research-article

Verified decision procedures for MSO on words based on derivatives of regular expressions

Authors:

Dmitriy Traytel,

Tobias NipkowAuthors Info & Claims

ICFP '13: Proceedings of the 18th ACM SIGPLAN international conference on Functional programming

Pages 3 - 12

https://doi.org/10.1145/2500365.2500612

Published: 25 September 2013 Publication History

Abstract

Monadic second-order logic on finite words (MSO) is a decidable yet expressive logic into which many decision problems can be encoded. Since MSO formulas correspond to regular languages, equivalence of MSO formulas can be reduced to the equivalence of some regular structures (e.g. automata). This paper presents a verified functional decision procedure for MSO formulas that is not based on automata but on regular expressions. Functional languages are ideally suited for this task: regular expressions are data types and functions on them are defined by pattern matching and recursion and are verified by structural induction.

Decision procedures for regular expression equivalence have been formalized before, usually based on Brzozowski derivatives. Yet, for a straightforward embedding of MSO formulas into regular expressions an extension of regular expressions with a projection operation is required. We prove total correctness and completeness of an equivalence checker for regular expressions extended in that way. We also define a language-preserving translation of formulas into regular expressions with respect to two different semantics of MSO. Our results have been formalized and verified in the theorem prover Isabelle. Using Isabelle's code generation facility, this yields purely functional, formally verified programs that decide equivalence of MSO formulas.

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Cited By

TRAYTEL DNIPKOW T(2015)Verified decision procedures for MSO on words based on derivatives of regular expressionsJournal of Functional Programming10.1017/S095679681500024625Online publication date: 5-Nov-2015
https://doi.org/10.1017/S0956796815000246
Nipkow THaslbeck M(2013)A Brief Survey of Verified Decision Procedures for Equivalence of Regular ExpressionsAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-642-40537-2_3(10-12)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40537-2_3
Rodrigues NSebe MChen XRoşu G(2024)A Logical Treatment of Finite AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-57246-3_20(350-369)Online publication date: 4-Apr-2024
https://doi.org/10.1007/978-3-031-57246-3_20
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Verified decision procedures for MSO on words based on derivatives of regular expressions

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cover image ACM Conferences

ICFP '13: Proceedings of the 18th ACM SIGPLAN international conference on Functional programming

September 2013

484 pages

ISBN:9781450323260

DOI:10.1145/2500365

General Chair:
Greg Morrisett
Harvard University, USA
,
Program Chair:
Tarmo Uustalu
Institute of Cybernetics at TUT, Estonia

ACM SIGPLAN Notices Volume 48, Issue 9
ICFP '13
September 2013
457 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2544174
Editor:
Mark W. Bailey
Hamilton College, Clinton, NY
Issue’s Table of Contents

Copyright © 2013 ACM.

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Published: 25 September 2013

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September 25 - 27, 2013

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Overall Acceptance Rate 333 of 1,064 submissions, 31%

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Cited By

TRAYTEL DNIPKOW T(2015)Verified decision procedures for MSO on words based on derivatives of regular expressionsJournal of Functional Programming10.1017/S095679681500024625Online publication date: 5-Nov-2015
https://doi.org/10.1017/S0956796815000246
Nipkow THaslbeck M(2013)A Brief Survey of Verified Decision Procedures for Equivalence of Regular ExpressionsAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-642-40537-2_3(10-12)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40537-2_3
Rodrigues NSebe MChen XRoşu G(2024)A Logical Treatment of Finite AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-57246-3_20(350-369)Online publication date: 4-Apr-2024
https://doi.org/10.1007/978-3-031-57246-3_20
Saarikivi OVeanes MWan TXu E(2019)Symbolic Regex MatcherTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-17462-0_24(372-378)Online publication date: 6-Apr-2019
https://dl.acm.org/doi/10.1007/978-3-030-17462-0_24

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