Succinctness of Descriptions of Context-Free, Regular, and Finite Languages

Abstract

This thesis analyzes the descriptional power of finite automata, regular expressions, pushdown automata, and certain generalized models of macro grammars. For finite automata and pushdown automata the emphasis is on ambiguity. It is shown that ambiguous nondeterminism allows more succinct definitions than unambiguous nondeterminism which in turn allows more succinct definitions than determinism. The succinctness gain is nonrecursive for pda's and nonpolynomial for finite automata.

The succinctness of regular expressions and macro grammars is measured in terms of complexity theory. It is shown that the inequivalence problem for Ol macro grammars generating finite languages is hard for nondeterministic double exponential time, and that the ''nonemptiness of complement'' problem for unambiguous regular expressions is in NP. This implies that unambiguous regular expressions are ''easier'' than general regular expressions (unless NP is equal to PSPACE).