Derivatives of Logical Formulas

Dmitriy Traytel 🌐

May 28, 2015

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

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 all mentioned 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 by the author.

License

BSD License

Topics

Session Formula_Derivatives

Session Formula_Derivatives-Examples

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Cite

× 
@article{Formula_Derivatives-AFP,
  author  = {Dmitriy Traytel},
  title   = {Derivatives of Logical Formulas},
  journal = {Archive of Formal Proofs},
  month   = {May},
  year    = {2015},
  note    = {\url{https://isa-afp.org/entries/Formula_Derivatives.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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