Regular Language Representations in the Constructive Type Theory of Coq

Regular Language Representations in the Constructive Type Theory of Coq We explore the theory of regular language representations in the constructive type theory of Coq. We cover various forms of automata (deterministic, nondeterministic, one-way, two-way), regular expressions, and the logic WS1S. We give translations between all representations, show decidability results, and provide operations for various closure properties. Our results include a constructive decidability proof for the logic WS1S, a constructive refinement of the Myhill-Nerode characterization of regularity, and translations from two-way automata to one-way automata with verified upper bounds for the increase in size. All results are verified with an accompanying Coq development of about 3000 lines. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Automated Reasoning Springer Journals

Regular Language Representations in the Constructive Type Theory of Coq

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Computer Science; Mathematical Logic and Formal Languages; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Symbolic and Algebraic Manipulation
ISSN
0168-7433
eISSN
1573-0670
D.O.I.
10.1007/s10817-018-9460-x
Publisher site
See Article on Publisher Site

Abstract

We explore the theory of regular language representations in the constructive type theory of Coq. We cover various forms of automata (deterministic, nondeterministic, one-way, two-way), regular expressions, and the logic WS1S. We give translations between all representations, show decidability results, and provide operations for various closure properties. Our results include a constructive decidability proof for the logic WS1S, a constructive refinement of the Myhill-Nerode characterization of regularity, and translations from two-way automata to one-way automata with verified upper bounds for the increase in size. All results are verified with an accompanying Coq development of about 3000 lines.

Journal

Journal of Automated ReasoningSpringer Journals

Published: Mar 10, 2018

References

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