SPIRAL is an autotuning, program generation and code synthesis system that offers a fully automatic generation of highly optimized target codes, customized for the specific execution platform at hand. Initially, SPIRAL was targeted at problem domains in digital signal processing, later also at basic linear algebra. We open SPIRAL up to a new, practically relevant and challenging domain: multigr...

A technique for generating invariant polynomial inequalities of bounded degree is presented using the abstract interpretation framework. It is based on overapproximating basic semi-algebraic sets, i.e., sets defined by conjunctions of polynomial inequalities, by means of convex polyhedra. While improving on the existing methods for generating invariant polynomial equalities, since polynomial in...

In this paper we have illustrated methods to address three types of problems in static analysis for Ada tasking: quantitative questions, safety problems and MAYhappen event problems. We have applied a two-phase methodology to automate analysis: first deriving a semantically rich model independent of any specific analysis issue, that is the original Ada nets, and then manipulating this model wit...

Algebraic specification languages have been successfully used for the formal specification of abstract data types (ADTs) and software components, and there are several approaches to automatically derive test cases that check the conformity between the implementation and the algebraic specification of a software component. However, existing approaches do not assure the coverage of conditional ax...

The polyhedral model is a powerful framework for automatic optimization and parallelization. It is based on an algebraic representation of programs, allowing to construct and search for complex sequences of optimizations. This model is now mature and reaches production compilers. The main limitation of the polyhedral model is known to be its restriction to statically predictable, loop-based pro...

Nowadays, water and electricity are closely interdependent essential sources in human life that affect socio-economic growth and prosperity. In other words, electricity is a fundamental source to supply a seawater desalination process, while fresh water is used for cooling this power plant. Therefore, mutual vulnerability of water treatment and power generation systems is growing because of inc...

This paper presents a method for generating semi-algebraic invariants for systems governed by non-linear polynomial ordinary differential equations under semi-algebraic evolution constraints. Based on the notion of discrete abstraction, our method eliminates unsoundness and unnecessary coarseness found in existing approaches for computing abstractions for non-linear continuous systems and is ab...

.This paper presents two approaches for planar grid generation. One of them is algebraic and it is based on equality of quad areas and the other one is an improved direct optimization method. The idea of the paper is to provide a fast algorithm for mesh generation to do a more realistic simulation of massspring models. Results and conclusions are presented at the end of the paper.

Animation of execution is a necessary feature of source level debuggers We present a framework where animators are generated from existing algebraic speci cations of interpreters To this end a pattern matching mechanism is used in conjunction with origin tracking a generic tracing technique The generation of animators is illustrated using an example language named CLaX a Pascal relative We stud...

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...