Deciding FO-definability of regular languages
Kurucz, A. and Ryzhikov, Vladislav and Savateev, Yury and Zakhariyashchev, Michael (2021) Deciding FO-definability of regular languages. In: RAMICS 2021: International Conference on Relational and Algebraic Methods in Computer Science, 2–5 November 2021, Marseille, France.
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Abstract
We prove that, similarly to known PSpace-completeness of recognising FO(<)-definability of the language L(A) of a DFA A, deciding bothFO(<,equiv)- and FO(<,MOD)-definability (corresponding to circuit complexity in AC0 and ACC0) are PSpace-complete. We obtain these results by first showing that known algebraic characterisations of FO-definability of L(A) can be captured by `localisable' properties of the transition monoid of A. Using our criterion, we then generalise the known proof of PSpace-hardness of FO(<)-definability, and establish the upper bounds not only for arbitrary DFAs but also for 2NFAs.
Metadata
| Item Type: | Conference or Workshop Item (Paper) |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Vladislav Ryzhikov |
| Date Deposited: | 10 May 2022 15:14 |
| Last Modified: | 09 Aug 2023 12:52 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/46962 |
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