We describe a SAT-solver, BerkMin, that inherits such features of GRASP, SATO, and Chaff as clause recording, fast BCP, restarts, and conflict clause “aging”. At the same time BerkMin introduces a new decision making procedure and a new method of clause database management. We experimentally compare BerkMin with Chaff, the leader among SAT-solvers used in the EDA domain. Experiments show that our solver is more robust than Chaff. BerkMin solved all the instances we used in experiments including very large CNFs from a microprocessor verification benchmark suite. On the other hand, Chaff was not able to complete some instances even with the timeout limit of 16 hours. 1.

Recently, it has been found that the cost distributions of randomized backtrack search in combinatorial domains are often heavytailed. Such heavy-tailed distributions explain the high variability observed when using backtrack-style procedures. A good understanding of this phenomenon can lead to better search techniques. For example, restart strategies provide a good mechanism for eliminating the heavy-tailed behavior and boosting the overall search performance. Several state-of-the-art SAT solvers now incorporate such restart mechanisms. The study of heavy-tailed phenomena in combinatorial search has so far been been largely based on empirical data. We introduce several abstract tree search models, and show formally how heavy-tailed cost distribution can arise in backtrack search. We also discuss how these insights may facilitate the development of better combinatorial search methods.

We present GrADSAT, a parallel satisfiability solver aimed at solving hard SAT instances using a large number of widely distributed commodity computational resources. The GrADSAT parallel algorithm uses intelligent backtracking, sharing of learned clauses and clause reduction. The distributed implementation allows for dynamic resource acquisition. We show how the large number of computational resources and communication overhead influence the implementation strategy. GrADSAT is compared against the best sequential solver using a wide variety of problem instances. The results show that GrADSAT delivers speed-up on most instances. Furthermore it is capable of solving problem instance which were never solved before.

We propose a method for local search of Boolean relations relating variables of a CNF formula. The method is to branch on small subsets of the set of CNF variables and to analyze results of unit propagation. By taking into account variable value assignments deduced during the unit propagation procedure the method is able to justify any relation represented by a Boolean expression. The proposed technique is based on bitwise logical operations over ternary vectors. We implement a restricted version of the method used for unit clause derivation and equivalentliteral identification in a preprocessor engine for a SATsolver. The experiments show that the proposed technique is useful for solving real-world instances of the formal verification domain.

We present an improved version of GridSAT, a distributed and complete satisfiability solver. The solver is used to solve a set of “hard ” and previously unsolved set of satisfiability problems. We enhance the GridSAT solver, which is based on the sequential solver Chaff, in two main ways. First the improved GridSAT solver uses immediate integration of shared clauses to achieve better solver performance. Second GridSAT’s scheduler is enhanced to reduce communication overhead. Using a set of experiments, we show that GridSAT is capable of using simultaneously a wide variety of resources which range from shared desktop machines to supercomputers. GridSAT’s scheduler was able to manage this diverse and dynamic resource pool for up to a month during some experiments to solve previously unsolved problems from the SAT 2002 [43] and the SAT 2003 [46] competitions. We present the improvements we made and the new results obtained using GridSAT.

The march ks Sat solver is an upgraded version of the successful march dl and march eq Sat solvers, which won several awards at the Sat 2004 and Sat 2005 competitions. For the latest detailed description, we refer to [2]. Like its predecessors, march ks integrates equivalence reasoning into a DPLL architecture and uses lookahead heuristics to determine the branch variable in all nodes of the DPLL search-tree. The main improvements in march ks are: • renewed pre-processing techniques: Removal of the 3-Sat translator and therefore a new procedure for the addition of resolvents. • an improved adaptive algorithm to trigger the DoubleLook procedure- inspired by the one used int satz by Li [1]. • a guided jumping strategy: Instead of the conventional depth-first search, march ks uses a jumping strategy based on the distribution of solutions measured on random 3-Sat instances [3]. 2 pre-processing The pre-processor of march dl, reduces the formula at hand prior to calling the main solving (DPLL) procedure. Earlier versions already contained unit-clause and binary equivalence propagation, as well as equivalence reasoning, a 3-Sat translator, and finally a full- using all free variables- iterative root look-ahead. However, march ks is the first version of march which does not use a 3-Sat translator by default (although it is still optional). The motivation for its removal is to examine the effect of (not) using a 3-Sat translator on the performance. Because the addition of resolvents was only based on the ternary clauses in the formula (after the translation) we developed a new algorithm for this addition which uses all clauses with at least three literals. 3 the architecture As a look-ahead Sat solver, the branch rule of march ks is based on a look-ahead evaluation function (Diff). The applied Diff measures the reduction of CNF- and equivalence-clauses between two formulas F and F ′ in a weighted manner. The solver differs from the straightforward look-ahead architecture in two aspects: (1) look-ahead is performed on a subset of the free (unfixed) variables, and (2) if a certain look-ahead significantly reduces the formula, the DoubleLookhead procedure is called to check whether this look-ahead will eventually result in a conflict. Algorithms below show the pseudocode of this architecture.

On the connections between backdoors, restarts, and heavy-tailedness in combinatorial search (Extended Abstract)