Review of "Lakshmanan Kuppusamy; A note on ambiguity of internal contextual grammars. Theoret. Comput. Sci. 369 (2006), no. 1-3, 436–441"

An internal contextual grammar (ICG) G=(V,A,(Si,Ci)ni=1) (n≥1) consists of an alphabet V, a finite set A⊆V∗ of axioms, sets of selectors Si⊆V∗, and finite sets of context Ci⊆V∗×V∗ (1≤i≤n). Then x⇒y (i.e., x derives y) iff x=x1x2x3, y=x1ux2vx3 for x1,x2,x3∈V∗, x2∈Si, (u,v)∈Ci for some 1≤i≤n. The language generated by this grammar is {x∈V∗∣w⇒∗x,w∈A}, where ⇒∗ is the reflexive and transitive closure of ⇒. Requiring that the languages Si belong to a family F—frequently restricted to the finite languages or to the regular languages—results in families of internal contextual languages parameterized by F. For a derivation δ of G, the sequence of axioms and contexts [and selectors, respectively] used in δ is called the [complete] control sequence of δ. G is 0-ambiguous if there are two different axioms leading to the same word. And G is 1-ambiguous [2-ambiguous] if there are two derivations of a word having different unordered [complete] control sequences. The main results are: (a) there are inherently 1-ambiguous languages generated by ICGs with arbitrary choice that are 0-ambiguous with respect to finite choice, (b) there are inherently 2-ambiguous languages generated by ICGs with arbitrary choice that are 1-ambiguous with respect to regular choice, and (c) there are inherently 2-ambiguous languages with respect to depth-first ICGs with arbitrary choice that are 1-ambiguous with respect to finite choice

A new automata for parsing semi-bracketed contextual grammars

Bracketed and fully bracketed contextual grammars were introduced to bring the concept of tree structure to the strings by associating a pair of parentheses to the adjoined contexts in the derivation. But these grammars fail to generate the basic non-context free languages thus unable to provide a syntactical representation to natural languages. To overcome this problem, a new variant called semi-bracketed contextual grammar was introduced recently, where the selectors can also be non-minimally Dyck covered strings. The membership problem for the new variant is left unsolved. In this paper, we propose a parsing algorithm (for non-projected strings) of maximal semi-bracketed contextual grammars. In this process, we introduce a new automaton called k-queue Self Modifying Weighted Automata (k-quSMWA)

P Systems with Minimal Insertion and Deletion

In this paper we consider insertion-deletion P systems with priority of deletion over the insertion.We show that such systems with one symbol context-free insertion and deletion rules are able to generate PsRE. If one-symbol one-sided context is added to insertion or deletion rules but no priority is considered, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important and in its absence the corresponding class of P systems is strictly included in MAT

Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L( ) ∩D), where is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.Ministerio de Educación y Ciencia TIN2006-1342

Array P Systems and t−Communication

The two areas of grammar systems and P systems, which have provided interesting computational models in the study of formal string language theory have been in the recent past effectively linked in [4] by incorporating into P systems, a communication mode called t−mode of cooperating distributed grammar systems. On the other hand cooperating array grammar systems [5]and array P systems [1] have been developed in the context of two-dimensional picture description. In this paper, motivated by the study of [4], these two systems are studied by linking them through the t−communication mode, thus bringing out the picture description power of these systems