Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929449849585664 |
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| author | Bojańczyk, Mikołaj Fijalkow, Joanna Klin, Bartek Moerman, Joshua |
| author_facet | Bojańczyk, Mikołaj Fijalkow, Joanna Klin, Bartek Moerman, Joshua |
| contents | We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_02438 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata Bojańczyk, Mikołaj Fijalkow, Joanna Klin, Bartek Moerman, Joshua Formal Languages and Automata Theory F.1.1; F.4.3 We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing. |
| title | Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata |
| topic | Formal Languages and Automata Theory F.1.1; F.4.3 |
| url | https://arxiv.org/abs/2104.02438 |