is possible to characterize a number of well-known families of languages between CF and RE, including the families of EOL, ETOL, matrix and scattered context languages.

Le cylindre des langages linéaires

Define a cylinder to be a family of languages which is closed under inverse homomorphisms and intersection with regular sets. A number of well-known families of languages are cylinders: —CFL, the family of context-free languages, is a principal cylinder, i.e. the smallest cylinder containing a languageLO described in [6]. —the family of deterministic context-free languages is proved to be a nonprincipal cylinder in [7]. —the family of unambiguous context-free languages is a cylinder: to prove that it is not principal seems to be a very hard problem.

The structure of context-free grammatical families

Let ℒCI be the family of context-free languages. Two characterization theorems are given for (context-free) grammatical families. The first says that the class of grammatical families not ℒCF is the smallest collection of sets of languages which contains the trivial ones and is closed under a union operator ∨, a concatenation operator ⊙, and ℐ, where ℐ is a ternary operator involving substitution into linear languages. The second asserts that the collection of all nontrivial grammatical families not ℒCF is the smallest collection of sets of languages which contains the family of regular sets, and is closed under ∨, ⊙, ℐ, and the full AFL operator ℱ^.

Interactive languages

The notion of interactive languages generated by interactions between two phrase-structure grammars are proposed and discussed. It is shown that a family of context-free languages does not include a family of interactive languages between two regular grammars and vice versa. The family of interactive languages, however, is not closed under any of the ordinary operations. The paper also includes discussions about n -cyclic interactive languages among n grammars.