Sequential grammars with activation and blocking of rules

Abstract : We introduce new possibilities to control the application of rules based on the preceding application of rules which can be defined for a general model of sequential grammars and we show some similarities with other control mechanisms such as graph-controlled grammars and matrix grammars with and without appearance checking, as well as grammars with random context conditions. Using both activation and blocking of rules, in the string and in the multiset case we can show computational completeness of context-free grammars equipped with the control mechanism of activation and blocking of rules even when using only two nonterminal symbols. With one- and two-dimensional # -context-free array grammars, computational completeness can already be obtained by only using activation of rules.