Equivalence of Functions Represented by Simple Context-Free Grammars with Output

Abstract

A partial function F:Σ ∗ →Ω ∗ is called a simple function if F(w) ∈Ω* is the output produced in the generation of a word w ∈Σ* from a nonterminal of a simple context free grammar G with output alphabet Ω. In this paper we present an efficient algorithm for testing equivalence of simple functions. Such functions correspond also to one-state deterministic pushdown transducers. Our algorithm works in time polynomial with respect to |G|+ v(G), where |G| is the size of the textual description of G, and v(G) is the maximum of the shortest lengths of words generated by nonterminals of G.