SIMULATION BY ROUNDS OF LETTER-TO-LETTER TRANSDUCERS

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 T₁ is k-round simulated by transducer T₂ if, intuitively, for every input word x, we can permute the letters within each round in x, such that the output of T₂ on the permuted word is itself a permutation of the output of T₁ on x. Finally, two transducers are k-round equivalent if they simulate each other. We solve two main decision problems, namely whether T₂ k-round simulates T₁ (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 identifiers of processes in a multi-process system naturally gives rise to two transducers, whose k-round equivalence corresponds to stability against such permutations.