NP-completeness of small conflict set generation for congruence closure

Andreas Fellner (1, 2) , Pascal Fontaine (3, 4) , Bruno Woltzenlogel Paleo (5)

1 AIT - Austrian Institute of Technology [Vienna]
2 TU Wien - Vienna University of Technology = Technische Universität Wien
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
4 MOSEL - Proof-oriented development of computer-based systems
5 ANU - Australian National University

The efficiency of Satisfiability Modulo Theories (SMT) solvers is dependent on the capability of theory reasoners to provide small conflict sets, i.e. small unsatisfiable subsets from unsatisfiable sets of literals. Decision procedures for uninterpreted symbols (i.e. congruence closure algorithms) date back from the very early days of SMT. Nevertheless, to the best of our knowledge , the complexity of generating smallest conflict sets for sets of literals with uninterpreted symbols and equalities had not yet been determined, although the corresponding decision problem was believed to be NP-complete. We provide here an NP-completeness proof, using a simple reduction from SAT.

Mots clés: Decision procedures; Satisfiability Modulo Theories; Congruence closure; Complexity

Domaines: Logique en informatique [cs.LO]

Andreas Fellner, Pascal Fontaine, Bruno Woltzenlogel Paleo. NP-completeness of small conflict set generation for congruence closure. Formal Methods in System Design, 2017, 51 (3), pp.533 - 544. ⟨10.1007/s10703-017-0283-x⟩. ⟨hal-01908684⟩