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# Simulation by Rounds of Letter-To-Letter Transducers

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LIPIcs.CSL.2022.3.pdf
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## Cite As

Antonio Abu Nassar and Shaull Almagor. Simulation by Rounds of Letter-To-Letter Transducers. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 3:1-3:17, Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik (2022)
https://doi.org/10.4230/LIPIcs.CSL.2022.3

## Abstract

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 π―β is k-round simulated by transducer π―β if, intuitively, for every input word x, we can permute the letters within each round in x, such that the output of π―β on the permuted word is itself a permutation of the output of π―β on x. Finally, two transducers are k-round equivalent if they simulate each other. We solve two main decision problems, namely whether π―β k-round simulates π―β (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.

## Subject Classification

##### ACM Subject Classification
• Theory of computation β Verification by model checking
• Theory of computation β Concurrency
• Theory of computation β Abstraction
• Transducers
• Permutations
• Parikh
• Simulation
• Equivalence

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