Answer Set Programming (ASP) is a declarative programming paradigm. The intrinsic complexity of the evaluation of ASP programs makes the development of more effective and faster systems a challenging research topic. This paper reports on the recent improvements of the ASP solver WASP. WASP is undergoing a refactoring process which will end up in the release of a new and more performant version of the software. In particular the paper focus on the improvements to the core evaluation algorithms working on normal programs. A preliminary experiment on benchmarks from the 3rd ASP competition belonging to the NP class is reported. The previous version of WASP was often not competitive with alternative solutions on this class. The new version of WASP shows a substantial increase in performance.
Some of these techniques were already adapted in non-disjunctive ASP solvers like Smodels @math @cite_15 , @cite_12 , Smodels @cite_11 , @cite_14 , and @cite_4 . More in detail, differs from @cite_14 that are based on a rewriting into a propositional formula and an external SAT solver. differs from @cite_0 and the Smodels variants, which features a native implementation of all inference rules. Our new solver is more similar to , but there are differences concerning the restart policy, constraint deletion and branching heuristics. adopts as default a policy based on the sequence of thresholds introduced in @cite_1 , whereas employs by default a different policy based on geometric series. Concerning deletion of learned constraints, adopts a criterion inspired by , while implements a technique introduced in Glucose @cite_5 . Moreover, adopts a branching heuristic based on BerkMin @cite_17 with a variant of the MOMS criterion which estimates the effect of the candidate literals in short clauses.
@cite_14 @cite_4 @cite_1 @cite_17 @cite_0 @cite_5 @cite_15 @cite_12 @cite_11
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We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. In this dissertation we show how conflict clause learning, a technique that has been very useful in improving the efficiency of Boolean logic satisfiability search, can be adapted to speed up dramatically the search for models of answer set programs. Answer set programming is a knowledge representation paradigm related to the areas of logic programming and nonmonotonic reasoning. Many of the applications of answer set programming come from the areas of artificial intelligence-related diagnosis and planning. The problem of finding an answer set for a normal or extended logic program is NP-hard. Current complete answer set solvers are patterned after the Davis-Putnam-Loveland-Logemann ( DPLL) algorithm for solving Boolean satisfiability (SAT) problems, but are adapted to the nonmonotonic semantics of answer set programming. Recent SAT solvers include improvements to the DPLL algorithm. Conflict clause learning has been particularly effective in this regard. A conflict clause represents a backtracking solver's analysis of why a conflict occurred. This analysis can be used to further prune the search space and to direct the search heuristic. The use of such clauses has improved significantly the efficiency of satisfiability solvers over the past few years, especially on structured problems arising from applications. In this dissertation we describe how we have adapted conflict clause techniques for use in the answer set solver Smodels. We experimentally compare the performance of the resulting program, Smodelscc, to that of the original Smodels program. Our tests show dramatic speedups for Smodelscc on a wide range of problems. We also compare the performance of Smodelscc with that of two other recent answer set solvers, ASSAT and Cmodels-2. ASSAT and Cmodels-2 directly call Boolean satisfiability solvers in order to search for answer sets. On so-called “non-tight” problems, Smodelscc showed substantially better performance than these solvers. The performance advantage that Smodels cc enjoys on non-tight problems is due to the unfounded set test that Smodelscc inherits from the Smodels solver, and the fact that this test is executed frequently throughout the program's search for answer sets. In this paper, we present a divide-and-conquer SAT solver, MapleAmpharos, that uses a novel propagation-rate (PR) based splitting heuristic. The key idea is that we rank variables based on the ratio of how many propagations they cause during the run of the worker conflict-driven clause-learning solvers to the number of times they are branched on, with the variable that causes the most propagations ranked first. The intuition here is that, in the context of divide-and-conquer solvers, it is most profitable to split on variables that maximize the propagation rate. Our implementation MapleAmpharos uses the AMPHAROS solver as its base. We performed extensive evaluation of MapleAmpharos against other competitive parallel solvers such as Treengeling, Plingeling, Parallel CryptoMiniSat5, and Glucose-Syrup. We show that on the SAT 2016 competition Application benchmark and a set of cryptographic instances, our solver MapleAmpharos is competitive with respect to these top parallel solvers. What is surprising that we