Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output letters within "rounds". In this work, we introduce and study notions of simulation by rounds and equivalence by rounds of transducers. In our setting, words are partitioned to consecutive subwords of a fixed length $k$, called rounds. Then, a transducer $\mathcal{T}_1$ is $k$-round simulated by transducer $\mathcal{T}_2$ if, intuitively, for every input word $x$, we can permute the letters within each round in $x$, such that the output of $\mathcal{T}_2$ on the permuted word is itself a permutation of the output of $\mathcal{T}_1$ on $x$. Finally, two transducers are $k$-round equivalent if they simulate each other. We solve two main decision problems, namely whether $\mathcal{T}_2$ $k$-round simulates $\mathcal{T}_1$ (1) when $k$ is given as input, and (2) for an existentially quantified $k$. We demonstrate the usefulness of the definitions by applying them to process symmetry: a setting in which a permutation in the identities of processes in a multi-process system naturally gives rise to two transducers, whose $k$-round equivalence corresponds to stability against such permutations.

中文翻译：

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几轮信纸转换器的仿真

字母到字母的换能器是用于对反应系统进行建模的标准形式。通常，对相似系统建模的两个换能器之间的行为相似，在局部上彼此不同，直至“回合”内输入和输出字母的排列。在这项工作中，我们引入并研究了逐轮模拟和换能器等效的模拟概念。在我们的设置中，单词被划分为固定长度$ k $的连续子单词，称为回合。然后，换能器$ \ mathcal {T} _1 $被换能器$ \ mathcal {T} _2 $模拟$ k $，如果直观地来说，对于每个输入单词$ x $，我们可以在$ x $，这样排列后的单词上$ \ mathcal {T} _2 $的输出本身就是$ x $上$ \ mathcal {T} _1 $的输出的排列。最后，如果两个换能器相互模拟，则它们的等效值为$ k $。我们解决了两个主要的决策问题，即$ \ mathcal {T} _2 $ $ k $ -round是否模拟$ \ mathcal {T} _1 $（1）当给出$ k $作为输入时，以及（2）存在时量化的$ k $。我们通过将定义应用于过程对称性来证明定义的有用性：在这种设置中，多过程系统中的过程标识的排列自然会产生两个换能器，其换能器的$ k $个等效值对应于相对于此类稳定性的稳定性。排列。