Efficiently Calculating Evolutionary Tree Measures Using SAT

We develop techniques to calculate important measures in evolutionary biology by encoding to CNF formulas and using powerful SAT solvers. Comparing evolutionary trees is a necessary step in tree reconstruction algorithms, locating recombination and lateral gene transfer, and in analyzing and visualizing sets of trees. We focus on two popular comparison measures for trees: the hybridization number and the rooted subtree-prune-and-regraft (rSPR) distance. Both have recently been shown to be NP-hard, and effcient algorithms are needed to compute and approximate these measures. We encode these as a Boolean formula such that two trees have hybridization number k (or rSPR distance k) if and only if the corresponding formula is satisfiable. We use state-of-the-art SAT solvers to determine if the formula encoding the measure has a satisfying assignment. Our encoding also provides a rich source of real-world SAT instances, and we include a comparison of several recent solvers (minisat, adaptg2wsat, novelty+p, Walksat, March KS and SATzilla).Postprint (author’s final draft

SmArT solving: Tools and techniques for satisfiability solvers

The satisfiability problem (Sat) lies at the core of the complexity theory. This is a decision problem: Not the solution itself, but whether or not a solution exists given a specified set of requirements is the central question. Over the years, the satisfiability problem has taken center stage as a means of effective representation to tackle problems with different characteristics: Many problems can first be translated into Sat and then solved by means of software dedicated to the Sat problem. Due to the increasing power of these Sat solvers, the number of applications climbs every year. Examples of this kind of translatable problems are scheduling problems, verification of software and hardware, bounded model checking and a wide variety of mathematical puzzles. Sat solvers come in two flavors: Complete and incomplete. Complete solvers systematically go over the whole search space and are able to determine with certainty whether a solution exists. Incomplete Sat solvers look for a solution at a venture. They dont follow a system, yet they might hit a solution. Most complete Sat solvers are based on the ConflictDriven architecture. At a dead end, they analyze what went wrong and where in the search space it happened. Then they resume the search from there. Conflict-driven solvers make relatively cheap decisions (in terms of computational costs), which enables them to search the space swiftly. Only a few complete Sat solvers are based on an architecture that chooses its battles, so to speak. The LookAhead architecture peers further into the search space before making the next move. Look-ahead solvers make expensive decisions in order to keep the search space as small as possible. Incomplete Sat solvers have a dominant and a rare type of architecture as well. The commonly used WalkSat makes cheap decisions, while UnitWalk a bit off the wall makes more costly moves. This thesis deals with a number of contributions to the development of Sat solvers both complete and incomplete. With the adagium poundwise, Pennyfoolish in mind, its focus is primarily set on both rare, more expensive approaches. On one hand, expensive procedures are implemented efficiently to reduce their relative costs, while they maintain their impact on the search space. On the other hand, building up reasoning power further limits the search space. The growing attention for Sat solvers generates a growing group of users. More and more of them will not be familiar with the specific ins and outs of their application, which makes it difficult to tune the Sat solvers. Here, adaptive heuristics may be of use. Given a specific problem, these heuristics set the parameters in such a way that the solver performs (almost) optimally. This thesis presents some elegant adaptive heuristics for a technique that looks even further ahead into the search area to learn even more: The DoubleLook procedure. Thanks to these adaptive heuristics that keep on fine-tuning the parameters on the fly this binocular-technique can be helpful to solve more problems. The raison dÊtre of incomplete Sat solvers is the assumption that on many problems, they find a solution faster than complete solvers. Yet they are only superior within a certain niche; they work well on big (random) problems. To extend the span of incomplete Sat solvers, this thesis presents a Sat solver with the more rarely used UnitWalk architecture. Several expensive calculations are run simultaneously on a single processor which keeps costs relatively low. In addition, the solver features some communicative skills: Whenever a solution is found for part of the problem, all further calculations will run more efficiently. Despite these enhancements and its good results, this solver is not (yet) competitive on structured problems; an field dominated by complete Sat solvers. However, our complete Sat solver march, based on the LookAhead architecture, has won many awards in the prestigious Sat competitions, among which the gold medal for random problems without solutions (2007); a traditional stronghold of LookAhead solvers. More intriguing is the gold medal for crafted problems with solutions (2007). This is a field which is dominated besides march by conflict-driven solvers. In conclusion, the new techniques presented in this thesis have enhanced the LookAhead architecture to such an extend, that this type of solvers can compete on more problems while sustaining dominance on random instances.Electrical Engineering, Mathematics and Computer Scienc

SAT-Inspired Eliminations for Superposition

Optimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to firstorder logic with equality. In this paper, we port inprocessing techniques to work with superposition, a leading first-order proof calculus, and we strengthen known preprocessing techniques. Specifically, we look into elimination of hidden literals, variables (predicates), and blocked clauses. Our evaluation using the Zipperposition prover confirms that the new techniques usefully supplement the existing superposition machinery.22312401

Using a satisfiability solver to identify deterministic finite state automata

We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach seems to be competitive with alternative techniques. Our contributions are threefold: First, we propose a compact translation of DFA identification into SAT. Second, we reduce the SAT search space by adding lower bound information using a fast max-clique approximation algorithm. Third, we include many redundant clauses to provide the SAT solver with some additional knowledge about the problem. Experiments on a well-known suite of random DFA identification problems show that SAT solvers can efficiently tackle all instances. Moreover, our exact algorithm outperforms state-of-the-art techniques on several hard problems.Software Computer TechnologyElectrical Engineering, Mathematics and Computer Scienc

March dl: Adding Adaptive Heuristics and a New Branching Strategy

We introduce the march dl satisability (SAT) solver, a successor of march eq. The latter was awarded state-of-the-art in two categories during the Sat 2004 competition. The focus lies on presenting those features that are new in march dl. Besides a description, each of these features is illustrated with some experimental results. By extending the pre-processor, using adaptive heuristics, and by using a new branching strategy, march dl is able to solve nearly all benchmarks faster than its predecessor. Moreover, various instances which were beyond the reach of march eq, can now be solved - relatively easily - due to these new features.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc

Whose side are you on?: Finding solutions in a biased search-tree

We introduce a new jump strategy for look-ahead based satisfiability (Sat) solvers that aims to boost their performance on satisfiable formulae, while maintaining their behavior on unsatisfiable instances. Direction heuristics select which Boolean value to assign to a decision variable. They are used in various state-of-the-art Sat solvers and may bias the distribution of solutions in the search-tree. This bias can clearly be observed on hard random k-Sat formulae. While alternative jump / restart strategies are based on exploring a random new part of the search-tree, the proposed one examines a part that is more likely to contain a solution based on these observations. Experiments with - so-called distribution jumping - in the march ks Sat solver, show that this new technique boosts the number of satisfiable formulae it can solve. Moreover, it proved essential for winning the satisfiable crafted category during the Sat 2007 competition.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc

Parallel SAT Solving using Bit-level Operations

We show how to exploit the 32/64 bit architecture of modern computers to accelerate some of the algorithms used in satisfiability solving by modifying assignments to variables in parallel on a single processor. Techniques such as random sampling demonstrate that while using bit vectors instead of Boolean values solutions to satisfiable formulae can be obtained faster. Here, we reveal that more complex algorithms, like unit propagation and detection of autarkies, can be parallelized efficiently, as well. We capitalize on the developed parallel algorithms by modifying the state-of-the-art local search Sat solver UnitWalk accordingly. Experiments show that the parallel version performs much faster than the original implementation.Software TechnologyElectrical Engineering, Mathematics and Computer Scienc