Regular transducer expressions for regular transformations

Functional MSO transductions, deterministic two-way transducers, as well streaming string transducers are all equivalent models for regular functions. In this paper, we show that every function, either on finite words or infinite words, captured by a transducer, can be described with transducer expression (RTE ). For the uses Muller acceptance and ω-regular look-ahead. RTEs constructed from constant functions using combinators if-then-else (deterministic choice), Hadamard product, unambiguous versions of Cauchy 2-chained Kleene-iteration omega-iteration. Our proof works transformations both extending result Alur et al. in LICS'14. The construction an RTE associated is guided which “good” wrt. its transition monoid. “Good” expressions unambiguous, ensuring functionality output computed. Moreover, expressions, iterations (Kleene-plus omega) restricted to subexpressions corresponding idempotent elements obtained version Imre Simon's famous forest factorization theorem. To handle introduce notion monoids look-ahead, where look-ahead some backward Büchi automaton. This paper extended [15] presented at LICS'18.