Complexity in Left-Associative Grammar

This paper presents a mathematical de nition of Left-Associative Grammar, and describes its formal properties. Conceptually, LA-grammar is based on the notion of possible continuations, in contrast to more traditional systems such as Phrase Structure Grammar and Categorial Grammar, which are linguistically motivated in terms of possible substitutions. It is shown that LA-grammar generates all and only the recursive languages. The Chomsky hierarchy of regular, context-free, and contextsensitive languages is reconstructed in LA-grammar by simulating nite state automata, push-down automata, and linearly bounded automata, respectively. Using alternative restrictions on LA-grammars, the new language hierarchy of A-LAGs, B-LAGs, C-LAGs is proposed. The class of C-LAGs is divided into three subclasses representing di erent degrees of ambiguity and associated computational complexity. The class of C-LAGs without recursive ambiguities (called the C1-LAGs) parses in linear time, and includes all deterministic CF-languages, plus CFlanguages with non-recursive ambiguities, e.g., abcd [ abcd, plus many context-sensitive languages, such as abc, abcde, fabcg ,