Jobs/M2 2015 ADL SAT-based Minimization


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Minimization of Büchi automata using SAT-solving
Reference id

M2 2015 ADL SAT-based Minimization


5-6 months in 2015

Research field

Automata Theory

Related project



Alexandre Duret-Lutz

General presentation of the field

The Spot library ( 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.


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.

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).

Benefit for the candidate
Place LRDE: How to get to us

1000 € gross/month

Future work opportunities

This internship can easily be prolonged as a PhD thesis.


<adl at lrde . epita . fr> <adl at lrde . epita . fr>