Reversible Transducers over Infinite Words
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929402512670720 |
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| author | Dartois, Luc Gastin, Paul Guizouarn, Loïc Germerie Govind, R. Krishna, Shankaranarayanan |
| author_facet | Dartois, Luc Gastin, Paul Guizouarn, Loïc Germerie Govind, R. Krishna, Shankaranarayanan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reversible Transducers over Infinite Words Dartois, Luc Gastin, Paul Guizouarn, Loïc Germerie Govind, R. Krishna, Shankaranarayanan Formal Languages and Automata Theory 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. |
| title | Reversible Transducers over Infinite Words |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2406.11488 |