Simple restriction in context-free rewriting

Abstract

Many rewriting systems with context-free productions and with controlled derivations have been studied. On one hand, these systems preserve the simplicity of applications of context-free productions and, on the other hand, they increase the generative power to cover more aspects of natural and programming languages. However, with λ-productions, many of these systems are computationally complete. It gives rise to a natural question of what are the simplest restrictions of the derivation process of context-free grammars to obtain the universal power. In this paper, we present such a simple restriction introducing so-called restricted context-free rewriting systems. These systems are contextfree grammars with a function assigning a nonterminal coupled with + or − to each nonterminal. A production is applicable if it is applicable as a context-free production and if the symbol assigned to the left-hand side of the production is coupled with +, then this symbol has to appear in the sentential form, while if coupled with −, it must not appear in the sentential form. This restriction is simpler than most of the other restrictions, since the context conditions are assigned to nonterminals, not to productions, and their type is the simplest possible -a nonterminal.

A Pumping Lemma for Permitting Semi-Conditional Languages

“…It turned out that RCGs have equal power to that of Turing machines (see e.g. [3]), thus recently a restricted variant of them was introduced and investigated [15]. In these grammars the permitting and forbidding sets are associated to the nonterminals rather than to the rules.…”

“…We will call these grammars restricted random context grammars (rRCGs). It was shown that even with this very limited ability of controlling the derivations these grammars are equivalent to random context grammars [2,15]. Moreover, permitting rRCGs are as powerful as permitting RCGs [2], and this is the case for the forbidding variants too if erasing rules are allowed [9].…”

“…also Definition 3.2.6 in [18]). We call these grammars generalized semi-conditional grammars or gSCGs to be short 15, 2017 21:31 WSPC/INSTRUCTION FILE permittingSCG˙IJFCS6 3 [8] L(rRCG λ ) [15] = L(RCG λ ) [3] = RE [17] = L(SCG λ ) [19] = L(CG λ ) L(SCG) [17] = L(CS) [19] = L(CG)…”

Comparison of Two Context-Free Rewriting Systems with Simple Context-Checking Mechanisms

“…Thus, this paper proves that they are as powerful as random context grammars. The reader is also referred to [6] for the discussion of some additional restrictions placed on these systems.…”