Left-forbidding cooperating distributed grammar systems

Abstract

a b s t r a c tA left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems with left-forbidding grammars as components and gives some new characterizations of language families of the Chomsky hierarchy. In addition, it also proves that twelve nonterminals are enough for cooperating distributed grammar systems working in the terminal derivation mode with two left-forbidding components (including erasing productions) to characterize the family of recursively enumerable languages.

Left Random Context ET0L Grammars

“…From this viewpoint, the present study thus contributes to the previous investigation of left versions of random context grammars (see [6,11,16]). Alternatively, LRC-ET0L grammars can be also seen as another context-conditional variant of ET0L grammars (see [14,23,25,27], Chapter 8 in [9], and Section 4.2 in [15]).…”

“…As a result, LF-EP0L grammars are more powerful than ordinary E0L grammars. This is in contrast to left forbidding contextfree grammars (see [11,16]), which characterize only the family of context-free languages (see Theorem 1 in [11]). …”

Cooperating Distributed Grammar Systems with Random Context Grammars as Components

“…First, let us recall that CF ⊂ PER λ = PER ⊂ RC ⊂ CS, CF ⊂ FOR λ ⊂ RC λ = RE, and CF ⊂ FOR ⊂ RC [7,15,16]. In addition, in the case of left-forbidding grammars FOR λ = FOR = CF [8], i.e., left-forbidding languages coincide with context-free languages. However, it is of interest to compare this with results concerning context-free CD grammar systems and left-forbidding CD grammar systems (below), where it turns out that although the components are of the same power, left-forbidding CD grammar systems are more powerful than context-free CD grammar systems.…”

“…A left-random context grammar [4,8] is a quadruple G = (N, T, P, S), where N, T , P, and S are the same as in random context grammars. For u, v ∈ V * and a production (A → x, Per, For) ∈ P, we define the relation uAv ⇒ uxv provided that Per ⊆ alph (u) and alph(u) ∩ For = / 0.…”

“…However, it might be possible to check for that property by using some mechanisms of CD grammar systems instead. The cases of CD grammar systems with left-permitting and left-forbidding grammars as components are studied in [4] and [8], respectively. In these cases, only definition (1) of the direct derivation step is considered.…”