obtain this result primarily by modifying the splitting heuristic. where (an)n ENo is some sequence of nonnegative numbers, (Sn),nENo is the sequence of partial sums, S0 = 0, Sn = XflXk, of another sequence (Xk)kEN of i.i.d. random variables, and A c R is a fixed Borel set such as [0,1] or [0, oo). Examples of such convolution series are subordinated distributions (f=0Oan = 1) which arise as distributions of random sums, and harmonic and ordinary renewal measures (a0 = 0, an = 1 n for all n C N in the first, an = 1 for all n C NO in the second case). These examples are in turn essential for the analysis of the large time behaviour of diverse applied models such as branching and queueing processes, they are also of interest in connection with representation theorems such as the Levy representation of infinitely divisible distributions. A traditional approach to such problems is via regular variation: If the underlying random variables are nonnegative we can use Laplace transforms and the related Abelian and Tauberian theorems [see, e.g., Stam (1973) in the context of subordination and Feller (1971, XIV.3) in connection with renewal theory; Embrechts, Maejima, and Omey (1984) is a recent treatment of generalized renewal measures along these lines]. The approach of the present paper is based on the Wiener-Levy-Gel'fand theorem and has occasionally been called the Banach algebra method. In Gruibel (1983) we gave a new variant of this method for the special case of lattice distributions, showing that by using the appropriate Banach algebras of sequences, arbitrarily fine expansions are possible under certain assumptions on the higher-order differences of (P(X1 = n))fnEN. Here we give a corresponding treatment of nonlattice distributions. We restrict ourselves to an analogue of first-order differences and obtain a number of theorems which perhaps are described best as next-term results. To explain this let us consider a special case in more detail. Horn clause logic programming can be extended to include abduction with integrity constraints. In the resulting extension of logic programming, negation by failure can be simulated by making negative conditions abducible and by imposing appropriate denials and disjunctions as integrity constraints. This gives an alternative semantics for negation by failure, which generalises the stable model semantics of negation by failure. The abductive extension of logic programming extends negation by failure in three ways: (1) computation can be perfonned in alternative minimal models, (2) positive as well as negative conditions can be made abducible, and (3) other integrity constraints can also be accommodated. * This paper was written while the first author was at Imperial College. 235 Introduction The tenn "abduction" was introduced by the philosopher Charles Peirce [1931] to refer to a particular kind of hypothetical reasoning. In the simplest case, it has the fonn: From A and A fB infer B as a possible "explanation" of A. Abduction has been given prominence in Charniak and McDennot's [1985] "Introduction to Artificial Intelligence", where it has been applied to expert systems and story comprehension. Independently, several authors have developed deductive techniques to drive the generation of abductive hypotheses. Cox and Pietrzykowski [1986] construct hypotheses from the "dead ends" of linear resolution proofs. Finger and Genesereth [1985] generate "deductive solutions to design problems" using the "residue" left behind in resolution proofs. Poole, Goebel and Aleliunas [1987] also use linear resolution to generate hypotheses. All impose the restriction that hypotheses should be consistent with the "knowledge base". Abduction is a fonn of non-monotonic reasoning, because hypotheses which are consistent with one state of a knowledge base may become inconSistent when new knowledge is added. Poole [1988] argues that abduction is preferable to noh-monotonic logics for default reasoning. In this view, defaults are hypotheses fonnulated within classical logic rather than conclusions derived withln some fonn of non-monotonic logic. The similarity between abduction and default reasoning was also pointed out in [Kowalski, 1979]. In this paper we show how abduction can be integrated with logic programming, and we concentrate on the use of abduction to generalise negation by failure. Conditional Answers Compared with Abduction In the simplest case, a logic program consists of a set of Horn Clauses, which are used backward to_reduce goals to sub goals. The initial goal is solved when there are no subgollls left; Mulmuley [Mul12a] recently gave an explicit version of Noether’s Normalization lemma for ring of invariants of matrices under simultaneous conjugation, under the conjecture that there are deterministic black-box algorithms for polynomial identity testing (PIT). He argued that this gives evidence that constructing such algorithms for PIT is beyond current techniques. In this work, we show this is not the case. That is, we improve Mulmuley’s reduction and correspondingly weaken the conjecture regarding PIT needed to give explicit Noether Normalization. We then observe that the weaker conjecture has recently been nearly