The long way from CDClL

Current SAT solvers are powerful enough to be used as engines in real applications. Those applications made the success of a special kind of SAT solvers, namely Conflict Driven Clause Learning SAT solvers (CDClL for short), developed initially by Joao Marques Silva with GRASP [8], and popularized by the SAT solver Chaff [9]. Despite SAT being a NP-complete problem in theory, it might look tractable in practice when looking at the huge size (several millions of variables and clauses) of some bounded model checking SAT encodings solved in a few minutes by current state of the art solvers. As a consequence, researchers are pushing the limit beyond SAT: Quantified Boolean Formulas (QBF) and Stochastic SATisfiability (SSAT) for instance are two extensions of SAT being studied recently. Another extension of SAT received some attention a decade ago: using pseudo boolean constraints instead of plain clauses [1, 2]. Most of the solvers for those extensions to SAT are developed using techniques that were demonstrated powerful for SAT. Those solvers in the early 90s were based on DPLL[5, 4] while the solvers developed today are often related to CDClL solvers. This is especially true for pseudo boolean solvers: Barth first developed a DPLL version of a pseudo boolean solver [2]. Walser [16] and later Prestwich [11, 12] developed local search or hybrid pseudo boolean solvers. Aloul et al [13] developed a version of Chaff handling pseudo boolean constraints instead of clauses as input, plus symmetry breaking predicates, with clause learning (same thing for the recent MiniSAT [14]). Dixon and Ginsberg[6] developed a pseudo boolean version of Relsat (PRS), which was the first pseudo boolean solver including true pseudo boolean learning. They developed a pseudo boolean version of Chaff (PBChaff[7]) in the same spirit while Chai and Kuehlmann [3] did extended all Chaff techniques (learning scheme and data structures) in the pseudo boolean solver Galena. Very recent work, and partially unpublished,