We describe the design, implementation, and empirical evaluation of some automated exercises that we are using in a lecture on Constraint Programming. Topics are propositional satisfiability, resolution, the DPLL algorithm, with extension to DPLL(T), and FD solving with arc consistency. The automation consists of a program for grading student answers, and in most cases also a program for genera...

We present a new Simplex-based linear arithmetic solver that can be integrated efficiently in the DPLL(T ) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of theory propagation. We also present a new and simple approach for solving strict inequalities. Experi...

We present a new Simplex-based linear arithmetic solver that can be integrated efficiently in the DPLL(T ) framework. The new solver improves over existing approaches by enabling fast backtracking, supporting a priori simplification to reduce the problem size, and providing an efficient form of theory propagation. We also present a new and simple approach for solving strict inequalities. Experi...

This paper describes a knowledge-based robot that explores an unknown environment for an unpredictable goal. Distinguishing characteristics of such environments for robotic navigation are that the goal’s position is unpredictable and some obstacles cannot be sensed directly. Considering such features we propose a search algorithm for finding the goal and a simplified DPLL to allow robotic reaso...

The paper is concerned with the computational evaluation of a new branching heuristic, called reverse assignment sequence (RAS), for evolved DPLL Satisfiability solvers. Such heuristic, like several other recent ones, is based on the history of the conflicts obtained during the solution of an instance. A score is associated to each literal. When a conflict occurs, some scores are incremented wi...

We present GDPLL, a generalization of the DPLL procedure. It solves the satisfiability problem for decidable fragments of quantifier-free firstorder logic. Sufficient properties are identified for proving soundness, termination and completeness of GDPLL. We show how the original DPLL procedure is an instance. Subsequently the GDPLL instances for equality logic, and the logic of equality over in...

A method to calculate the average size of Davis-PutnamLoveland-Logemann (DPLL) search trees for random computational problems is introduced, and applied to the satisfiability of random CNF formulas (SAT) and the coloring of random graph (COL) problems. We establish recursion relations for the generating functions of the average numbers of (variable or color) assignments at a given height in the...