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