On the equivalence problem for deterministic multitape automata and transducers

Abstract

We discuss the technique for testing the equivalence of two deterministic automata by constructing a language that matches the computations of two equivalent automata on the same input word. Specifically, we propose to use HDTOL languages that are powerful enough to match computations of many equivalent deterministic multitape automata, and at the same time, have nice decidable properties. Using this new technique of HDTOL matching, we show that the inclusion problem between an arbitrary deterministic multitape automaton and a simple one is decidable in both directions. Further, we show that the computations of two simple automata can be HDTOL matched on their common domain. This implies that the equivalence problem for transducers based on simple automata is decidable. The latter result is the best possible since the problem is undecidable even for transducers based on automata with parallel loops.