On the relations between SAT and CSP enumerative algorithms

AbstractWe show the equivalence between the so-called Davis–Putnam procedure (Davis et al., Comm. ACM 5 (1962) 394–397; Davis and Putnam (J. ACM 7 (1960) 201–215)) and the Forward Checking of Haralick and Elliot (Artificial Intelligence 14 (1980) 263–313). Both apply the paradigm choose and propagate in two different formalisms, namely the propositional calculus and the constraint satisfaction problems formalism. They happen to be strictly equivalent as soon as a compatible instantiation order is chosen. This equivalence is shown considering the resolution of the clausal expression of a CSP by the Davis–Putnam procedure

Computing stable models by program transformation

In analogy to the Davis--Putnam procedure we develop a new procedure for computing stable models of propositional normal disjunctive logic programs, using case analysis and simplification. Our procedure enumerates all stable mofels without repetition and without the need for a minimality check. Since it is not necessary to store the set of stable models explicitly, the procedure runs in polynomial space. We allow clauses with empty heads, in order to represent truth or falsity of a proposition as a one--literal clause. In particular, a clause of form $\sim A \rightarrow$ expresses that $A$ is contrained to be true, without providing a justification for $A$. Adding this clause to a program restricts its stable models to those containing A, without introducing new stable models. Together with $A \rightarrow$ this provides the basis for case analysis. We present our procedure as a set of rules which transform a program into a set of solved forms, which resembles the standard method for presenting unification algorithms. Rules are sound in the sense that they preserve the set of stable models. $A$ subset of the rules is shown to be complete in the sense that for each stable model a solved form can be obtained. The method allows for concise presentation, flexible choice of a control strategy and simple correctness proofs

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan

Science Teacher Learning of MBL-Supported Student-Centered Science Education in the Context of Secondary Education in Tanzania

Science teachers from secondary schools in Tanzania were offered an in-service arrangement to prepare them for the integration of technology in a student-centered approach to science teaching. The in-service arrangement consisted of workshops in which educative curriculum materials were used to prepare teachers for student-centered education and for the use and application of Microcomputer Based Laboratories (MBL)—a specific technology application for facilitating experiments in science education. Quantitative and qualitative data were collected to study whether the in-service arrangement impacted teacher learning. Teacher learning was determined by three indicators: (1) the ability to conduct MBL-supported student centered science lessons, (2) teachers’ reflection on those lessons and (3) students’ perceptions of the classroom environment. The results of the research indicate that the teachers’ were able to integrate MBL in their science lessons at an acceptable level and that they were able to create a classroom environment which was appreciated by their students as more investigative and open-ended

GRASP: A New Search Algorithm for Satisfiability

This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances

Spartan Daily, November 13, 2014

Volume 143, Issue 32https://scholarworks.sjsu.edu/spartandaily/1531/thumbnail.jp

Towards Understanding and Harnessing the Potential of Clause Learning

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas

On the possible Computational Power of the Human Mind

The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of Liverpool, UK. 23 page