Solving temporal problems using SMT: strong controllability

  • Authors:

  • Alessandro Cimatti;Andrea Micheli;Marco Roveri

  • Affiliations:

  • Fondazione Bruno Kessler -- Irst, Italy;Fondazione Bruno Kessler -- Irst, Italy;Fondazione Bruno Kessler -- Irst, Italy

  • Venue:
  • CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
  • Year:
  • 2012

  • The MathSAT5 SMT solver

    TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems

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Abstract

Many applications, such as scheduling and temporal planning, require the solution of Temporal Problems (TP's) representing constraints over the timing of activities. A TP with uncertainty (TPU) is characterized by activities with uncontrollable duration. Depending on the Boolean structure of the constraints, we have simple (STPU), constraint satisfaction (TCSPU), and disjunctive (DTPU) temporal problems with uncertainty. In this work we tackle the problem of strong controllability, i.e. finding an assignment to all the controllable time points, such that the constraints are fulfilled under any possible assignment of uncontrollable time points. We work in the framework of Satisfiability Modulo Theory (SMT), where uncertainty is expressed by means of universal quantifiers. We obtain the first practical and comprehensive solution for strong controllability: the use of quantifier elimination techniques leads to quantifier-free encodings, which are in turn solved with efficient SMT solvers. We provide a detailed experimental evaluation of our approach over a large set of benchmarks. The results clearly demonstrate that the proposed approach is feasible, and outperforms the best state-of-the-art competitors, when available.