Least Reflexive Points of Relations

Assume a partially ordered set (S, ≤) and a relation R on S. We consider various sets of conditions in order to determine whether they ensure the existence of a least reflexive point, that is, a least x such that xRx. This is a generalization of the problem of determining the least fixed point of a function and the conditions under which it exists. To motivate the investigation we first present a theorem by Cai and Paige giving conditions under which iterating R from the bottom element necessarily leads to a minimal reflexive point; the proof is by a concise relation-algebraic calculation. Then, we assume a complete lattice and exhibit sufficient conditions, depending on whether R is partial or not, for the existence of a least reflexive point. Further results concern the structure of the set of all reflexive points; among other results we give a sufficient condition that these form a complete lattice, thus generalizing Tarski’s classical result to the nondeterministic case.This research is supported by a grant from NSERC (Natural Sciences and Engineering Research Council of Canada).     

Initiating software process improvement in very small enterprises: Experience with a light assessment tool

The paper concerns software process improvement in Very Small Enterprises (VSEs). It presents briefly a gradual methodology to initiate software process improvement in VSE through three steps approach and develops the first and most original step. This first step is based on a light evaluation achieved by means of a dedicated Micro-Evaluation approach. It has been experimented during 7 years in 86 organizations from three countries. The experience with that utilization tends to show that such a light approach is practicable and promising, at least for the targeted enterprises.     

Honest answers to embarrassing questions: Detecting cheating in the randomized response model.

Surveys and questionnaires are frequently used by psychologists, social scientists, and epidemiologists to collect data about behavior, attitudes, emotions, and so on. However, when asked about sensitive topics such as their sexual behavior or illegal activity, some respondents lie or refuse to answer. The randomized response method was developed to reduce these evasive answer biases by guaranteeing subject privacy. However, the method has been criticized as being susceptible to cheaters, that is, respondents who do not answer as directed by the randomizing device. Here the authors show that by splitting the sample into 2 groups and assigning each group a different randomization probability, it is possible to detect whether significant cheating is occurring and to estimate its extent while simultaneously protecting the identity of cheaters and those who may have engaged in sensitive behaviors. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Relational heuristics for the design of deterministic programs

Summary It has been shown that the design of deterministic programs can be formulated as the resolution of relational equations. Because relational calculi are not sufficiently structured, there are no algorithmic solutions to relational equations. In this paper, we formulate some heuristic solutions to these equations.Part of this work was carried out while the first and second author were at Laval University in Québec. Canada: it was supported by the National Research Council of Canada through a research grant to the first author and a scholarship to the second author. Presently, this research is supported by a grant to the first and third authors from the Tunisian Council on Scientific and Technical Research     

Bisimulation for Labelled Markov Processes

In this paper we introduce a new class of labelled transition systems—labelled Markov processes— and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete. We assume that the state space is a certain type of common metric space called an analytic space. We show that our definition of probabilistic bisimulation generalizes the Larsen–Skou definition given for discrete systems. The formalism and mathematics is substantially different from the usual treatment of probabilistic process algebra. The main technical contribution of the paper is a logical characterization of probabilistic bisimulation. This study revealed some unexpected results, even for discrete probabilistic systems.

• Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition.

• We do not need any finite branching assumption, yet there is no need of infinitary conjunction.

We also show how to construct the maximal autobisimulation on a system. In the finite state case, this is just a state minimization construction. The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts about analytic spaces and appear, at first sight, to be entirely nonconstructive. Yet one can give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.     

Control of Parameterized Discrete Event Systems

This paper investigates the control of parameterized discrete event systems when specifications are given in terms of predicates and satisfy a similarity assumption. This study is motivated by a weakness in current synthesis methods that do not scale well to huge systems. For systems consisting of similar processes under total or partial observation, conditions are given to deduce properties of a system of n processes (arbitrary size) from properties of a system of n ₀ processes (bounded size), with n ≥ n ₀. Furthermore, it is shown how to infer a control policy for the former from the latter’s, while taking into account interconnections between processes.