c ○ World Scientific Publishing Company COVER TRANSDUCERS FOR FUNCTIONS WITH FINITE DOMAIN

Cover automata were introduced a few years ago for designing a compact representation of finite languages. Our aim is to extend this notion to cover transducers for functions with finite domain. Given two alphabets Σ and Ω, and a function α:Σ ∗ → Ω ∗ of order l (the maximal length of a word in the domain of α), a cover transducer for α is any subsequential transducer that realizes the function α when its input is restricted to the set of words of Σ ∗ having a length not greater than l. We study the problem of reducing the number of states of a cover transducer. We report experimental results, from an implementation using WFSC (Weighted Finite State Compiler), a Xerox tool for handling weighted finite state automata and transducers. 1