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

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 onestate 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.