Master 2015 2016
Stages de la spécialité SAR
Minimization of Büchi automata using SAT-solving


Site : Minimization of Büchi automata using SAT-solving
Lieu : LRDE-EPITA 14 - 16 rue Voltaire 94276 Le Kremlin-Bicêtre Cedex www.lrde.epita.fr
Encadrant : Alexandre Duret-Lutz, <adl at lrde . epita . fr>
Dates :Février - Août 2016 (5-6 mois)
Rémunération :1000 Euros brut/mois
Mots-clés : Master SAR, autre qu’ATIAM

Description

* General presentation of the field :

The Spot library (http://spot.lip6.fr/) contains many algorithms for translating LTL formulas into Büchi automata, and to simplify these formulas and automata. A recently added technique allows us to minimize deterministic Büchi automata using a SAT-solver ; the implementation is actually not restricted to Büchi and can work with deterministic omega-automata with any acceptance conditions. To minimize a n-state deterministic omega-automaton (an NP-complete problem) we encode its equivalence with a (n-1)-state deterministic omega-automaton as a SAT problem, and let a SAT solver do the work of finding a solution. If such a solution is found, we try again, looking for a (n-2) state automaton, etc.

* Prerequisites : This internship targets students who :
- have some experience in C++ programming and Unix development (experience with git and emacs would be a welcome bonus)
- like to write clean and useful code (Spot is an open-source library used by other projects)
- like to optimize
- would like do get familiar with the amazing world of SAT-solvers and Büchi automata.

* Objectives :

Presently, our first implementation saves the SAT problem as a huge file before calling the SAT-solver, and it does this for each iteration. The goal of this internship is to improve this situation in multiple ways :
- implement purely technical optimizations (like direct communication with the SAT solver, bypassing any temporary files)
- take advantage of features offered by modern SAT solvers (for instance an "incremental SAT-solver" can be given new constraints after it has found a solution, without needing to restart from scratch)
- implement optimizations to the encoding of the SAT-problem, based on structural properties of the automaton (we have some ideas)

In a second step, we would like to generalize the existing technique to non-deterministic automata (first as input, and then as output as well).

This internship can easily be prolonged as a PhD thesis.

Bibliographie

On the usage of a SAT-solver for minimization : https://www.lrde.epita.fr/ adl/dl/a...

For the present usage of SAT-based minimization in Spots : https://spot.lrde.epita.fr/satmin.html