Automatic and Polynomial-Time Algebraic Structures

Nikolay Bazhenov, Matthew Harrison-Trainor, Iskander Kalimullin, Alexander Melnikov, Keng Meng Ng

Результат исследования: Научные публикации в периодических изданияхстатья

4 Цитирования (Scopus)

Аннотация

A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is Σ 1 1-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel.

Язык оригиналаанглийский
Страницы (с-по)1630-1669
Число страниц40
ЖурналJournal of Symbolic Logic
Том84
Номер выпуска4
DOI
СостояниеОпубликовано - 1 дек 2019

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  • Цитировать

    Bazhenov, N., Harrison-Trainor, M., Kalimullin, I., Melnikov, A., & Ng, K. M. (2019). Automatic and Polynomial-Time Algebraic Structures. Journal of Symbolic Logic, 84(4), 1630-1669. https://doi.org/10.1017/jsl.2019.26