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.

中文翻译：

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从功能非确定性转换器到确定性两带自动机

是否 P = NP 的问题围绕着主动生产与仅由图灵机验证之间的差异展开。在本文中，我们研究了有限换能器和自动机的类似问题。每个非确定性有限变换器都定义了一种二进制关系，将输入词与变换器计算并接受的输出词相关联。功能转换器是那些关系是函数的转换器。我们描述了有限值、功能性和明确的非确定性转换器的特征，其关系可以通过确定性双带自动机来验证，展示如何构建这样的自动机（如果存在），并证明标准的不可判定性。