Adding bells and whistles the routine on the previous slide is not very efficient. We present a fast parallel satsolver on a message based mimd machine. Find materials for this course in the pages linked along the left. A sat solver using software and reconfigurable hardware. A sat problem instance is a formula in propositional logic. Sbsat combines bdd manipulation and search methods to support efficient implementation of complex search heuristics and effective use of early preprocessor learning. The davis putnam dp algorithml2, published in 1960, is typically cited as the first entry in the solver timeline. Sequential sat solvers stateoftheart sat solvers are based on the historical davis, putnam, logemann and loveland procedure, commonly called dpll davis, logemann, and loveland 1962. First, the davis putnam procedure for the satisability problem sat is described. In particular, you will implement the davisputnamlogemannloveland dpll algorithm.
In particular, you will implement the davis putnam logemannloveland dpll algorithm. A classification of sat algorithms davis putnam dp based on resolution davis logemannloveland dlldpll searchbased basis for current most successful solvers stalmarcks algorithm more of a breadth first search, proprietary algorithm stochastic search local search, hill climbing, etc. The study proposes a new decision heuristic for davis putnam, loveland and logemann algorithm dpllbased satisfiability sat solvers based on cube subtraction. The quality of such a solver heavily depends on the ability of. A exponentialtime algorithm for boolean sat problem davis, putnam, loveland, loggeman in 1962 systems of diophantine equations are not solvable matiyasevich. A variant of the 3satisfiability problem is the oneinthree 3 sat also known variously as 1in3 sat and exactly1 3 sat.
This thesis focuses on the design of feasible solvers for this problem. While there have been many significant enhancements since then, most successful complete solvers use the basic concepts of dpll at their core. We first introduce abstract dpll, a rulebased formulation of the davis putnam logemannloveland dpll procedure for propositional satisfiability. The sat solver produces the sets of bd constraints to be checked for consistency. Sat solver using the davis putnam logemannloveland algorithm implemented in python 3. Cube subtraction systematically subtracts all clause cubes from the universal cube. Each negated clause is viewed as a cube in the ndimensional boolean search space denoting a subspace where no satisfying assignments can be found.
The davis putnam logemannloveland page on wikipedia has a good overview then you should be able to follow the minisat paper an extensible sat solver you should also read grasp a new search algorithm for satisfiability to understand the conflictdriven learning algorithm used in minisat i was able to write a sat solver in python quite easily using those resources. Calendar elements of software construction electrical. Since this reasoning is performed dynamically many more opportunities arise as we descend the search tree. It still forms the basis for todays as of 2015 most efficient complete sat solvers. Such good results could suggest that all the techniques used in cdcl sat solvers could be generalized and e ciently used in a more generic kind of solver so called dpllt where t. S return satisfiables l strategically add clause deletion strategies e. Since the seminal 1962 paper, which introduced the davisputnamlogemannloveland dpll algorithm, dpll has been the prominent algorithm used for complete sat solvers.
But, as noted in 8, an essentially identical algorithm was in fact developed. Most modern sat solvers are based on the davisputnam logemannloveland dpll algorithm. In logic and computer science, the davisputnamlogemannloveland dpll algorithm is a complete, backtracking based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i. This algorithm takes as input a logical statement in cnf format and outputs a assignment of true or false to each propositional symbol. Sat 3 problem, making it an essential tool in solving this class of problems.
Each clause is written in single line with literals from 0 to n that are negated with a prepending. A computing procedure for quantification theory, 1960. Davis and putnam 55 came up with the basic idea behind this. First, the davisputnam procedure for the satisability problem sat is described.
A new rewarding mechanism for branching heuristic in sat. To run use an instances file as input to the program. In particular, we are able to generate full collisions for md4. In this paper, we present a sat solver based on the combination of dpll davis putnam logemann and loveland algorithm and failed literal detection fld, one of the advanced reasoning techniques. Sat solver using the davisputnamlogemannloveland algorithm implemented in python 3. Hybrid solvers for the boolean satisfiability problem. We first introduce abstract dpll, a rulebased formulation of the davisputnamlogemannloveland dpll procedure for propositional satisfiability. The dpll algorithm finds a solution if and only if the formula is satisfiable.
Davis putnam procedure an overview sciencedirect topics. Heuristics that do well on random instances tend to do poorly on realworld instances and vice versa. We show that when the heuristic is used by a davisputnam sat solver that employs conflictdirected backtracking, it produces a divideandconquer behavior in which the sat problem is recursively decomposed into smaller problems that are solved independently. Solving sat and sat modulo theories 939 the second main contribution of this article is a new modular architecture for building smt solvers in practice, called dpllt, and a careful study of theorypropagation, a re. A variant of the 3satisfiability problem is the oneinthree 3sat also known variously as 1in3sat and exactly1 3sat. This is an implementation of the davisputnam dll algorithm sat solver in java. We first have developed a davisputnam based satisfiability solver. Small subformulas are solved by a fast sequential sat solver running on every processor, which is based on the davis putnam procedure with a special heuristic for variable selection. The input formula is dynamically divided into disjoint subformulas. The sat solver implementation as it appears in opensuse 11. The boolean satisfiability problem sat is one of the most extensively researched npcomplete problems in computer science.
