Boolean and Finite Domain Solvers Compared Using Self Referential Quizzes

A Hybrid BDD and SAT Finite Domain Constraint Solver

Finite-domain constraint solvers based on Binary Decision Diagrams (BDDs) are a powerful technique for solving constraint problems over finite set and integer variables represented as Boolean formulæ. Boolean Satisfiability (SAT) solvers are another form of constraint solver that operate on constraints on Boolean variables expressed in clausal form. Modern SAT solvers have highly optimized prop...

Propagation = Lazy Clause Generation

Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how we can mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This immediately results in strong nogoods for finite domain propagation. But a naive static translati...

Mapping Problems with Finite-Domain Variables into Problems with Boolean Variables

We define a collection of mappings that transform many-valued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks with state-of-the-art SAT solvers. Our results provide empirical evidence that encoding combinatorial problems with the mappings defined here can lead to substantial performance improvement...

Don't Be Puzzled!

This paper is about how to solve a class of puzzles, called self-referential quizzes (srq), with constraint programming. An srq is a sequence of multiple choice questions that are about the puzzle itself. srqs are an attractive pastime, when they provide the possibility of drawing non-trivial conclusions on the way to the solution. We introduce a typical srq, and represent it as a propositional...

Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements