From Resolution and DPLL to Solving Arithmetic Constraints
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Reasoning methods based on resolution and DPLL have enjoyed many success stories in real-life applications. One of the challenges is whether we can go beyond and extend this technology to other domains such as arithmetic. In our recent work we introduced two methods for solving systems of linear inequalities called conflict resolution (CR) [6,7] and bound propagation (BP) [3,8] which aim to address this challenge. In particular, conflict resolution can be seen as a refinement of resolution and bound propagation is analogous to DPLL with constraint propagation, backjumping and lemma learning. There are non-trivial issues when considering arithmetic constraints such as termination, dynamic variable ordering and dealing with large coefficients. In this talk I will overview our approach and some related work [1,2,4,5,9]. This is a joint work with Ioan Dragan, Laura Kovács, Nestan Tsiskaridze and Andrei Voronkov.
- 1.Bobot, F., Conchon, S., Contejean, E., Iguernelala, M., Mahboubi, A., Mebsout, A., Melquiond, G.: A simplex-based extension of Fourier-Motzkin for solving linear integer arithmetic. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 67–81. Springer, Heidelberg (2012)CrossRefGoogle Scholar
- 3.Dragan, I., Korovin, K., Kovács, L., Voronkov A.: Bound propagation for arithmetic reasoning in Vampire (submitted, 2013)Google Scholar