Automatic and polynomial-time algebraic structures

Automatic and polynomial-time algebraic structures

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 aske...

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Bibliographic Details
Main Authors: Bazhenov, Nikolay, Harrison-Trainor, Matthew, Kalimullin, Iskander, Melnikov, Alexander, Ng, Keng Meng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Mathematics
Automatic Structures
Classification
Online Access:https://hdl.handle.net/10356/145007
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Institution: Nanyang Technological University
Language: English
Description
Summary: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 -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.

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