Complexity of injection structures induced by finite state transducers

Abstract

Abstract An injection structure ${{\mathcal {A}}} = (A,f)$ is a set $A$ together with a one-place one-to-one function $f$. ${{\mathcal {A}}}$ is a Finite State Transducer (abbreviated FST) injection structure if $A$ is a regular set, i.e. the set of words accepted by some finite automaton, and $f$ is realized by a deterministic FST. We study the complexity of the character of an FST injection structure. We examine the effective categoricity of such structures. We show that the isomorphism problem for unary FST structures is decidable in quadratic time.