The IntSat method for integer linear programming

Conflict-Driven Clause-Learning (CDCL) SAT solvers can automatically solve very large real-world problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, here we introduce IntSat, a generalization of CDCL to Integer Linear Programming (ILP). Our simple 1400-line C++ prototype IntSat implementation already shows some competitiveness with commercial solvers such as CPLEX or Gurobi. Here we describe this new IntSat ILP solving method, show how it can be implemented efficiently, and discuss a large list of possible enhancements and extensions.Postprint (author’s final draft

07401 Abstracts Collection -- Deduction and Decision Procedures

From 01.10. to 05.10.2007, the Dagstuhl Seminar 07401 ``Deduction and Decision Procedures\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper

10161 Abstracts Collection -- Decision Procedures in Software, Hardware and Bioware

From April 19th, 2010 to April 23rd, 2010, the Dagstuhl Seminar 10161 "Decision Procedures in Soft, Hard and Bio-ware" was held in Schloss Dagstuhl Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as links to slides and links to papers behind the presentations and papers produced as a result of the seminar are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

05431 Abstracts Collection -- Deduction and Applications

From 23.10.05 to 28.10.05, the Dagstuhl Seminar 05431 ``Deduction and Applications\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

SAT Modulo the Theory of Linear Arithmetic: Exact, Inexact and Commercial Solvers

International audienceMany highly sophisticated tools exist for solving linear arith- metic optimization and feasibility problems. Here we analyze why it is difficult to use these tools inside systems for SAT Modulo Theories (SMT) for linear arithmetic: one needs support for disequalities, strict inequalities and, more importantly, for dealing with incorrect results due to the internal use of imprecise floating-point arithmetic. We explain how these problems can be overcome by means of result checking and error recovery policies. Second, by means of carefully designed experiments with, among other tools, the newest version of ILOG CPLEX and our own new Barcelogic T -solver for arithmetic, we show that, interestingly, the cost of result checking is only a small fraction of the total T -solver time. Third, we report on extensive experiments running exactly the same SMT search using CPLEX and Barcelogic as T -solvers, where CPLEX tends to be slower than Barcelogic. We analyze these at first sight surpris- ing results, explaining why tools such as CPLEX are not very adequate (nor designed) for this kind of relatively small incremental problems. Finally, we show how our result checking techniques can still be very use- ful in combination with inexact floating-point-based T -solvers designed for incremental SMT problems

Community development in the school workplace

Purpose – The aim of this study is to explore whether and to what degree community development of teacher teams takes place and how community development comes about, that is, what community-building efforts teacher teams undertake. Design/methodology/approach – Using a multi method approach, quantitative and qualitative data were gathered from seven interdisciplinary teacher teams in a secondary school during one school year. Teachers’ perceptions of community development were complemented with video-observations of team meetings by relative outsiders. Findings – Data showed that the teacher teams undertook a wide variety and amount of community-building efforts. However, community development of the teacher teams as perceived by the teachers was limited. Relative outsiders observed some community development. Practical implications – From the findings the authors conclude that school managers could play a more proactive role in supporting teacher teams’ community-building efforts. Strategies embedding community-building into the culture and policy of the school, including diagnosing, custom-made support and making efforts explicit, could be effective. Originality/value – The current study takes a long-term approach, investigating the community development of teacher teams during the course of one school year. In addition, community development is measured using two perspectives, i.e. that of the community members and that of the relative outsider.NW

Communities of practice in the school workplace

Purpose – The first aim of this study is to explore to what extent communities of practice occur in the school workplace. The second aim is to explore the relation between communities of practice and diversity in composition of teacher teams. Design/methodology/approach – Quantitative as well as qualitative data were gathered from seven teacher teams in a school for secondary education. Questionnaires and observation instruments were used to measure and analyze teacher teams’ collaborative activities and diversity in composition. Findings – Data suggest that communities of practice actually occur in the school workplace, but to a moderate extent. Also, communities of practice are related to four of the five diversity attributes that were investigated. Research limitations/implications – The current study is a snapshot measurement of communities of practice. Future research is recommended to focus on the development of communities of practice in the school workplace by including longitudinal measurements. Practical implications – Implications for teachers and administrators include follow-up activities aimed at stimulating and sustaining communities of practice as well as taking diversity considerations in team composition into account. Originality/value – Studies suggest that a community is a promising context for embedding collaboration into the culture of the school. However, empirical research that focuses on communities in the school workplace seems largely absent. This study provides insight in the occurrence of communities of practice from two perspectives: the perception of community members and the observation from outsiders.NWO-PRO

A parametric approach for smaller and better encodings of cardinality constraints

Adequate encodings for high-level constraints are a key ingredient for the application of SAT technology. In particular, cardinality constraints state that at most (at least, or exactly) k out of n propositional variables can be true. They are crucial in many applications. Although sophisticated encodings for cardinality constraints exist, it is well known that for small n and k straightforward encodings without auxiliary variables sometimes behave better, and that the choice of the right trade-off between minimizing either the number of variables or the number of clauses is highly application-dependent. Here we build upon previous work on Cardinality Networks to get the best of several worlds: we develop an arc-consistent encoding that, by recursively decomposing the constraint into smaller ones, allows one to decide which encoding to apply to each sub-constraint. This process minimizes a function λ·num- vars + num-clauses, where λ is a parameter that can be tuned by the user. Our careful experimental evaluation shows that (e.g., for λ = 5) this new technique produces much smaller encodings in variables and clauses, and indeed strongly improves SAT solvers' performance.Postprint (author’s final draft

Resolvedor SAT, basado en procedimientos Davis-Putnam-Longemann-Loveland

El problema de satisfación de fórmulas lógicas (SAT), es un problema NP-Hard. Una forma de resolverlo es por medio de procedimientos Davis-Putnam-Longemann-Loveland (DPLL), ahora presentamos una implementación de un resolvedor SAT a partir de procedimientos DPLL.The problem of SAT is a problem NP-HARD, a way for solve is by Davis-Putnam-Longemann_Lovelan procedure (DPLL), here there is a SAT solver by this type of procedurePostprint (published version