An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation

 

Title: An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation
Author: Salomon Sickert (s /dot/ sickert /at/ tum /dot/ de)
Submission date: 2020-05-08
Abstract: In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form $\bigwedge_{i=1}^n \mathbf{G}\mathbf{F} \varphi_i \vee \mathbf{F}\mathbf{G} \psi_i$, where $\varphi_i$ and $\psi_i$ contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalisation procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. We improve on both points. We present an executable formalisation of a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blow-up.
BibTeX:
@article{LTL_Normal_Form-AFP,
  author  = {Salomon Sickert},
  title   = {An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation},
  journal = {Archive of Formal Proofs},
  month   = may,
  year    = 2020,
  note    = {\url{http://isa-afp.org/entries/LTL_Normal_Form.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: LTL, LTL_Master_Theorem