settled by the authors ([FS12]), who gave quasipolynomial size hitting sets for the class of read-once oblivious algebraic branching programs (ROABPs). This gives the desired explicit Noether Normalization unconditionally, up to quasipolynomial factors. As a consequence of our proof we give a deterministic parallel polynomial-time algorithm for deciding if two matrix tuples have intersecting orbit closures, under simultaneous conjugation. We also study the strength of conjectures that Mulmuley requires to obtain similar results as ours. We prove that his conjectures are stronger, in the sense that the computational model he needs PIT algorithms for is equivalent to the well-known algebraic branching program (ABP) model, which is provably stronger than the ROABP model. Finally, we consider the depth-3 diagonal circuit model as defined by Saxena [Sax08], as PIT algorithms for this model also have implications in Mulmuley’s work. Previous work (such as [ASS12] and [FS12]) have given quasipolynomial size hitting sets for this model. In this work, we give a much simpler construction of such hitting sets, using techniques of Shpilka and Volkovich [SV09]. We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method by providing a new SDP-hierarchy based algorithm for constraint satisfaction problems with 2-variable constraints (2-CSP's). More concretely, we show for every 2-CSP instance I a rounding algorithm for r rounds of the Lasserre SDP hierarchy for I that obtains an integral solution that is at most worse than the relaxation's value (normalized to lie in [0,1]), as long as r > k ( ) ( ) ;, where k is the alphabet size of I, @math , and @math denotes the number of eigenvalues larger than @math in the normalized adjacency matrix of the constraint graph of @math . In the case that @math is a instance, the threshold @math is only a polynomial in @math , and is independent of the alphabet size. Also in this case, we can give a non-trivial bound on the number of rounds for instance. In particular our result yields an SDP-hierarchy based algorithm that matches the performance of the recent subexponential algorithm of Arora, Barak and Steurer (FOCS 2010) in the worst case, but runs faster on a natural family of instances, thus further restricting the set of possible hard instances for Khot's Unique Games Conjecture. Our algorithm actually requires less than the @math constraints specified by the @math level of the Lasserre hierarchy, and in some cases @math rounds of our program can be evaluated in time @math . Model checking and counter-example guided abstraction refinement are examples of applications of SAT solving requiring the production of models for satisfiable formulas. Better than giving a truth value to every variable, one can provide an implicant, i.e. a partial assignment of the variables such that every full extension is a model for the formula. An implicant is prime if every assignment is necessary. Since prime implicants contain no literal irrelevant for the satisfiability of the formula, they are considered as highly refined information. We here propose a novel algorithm that uses data structures found in modern CDCL SAT solvers to efficiently compute prime implicants starting from an existing model. The original aspects are (1) the algorithm is based on watched literals and a form of propagation of required literals, adapted to CDCL solvers (2) the algorithm works not only on clauses, but also on generalized constraints (3) for clauses and, more generally for cardinality constraints, the algorithm complexity is linear in the size of the constraints found. We implemented and evaluated the algorithm with the Sat4j library. The paper focuses on the problems of passive and active FSM inference as well as checking sequence generation. We consider the setting where an FSM cannot be reset so that its inference is constrained to a single trace either given a priori in a passive inference scenario or to be constructed in an active inference scenario or aiming at obtaining checking sequence for a given FSM. In each of the last two cases, the expected result is a trace representing a checking sequence for an inferred machine, if it was not given. We demonstrate that this can be achieved by a repetitive use of a procedure that infers an FSM from a given trace (identifying a minimal machine consistent with a trace) avoiding equivalent conjectures. We thus show that FSM inference and checking sequence construction are two sides of the same coin. Following an existing approach of constructing conjectures by SAT solving, we elaborate first such a procedure and then based on it the methods for obtaining checking sequence for a given FSM and inferring a machine from a black box. The novelty of our approach is that it does not use any state identification facilities. We demonstrate that the proposed approach can also be constrained to find a solution in a subset of FSMs represented by a nondeterministic mutation machine. Experiments with a prototype implementation of the developed approach using an existing SAT solver indicate that it scales for FSMs with up to a dozen of states and requires relatively short sequences to identify a black box machine.