A Note on Compiling Arithmetic Expressions

A Note on Arithmetic Constraint Propagation

We consider the resolution by constraint programming of large problems, i.e. involving millions of constraints, which mainly imply arithmetic constraints, like shortest path problems or other related problems. We show that a simple constraint programming model is not competitive with dedicated algorithms (or dedicated constraints). This mainly comes from the propagation mechanism, i.e. the orde...

A Note on Rational Arithmetic Functions

A Note on Bootstrapping Intuitionistic Bounded Arithmetic

This paper, firstly, discusses the relationship between Buss’s definition and Cook and Urquhart’s definition of BASIC axioms and of IS 2 . The two definitions of BASIC axioms are not equivalent; however, each intuitionistically implies the law of the excluded middle for quantifier-free formulas. There is an elementary proof that the definitions of IS 2 are equivalent which is not based on reali...

A Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

Compiling Array Expressions for Efficient Execution on Distributed-Memory Machines

Array statements are often used to express data-parallelism in scientiic languages such as Fortran 90 and High Performance Fortran. In compiling array statements for a distributed-memory machine, eecient generation of communication sets and local index sets is important. We show that for arrays distributed block-cyclically on multiple processors, the local memory access sequence and communicati...