From Functional Nondeterministic Transducers to Deterministic Two-Tape Automata

05/27/2020

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by   Elisabet Burjons, et al.

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The question whether P = NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata. Every nondeterministic finite transducer defines a binary relation associating input words with output words that are computed and accepted by the transducer. Functional transducers are those for which the relation is a function. We characterize finite-valued, functional, and unambiguous nondeterministic transducers whose relations can be verified by a deterministic two-tape automaton, show how to construct such an automaton if one exists, and prove the undecidability of the criterion.