Stateoftheart complete sat solvers are predominantly based on conflictdriven clause learning cdcl algorithm, which extends the davisputnamlogemannloveland dpll algorithm by adding effective search techniques, including fast boolean constraint propagate bcp, variable state independent decaying sum vsids branching heuristics. The sat solver may be modified to work directly on the boolean circuit representation. It currently does not support vsids currently chooses literals at. Our research focuses on a newer solver paradigm, hybrid. A fast parallel satsolver efficient workload balancing. Citeseerx document details isaac councill, lee giles, pradeep teregowda. In this paper, we attempt to bridge this bifurcation. As mentioned above, our parallel sat solver runs a copy of the sequential sat solver on every processor, and the n processors cooperate, when searching for m. It reduces the calculations needed to solve a problem. Sat solvers are now mature enough to be used in hardware or software. Then we explain efcient known data structures for sat and extensions to qbf which we used in our solver. The use of sat solvers to handle practical problems has grown dramatically over the last decade.
The performance of sat solvers based on the davis putnam logemannloveland procedure 6, 5 is sensitive to the choice of branch variable selection heuristic 14. Finally, we introduce the concept of autarky and describe how detecting 2autarky structures in a given qbf. This is an implementation of the davis putnam dll algorithm sat solver in java. One standard algorithm to solve sat is the davis putnam logemannloveland dpll 4, introduced in 1962 as an improvement of the dp algorithm 5, proposed two years before. Check the competition web site for information about how well. Speckenmeyer, a fast parallel sat solver 383 a solution in the space of partial truth assignments, by partitioning this space.
Boolean satisfiability is wellstudied, and sat solvers have a long history. Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one true literal and thus exactly two false literals. The algorithm uses optimized data structures to modify boolean formulas. We propose a dynamic filtering method that consists of two restriction rules for fld. This abstract framework allows one to cleanly express practical dpll algorithms and to formally reason about them in a simple way. It currently does not support vsids currently chooses literals at random, random restarts, nor pure literals. Extending sat solver with parity constraints tero laitinen. We present a fast parallel sat solver on a message based mimd machine. A sat solver attempts to find a solution for the formula. Most of the state of the art sat solvers are simply based on the davis, putnam, logemann and loveland procedure, commonly called dpll 10. Satsmt solvers and applications university of waterloo.
Understanding and using sat solvers max planck society. The davisputnamlogemannloveland algorithm is a 1962 refinement of the propositional satisfiability step of the davisputnam procedure which requires only a linear amount of memory in the worst case. The barcelogictools solver participated to the sat race 2006 and showed very good performances 6 out of 16 for \parameterized sat solver. In logic and computer science, the davisputnamlogemannloveland dpll algorithm is a complete, backtrackingbased search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i. Motivations zas a curiosity of mathematicians and inventers. Satisfiability solver file exchange matlab central.
Winning all the industrial categories of the sat 2005 competition, minisat is a good starting point both for future research in sat, and for applications using sat. The term constraint solver, however, usually refers to a csp solver. The method proposed by davis, putnam, logemann, and loveland for propositional reasoning 3, 4, often referred as the davisputnam method, has long been a major practical method for solving sat problems. Sbsat is a research platform for testing ideas that will improve sat solver performance on these and other problems. Hardware accelerated sat solversa survey sciencedirect. From an abstract davisputnamlogemannloveland procedure to dpllt robert nieuwenhuis and albert oliveras technical university of catalonia, barcelona, spain and cesare tinelli the university of iowa, iowa city, iowa abstract. It was introduced in 1962 by martin davis, george logemann and donald w. In this assignment you will implement a solver for the satisfiability sat problem. We show that when the heuristic is used by a davis putnam sat solver that employs conflictdirected backtracking, it produces a divideandconquer behavior in which the sat problem is recursively decomposed into smaller problems that are solved independently.
Some essential building blocks of these attacks lend themselves well to automation by encoding them as cnf formulas, which are within reach of modern sat solvers. Dpll davisputnamlogemannloveland algorithm sql structured query language. Example s, a satisfya the input argument a is a sparse matrix representation of the conjunctive normal form cnf of the boolean formula to solver. Oct 24, 2017 in this assignment you will implement a solver for the satisfiability sat problem. The xorreasoning module has to be able to infer results. It is a modification of the wellknown sat solver minisat where the constructor of the literals has been adjusted to start with the negated literals first. A structurebased variable ordering heuristic for sat. Applications of sat solvers to cryptanalysis of hash. Each negated clause is viewed as a cube in the n dimensional boolean search space denoting a subspace where no satisfying assignments can be found. Learning material on sat boolean satisfiability problem. Enhancing davis putnam with extended binary clause. Decision heuristic strategy can be viewed as one of the most central features of stateoftheart conflictdriven clauselearning sat solvers.
Decision heuristic for davis putnam, loveland and logemann. Vsids consists of a rewarding mechanism for variables participating in the conflict. Sat solving an alternative to brute force bitcoin mining. Using autarky to evaluate quantied boolean formulae. Minisat is small and welldocumented, and possibly also welldesigned, making it an ideal starting point for adapting sat based techniques to domain specific problems. Variable state independent decaying sum vsids still is the dominant branching heuristics because of its low cost.
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