The theory of NP-completeness has its roots in a foundational result by Cook, who showed that Boolean satisfiability (SAT) is NP-complete and thus unlikely to admit an efficient solution. We prove an analogous result using binary integer programming in the place of SAT. The proof gives deeper insight into the theory of NP-completeness to operations researchers for whom the language of integer p...

The Veri ed Programming Language Implementation project has developed a formally veri ed implementation of the Scheme programming language. This report documents the byte-code interpreter, which executes a user program presented in the form of a binary image. It speci es several intermediate abstract machines, and proves that they are (successive) faithful implementations of the Vlisp operation...

A standard trick in integer programming is to replace each bounded integer-constrained variable with a small number of binary variables, using the bit representation of the given variable. We show that, in the case of mixed-integer quadratic programs (MIQPs), this process can enable one to obtain stronger linear programming relaxations. Moreover, we give a simple sufficient condition under whic...

Thread level parallelism (TLP) is a key technology to coming generation of high performance processors. Although it provides higher processing capability, the loss of compatibility with existing processors is a crucial issue. This research is motivated by the following two points: (1) TLP requires multithread programming which is rather di cult for ordinary programmers, or complexed compilation...

Rank K Binary Matrix Factorization (BMF) approximates a binary matrix by the product of two binary matrices of lower rank, K, using either L1 or L2 norm. In this paper, we first show that the BMFwithL2 norm can be reformulated as an Unconstrained Binary Quadratic Programming (UBQP) problem. We then review several local search strategies that can be used to improve the BMF solutions obtained by ...

Constraint programming is gaining a great deal of attention because many combinatorial problems especially in areas of planning and scheduling can be expressed in a natural way as a Constraint Satisfaction Problem (CSP). It is well known that a non-binary CSP can be transformed into an equivalent binary CSP using some of the actual techniques. However, when the CSP is not discrete or the number...

Hoare and He’s unifying theories of programming (UTP) is a model of alphabetised relations expressed as predicates, which supports development in several programming paradigms. The aim is the unification of languages and techniques, so that we can benefit from results in different contexts. In this paper, we investigate the integration of angelic nondeterminism in the UTP; we propose the unific...