Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions. 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). We verify an executable decision procedure for MSO formulas that is not based on automata but on regular expressions. 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. The formalization is described in this ICFP 2013 functional pearl.
Keywords for this software
References in zbMATH (referenced in 7 articles , 1 standard article )
Showing results 1 to 7 of 7.
- Doczkal, Christian; Smolka, Gert: Regular language representations in the constructive type theory of Coq (2018)
- Unel, Gulay; Toman, David: Logic programming approach to automata-based decision procedures (2017)
- Doczkal, Christian; Smolka, Gert: Two-way automata in Coq (2016)
- Thiemann, Peter: Derivatives for enhanced regular expressions (2016)
- Traytel, Dmitriy; Nipkow, Tobias: Verified decision procedures for MSO on words based on derivatives of regular expressions (2015)
- Nipkow, Tobias; Traytel, Dmitriy: Unified decision procedures for regular expression equivalence (2014)
- Traytel, Dmitriy; Nipkow, Tobias: Verified decision procedures for MSO on words based on derivatives of regular expressions (2013)