We present a new calculus where recent model-based decision procedures and techniques can be justified and combined with the standard DPLL(T) approach to satisfiability modulo theories. The new calculus generalizes the ideas found in CDCL-style propositional SAT solvers to the first-order setting.

We present a preprocessing algorithm for SAT, based on the HypBinRes inference rule, and show that it does not improve the performance of a DPLL-based SAT solver with conflict recording. We also present evidence that the ineffectiveness of the preprocessing algorithm is the result of interaction with the branching heuristic used by the solver.

The search of a precise measure of what hardness of SAT instances means for state-of-the-art solvers is a relevant research question. Among others, the space complexity of treelike resolution (also called hardness), the minimal size of strong backdoors and of cycle-cutsets, and the treewidth can be used for this purpose. We propose the use of the tree-like space complexity as a solid candidate ...

The Prover/Delayer game is a combinatorial game that can be used to prove upper and lower bounds on the size of Tree Resolution proofs, and also perfectly characterizes the space needed to compute them. As a proof system, Tree Resolution forms the underpinnings of all DPLL-based SAT solvers, so it is of interest not only to proof complexity researchers, but also to those in the area of proposit...

Here we give a short overview of the DPLL(T ) approach to Satisfiability Modulo Theories (SMT), which is at the basis of current state-of-the-art SMT systems. After that, we provide a documented list of theoretical and practical current challenges related to SMT, including some new ideas to exploit SAT techniques in Constraint Programming.

We introduce in this paper a lightweight technique for reducing work repetition caused by non–chronological backtracking commonly practiced by DPLL–based SAT solvers. The presented technique can be viewed as a partial component caching scheme. Empirical evaluation of the technique reveals significant improvements on a broad range of in-

Resolution trees with lemmas (RTL) are a resolution-based propositional proof system that is related to the DPLL algorithm with clause learning. Its fragments RTL(k) are related to clause learning algorithms where the width of learned clauses is bounded by k. For every k up to O(logn), an exponential separation between the proof systems RTL(k) and RTL(k + 1) is shown.

The Stone tautologies are known to have polynomial size resolution refutations and require exponential size regular refutations. We prove that the Stone tautologies also have polynomial size proofs in both pool resolution and the proof system of regular tree-like resolution with input lemmas (regRTI). Therefore, the Stone tautologies do not separate resolution from DPLL with clause learning.

SAT Modulo Theories (SMT) is the problem of determining the satisfiability of a formula in which constraints, drawn from a given constraint theory T , are composed with logical connectives. The DPLL(T ) approach to SMT has risen to prominence as a technique for solving these quantifier-free problems. The key idea in DPLL(T ) is to couple unit propagation in the propositional part of the problem...

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated using statistical physics concepts and techniques related to phase transitions, growth processes and (real–space) renormalization flows. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of αN randomly drawn logical constraints involving N Boolean va...