Equivalence of simple functions

• Published in: Theoretical computer science Vol. 376; no. 1; pp. 42 - 51
• Main Authors: Bastien, Cédric, Czyzowicz, Jurek, Fraczak, Wojciech, Rytter, Wojciech
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 10.05.2007; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Context-free grammar; Equivalence problem; Exact sciences and technology; Formal language; Language theory and syntactical analysis; Push-down transducer; Simple function; Simple grammar; Theoretical computing; Formal language; Simple function; Push-down transducer; Simple grammar; Context-free grammar; Equivalence problem; Alphabet; Computer theory; Word length; Algorithm; Polynomial time; Transducer; Context free grammar
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2007.01.011

A partial function F : Σ ∗ → Ω ∗ is called a simple function if F ( w ) ∈ Ω ∗ is the output produced in the leftmost derivation 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 the 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 .