From Finite-Valued Nondeterministic Transducers to Deterministic Two-Tape Automata

TL;DR

This paper explores the relationship between nondeterministic finite transducers and deterministic two-tape automata, characterizing when such transducers can be verified by deterministic automata and proving the problem's undecidability.

Contribution

It provides a characterization and construction method for finite-valued, functional, and unambiguous transducers verified by deterministic automata, and establishes the undecidability of this verification.

Findings

Characterization of transducers verified by deterministic automata

Construction method for such automata

Proof of undecidability of the verification criterion

Abstract

The question whether P equals 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 each input word with all output words that the transducer can successfully produce on the given input. Finite-valued transducers are those for which there is a finite upper bound on the number of output words that the relation associates with every input word. 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.