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Extending SMT solvers with support for finite domain alldifferent constraint

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Abstract

In this paper we consider integration of SMT solvers with the filtering algorithms for the finite domain alldifferent constraint. Such integration makes SMT solvers suitable for solving constraint satisfaction problems with the alldifferent constraint involved. First, we present a novel algorithm for explaining inconsistencies and propagations in the alldifferent constraint. We compare it to Katsirelos’ algorithm and flow-based algorithms that are commonly used for that purpose. Then we describe our DPLL(T)-compliant SMT theory solver for constraint satisfaction problems that include alldifferent constraints. We also provide an experimental evaluation of our approach.

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Notes

  1. Notice that our definition of the residual graph from Section 3.1 is rather simplified, compared to the usual general definition of the residual graph in the flow networks [31], but the two definitions coincide in case of the graph assigned to the alldifferent constraint.

  2. The CSP theory refers to the standard first-order theory of integers (as described in SMT-LIB [3]) extended with the axioms that define the meaning of the global constraints.

  3. http://www.matf.bg.ac.rs/milan/argosmt/

  4. http://minisat.se/

  5. http://www.minizinc.org/g12distrib.html

  6. http://www.opturion.com/

  7. All instances can be found at: http://www.math.rs/milan/argosmt/instances.zip

  8. As stated in [36], this problem, as a typical example of a combinatorial design problem, has structural properties that are often seen in many practical applications.

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Acknowledgements

This work was partially supported by the Serbian Ministry of Science grant 174021 and by the SNF grant SCOPES IZ73Z0_127979/1. The author is grateful to Filip Marić and to anonymous reviewers for very careful reading of the text and providing detailed and useful comments and remarks.

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  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Milan Banković

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  1. Milan Banković
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Banković, M. Extending SMT solvers with support for finite domain alldifferent constraint. Constraints 21, 463–494 (2016). https://doi.org/10.1007/s10601-015-9232-8

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