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arXiv · 2406.11488

Reversible Transducers over Infinite Words

Luc Dartois·Paul Gastin·Loïc Germerie Guizouarn·R. Govind·Shankaranarayanan Krishna
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Abstract

Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to reactive synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification. An important result by Dartois et al. shows that composition of two-way transducers enjoy a polynomial composition when the underlying transducer is reversible, that is, if they are both deterministic and co-deterministic. This is a major improvement over general deterministic two-way transducers, for which composition causes a doubly exponential blow-up in the size of the inputs in general. Moreover, they show that reversible two-way transducers have the same expressiveness as deterministic two-way transducers. However, the question of expressiveness of reversible transducers over infinite words is still open. In this article, we introduce the class of reversible two-way transducers over infinite words and show that they enjoy the same expressive power as deterministic two-way transducers over infinite words. This is done through a non-trivial, effective construction inducing a single exponential blow-up in the set of states. Further, we also prove that composing two reversible two-way transducers over infinite words incurs only a polynomial complexity, thereby providing foundations for efficient procedure for composition of transducers over infinite words.

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Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, Shankaranarayanan Krishna. 2024-06-17. Reversible Transducers over Infinite Words. https://arxiv.org/abs/2406.11488

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