Demonic fixed points

We deal with a relational model for the demonic semantics of programs. The demonic semantics of a while loop is given as a fixed point of a function involving the demonic operators. This motivates us to investigate the fixed points of these functions. We give the expression of the greatest fixed point with respect to the demonic ordering (demonic inclusion) of the semantic function. We prove that this greatest fixed coincides with the least fixed point with respect to the usual ordering (angelic inclusion) of the same function. This is followed by an example of application

Relational Demonic Fuzzy Refinement

We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join (⊔fuz), fuzzy demonic meet (⊓fuz), and fuzzy demonic composition (□fuz). Our definitions and properties are illustrated by some examples using mathematica software (fuzzy logic)

Nondeterministic Relational Semantics of a while Program

A relational semantics is a mapping of programs to relations. We consider that the input-output semantics of a program is given by a relation on its set of states; in a nondeterministic context, this relation is calculated by considering the worst behavior of the program (demonic relational semantics). In this paper, we concentrate on while loops. Calculating the relational abstraction (semantics) of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For functional programs, Mills has described a checking method known as the while statement verification rule. A programming theorem for iterative constructs is proposed, proved, demonstrated and applied for an example. This theorem can be considered as a generalization of the while statement verification to nondeterministic loops.&nbsp

Some notes on a second-order random boundary value problem

We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution

Quelques propriétés des opérateurs doublement stochastiques

Depuis leur introduction dans la littérature, plusieurs travaux ont traité des propriétés des matrices doublement stochastiques, mais indiscutablement ce sont deux théorèmes fondamentaux, prouvés par HARDY LITTLEWOOD et POLYA en 1929 et par G.BIRKHOFF en 1946, qui ont dominé ce champ d'étude. D'une façon générale le présent travail consiste à présenter ces deux théorèmes pour le cas discret et pour le cas continu. Après avoir rappelé quelques résultats sur les treillis, nous allons présenter certaines notions sur les classes de matrices positives, en particulier les deux théorèmes fondamentaux pour le cas fini. Cette étude est ensuite complétée par la présentation de ces deux théorèmes pour des classes de matrices positives infinies. En dernier lieu, nous avons achevé ce travail en nous attardant sur les propriétés des opérateurs doublement stochastiques et plus précisément sur leur approximation et sur l'étude de leurs points extrêmes ainsi que sur la généralisation du théorème de HARDY LITTLEWOOD et POLYA dans ce contexte

Quelques propriétés des opérateurs doublement stochastiques

Depuis leur introduction dans la littérature, plusieurs travaux ont traité des propriétés des matrices doublement stochastiques, mais indiscutablement ce sont deux théorèmes fondamentaux, prouvés par HARDY LITTLEWOOD et POLYA en 1929 et par G.BIRKHOFF en 1946, qui ont dominé ce champ d'étude. D'une façon générale le présent travail consiste à présenter ces deux théorèmes pour le cas discret et pour le cas continu. Après avoir rappelé quelques résultats sur les treillis, nous allons présenter certaines notions sur les classes de matrices positives, en particulier les deux théorèmes fondamentaux pour le cas fini. Cette étude est ensuite complétée par la présentation de ces deux théorèmes pour des classes de matrices positives infinies. En dernier lieu, nous avons achevé ce travail en nous attardant sur les propriétés des opérateurs doublement stochastiques et plus précisément sur leur approximation et sur l'étude de leurs points extrêmes ainsi que sur la généralisation du théorème de HARDY LITTLEWOOD et POLYA dans ce contexte

Software testing: concepts and operations

Explores and identifies the main issues, concepts, principles and evolution of software testing, including software quality engineering and testing concepts, test data generation, test deployment analysis, and software test managementThis book examines the principles, concepts, and processes that are fundamental to the software testing function. This book is divided into five broad parts. Part I introduces software testing in the broader context of software engineering and explores the qualities that testing aims to achieve or ascertain, as well as the lifecycle of software testing. Part II

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

summary:This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme

Kleene under a demonic star

In relational semantics, the input-output semantics of a program is a relation on its set of states. We generalize this in considering elements of Kleene algebras as semantical values. In a nondeterministic context, the demonic semantics is calculated by considering the worst behavior of the program. In this paper, we concentrate on while loops. Calculating the semantics of a loop is difficult, but showing the correctness of any candidate abstraction is much easier. For deterministic programs, Mills has described a checking method known as the while statement verification rule. A corresponding programming theorem for nondeterministic iterative constructs is proposed, proved and applied to an example. This theorem can be considered as a generalization of the while statement verification rule to nondeterministic loops