Derivatives of Logical Formulas

3 years 7 months ago
Derivatives of Logical Formulas
We formalize new decision procedures for WS1S, M2L(Str), and Presburger Arithmetics. Formulas of these logics denote regular languages. Unlike traditional decision procedures, we do not translate formulas into automata (nor into regular expressions), at least not explicitly. Instead we devise notions of derivatives (inspired by Brzozowski derivatives for regular expressions) that operate on formulas directly and compute a syntactic bisimulation using these derivatives. The treatment of Boolean connectives and quantifiers is uniform for ioned logics and is abstracted into a locale. This locale is then instantiated by different atomic formulas and their derivatives (which may differ even for the same logic under different encodings of interpretations as formal words). The WS1S instance is described in the draft paper A Coalgebraic Decision Procedure for WS1S 1 by the author. Contents 1 Equivalence Framework 2
Dmitriy Traytel
Added 13 Apr 2016
Updated 13 Apr 2016
Type Journal
Year 2015
Where AFP
Authors Dmitriy Traytel
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