The complexity of the membership problem for some extensions of context-free languagest†

Abstract

The time and tape complexity of some families of languages defined in the literature by altering methods of generation by context-free grammars is considered. Specifically; it is shown that the following families of languages can be recognized by deterministic multitape Turing machines either in polynomial time or within (log n)2 tape: 1) the context independent developmental (EOL) languages; 2) the simple matrix languages; 3) the languages generated by derivation restricted state grammars.: 4) the languages generated by linear context-free grammars with certain non-regular control sets; 5) the languages generated by certain classes of vector grammars. In fact, these languages are of the same tape complexity as context-free languages. Other results indicate the complexity of EDOL languages and the effects on complexity of applying the homomorphic replication operator to regular and context-free languages.