On the computational completeness of matrix simple semi-conditional grammars

Abstract

In matrix grammars, context-free rules have to be applied in a certain order. In simple semi-conditional (SSC) grammars, the derivations are controlled either by a permitting string or by a forbidden string associated to each rule. In SSC grammars, the maximum length i of permitting strings and the maximum length j of forbidden strings, the numbers of conditional rules and of nonterminals serve as measures of descriptional complexity and the pair (i,j) is called the degree of such SSC grammars. Matrix grammars with appearance checking with three nonterminals are computationally complete; however, the matrix length is unbounded. Matrix SSC grammars (MSSC) put matrix grammar control on SSC rules. In this paper, we show that MSSC grammars with degrees (2,1), (2,0) and (3,0) are computationally complete, restricting several other descriptional complexity measures. With our constructions, we even bound the matrix length for MSSC grammars.