Family Of Context-sensitive Languages Research Articles

CD Grammar Systems with Two Propagating Scattered Context Components Characterize the Family of Context Sensitive Languages

The [Formula: see text] problem asks whether propagating scattered context grammars and context sensitive grammars are equivalent. The presented paper reformulates and answers this problem in terms of CD grammar systems. More specifically, it characterizes the family of context sensitive languages by two-component CD grammar systems with propagating scattered context rules.

CD Grammar Systems with Two Propagating Scattered Context Components Characterize the Family of Context Sensitive Languages

The L(PSCG)=L(CS) problem asks whether propagating scattered context grammars and context sensitive grammars are equivalent. The presented paper reformulates and answers this problem in terms of CD grammar systems. More specifically, it characterizes the family of context sensitive languages by two-component CD grammar systems with propagating scattered context rules.

Splicing Systems over Permutation Groups of Length Two

The first theoretical model of DNA computing, called a splicing system, for the study of the generative power of deoxyribonucleic acid (DNA) in the presence of restriction enzymes and ligases was introduced by Head in 1987. Splicing systems model the recombinant behavior of double-stranded DNA (dsDNA) and the enzymes which perform operation of cutting and pasting on dsDNA. Splicing systems with finite sets of axioms and rules generate only regular languages when no additional control is assumed. With several restrictions to splicing rules, the generative power increase up to recursively enumerable languages. Algebraic structures can also be used in order to control the splicing systems. In the literature, splicing systems with additive and multiplicative valences have been investigated, and it has been shown that the family of languages generated by valence splicing systems is strictly included in the family of context-sensitive languages. This motivates the study of splicing systems over permutation groups. In this paper, we define splicing systems over permutation groups and investigate the generative power of the languages produced.

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.

On representing recursively enumerable languages by internal contextual languages

We prove that each recursively enumerable language L can be written in the form L = cut c ( L 0 ∩ R), where L 0 is an internal contextual language, R is a regular language, and cut c is the operation which for a word x removes the prefix of x to the left of the unique occurrence of ± in x. As corollaries of this result we obtain representations of recursively enumerable languages as (1) weak codings of inverse morphic images, (2) left quotients by regular languages, and (3) images of gsm mappings of internal contextual languages. These representations imply that the family of internal contextual languages, which includes the family of regular languages and is strictly included in the family of context-sensitive languages, contains languages which cannot be generated by programmed grammars with arbitrary rules and empty failure fields. The case of grammars with one-sided contexts is also briefly investigated.

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

On a Hierarchy of Slender Languages Based on Control Sets

We study slender context-sensitive languages, i.e., those containing at most a constant number of words of each length. Recently, it was proved that every slender regular language can be described by a finite union of terms of the form uv iw [9] and every slender context-free language can be described by a finite union of terms of the form uv iwx iy [4, 10]. We show a hierarchy of slender languages which is properly contained in the family of context-sensitive languages and which starts with the family of slender context-free languages, or slender regular languages. Each slender context-sensitive language in the hierarchy can be described by a finite union of terms of the form x 1y i 1x 2y i 2 ··· x ny i nx n+1.

Dynamically controlled cooperating/distributed grammar systems

Motivated by systems of artificial intelligence with distributed knowledge bases, we introduce the concept of a cooperating/distributing grammar system. In this paper, we study the effect of different conditions for starting and stopping of the components of the grammar system. If the start condition is of random context type, we obtain at most all matrix languages; if conditional or semiconditional start conditions are used, we get the family of context-sensitive languages. Time limitations have no further effect in these cases.

A formalization of sequential, parallel, and continuous rewriting

A formalization of the sequential, parallel, and continuous rewriting based on a uniform underlying concept of selective substitution grammars is presented. Each of the rewriting modes is formalized through a universal derivation restriction characterizing the rewriting in question. It is shown that whichever of the three rewriting modes is formalized, the resulting grammars generate precisely the family of context sensitive languages. Moreover, when erasing productions are allowed, these grammars generate all recursively enumerable languages.

The method of forced enumeration for nondeterministic automata

Every family of languages, recognized by nondeterministic L(n) tape-bounded Turing machines, where L(n)≥logn, is closed under complement. As a special case, the family of context-sensitive languages is closed under complement. This solves the open problem from [4].

On the generative power of regular pattern grammars

It is shown that for every recursively enumerable language L $$ \subseteq $$ ?* there exists a selective substitution grammar with a regular selector over a binary alphabet that generates L¢5, where ¢??. By requiring additional structural properties of the (already simple) selectors the language generating power is reduced in such a way that the resulting class lies strictly in between the family of EOL languages and the family of context-sensitive languages. For this class of languages some decision problems and normal forms are considered.

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 Languages Accepted in Polynomial Time

The family NP (P) of languages accepted by nondeterministic (deterministic) Turing machines operating in polynomial time is distinct from many well-known families of languages defined by tape-bounded or time-bounded Turing machines. In particular, it is shown that NP (P) is not equal to the family of context-sensitive languages, the family of languages accepted by deterministic linear bounded automata, or the family of languages accepted by deterministic Turing machines operating within exponential time.

An hierarchy between context-free and context-sensitive languages

Infinite subfamilies ℒ 1 , ℒ 2 ..., ℒ ∞ , ℒ ω of the family consisting of contextsensitive languages, are introduced such that ℒ 1 C ≠ ℒ 2 C ≠ ⋯C ≠ ℒ ∞ ℒ ω , where ℒ 1 is the family of ∈-free context-free languages, ℒ ω is the family of context-sensitive languages, and each ℒ n is an Abstract Family of Languages, i.e., closed under +, ·, U, inverse-homomorphism, ∈-free homomorphism, and intersection with regular sets. Each language of ℒ n is defined by a grammar, called a state grammar, that may be thought of as a context-free gramma with states.

A generator of context-sensitive languages

The existence of a context-sensitive grammar, G u , which acts as a “generator” of all context-sensitive languages is established. Specifically, G u has the property that for each context-sensitive language, L, there exists a regular set, R L , and an e-limited gsm, g L , such that L= g L(L(G u)∩R L) . It follows that the family of context-sensitive languages is a principal AFL. An analogous result is proved for deterministic contextsensitive languages.

Scattered context grammars

Scattered context grammars are defined and the closure properties of the family of languages generated are considered. This family of languages is contained in the family of context sensitive languages and contains all languages accepted by linear time nondeterministic Turing machines.

Writing pushdown acceptors

This paper introduces a new automaton, called a writing pushdown acceptor (abbreviated wpda), and investigates some of its properties. A wpda is essentially a two-way pushdown acceptor that can write on its input tape. A number of results about wpda are established. In particular, it is shown that o (1) Each set accepted by a wpda is accepted by some wpda that halts for all inputs. (2) The family of sets accepted by deterministic wpda forms a Boolean algebra of sets, contains the family of context sensitive languages, and properly contains the family of sets accepted by deterministic two-way pushdown acceptors. (3) The family of sets accepted by (deterministic) wpda is contained in the family of sets accepted by (deterministic) stack acceptors. In the deterministic case, the containment is shown to be proper.