Programming Telepathy: Implementing Quantum Non-Locality Games

Quantum pseudo-telepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum non-locality games. The setting of these games is as follows: the players are separated so that no communication between them is possible and are given a certain computational task. When the players have access to a quantum resource called entanglement, they can accomplish the task: something that is impossible in a classical setting. To an observer who is unfamiliar with the laws of quantum mechanics it seems that the players employ some sort of telepathy; that is, they somehow exchange information without sharing a communication channel. This paper provides a formal framework for specifying, implementing, and analysing quantum non-locality games

Logic programming with pseudo-Boolean constraints

Boolean constraints play an important role in various constraint logic programming languages. In this paper we consider pseudo-Boolean constraints, that is equations and inequalities between pseudo-Boolean functions. A pseudo-Boolean function is an integer-valued function of Boolean variables and thus a generalization of a Boolean function. Pseudo-Boolean functions occur in many application areas, in particular in problems from operations research. An interesting connection to logic is that inference problems in propositional logic can be translated into linear pseudo-Boolean optimization problems. More generally, pseudo-Boolean constraints can be seen as a particular way of combining two of the most important domains in constraint logic programming: arithmetic and Boolean algebra. In this paper we define a new constraint logic programming language {\em CLP(PB)} for logic progamming with pseudo-Boolean constraints. The language is an instance of the general constraint logic programming language scheme {\em CLP(X)} and inherits all the typical semantic properties. We show that any pseudo-Boolean constraint has a most general solution and give variable elimination algorithms for pseudo-Boolean unification and unconstrained pseudo-Boolean optimization. Both algorithms subsume the well-known Boolean unification algorithm of B\"uttner and Simonis

A polynomial-time algorithm for optimization of quadratic pseudo-boolean functions

We develop a polynomial-time algorithm to minimize pseudo-Boolean functions. The computational complexity is O(n □(15/2)), although very conservative, it is su_cient to prove that this minimization problem is in the class P. A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O(n □(45/2)). The algorithm was implemented in MATLAB and checked by generating one million matrices of arbitrary dimension up to 24 with random entries in the range [-50; 50]. All the experiments were successful