Controllability problems in MSC-based testing

This is a pre-copyedited, author-produced PDF of an article accepted for publication in The Computer Journal following peer review. The definitive publisher-authenticated version [Dan, H and Hierons, RM (2012), "Controllability Problems in MSC-Based Testing", The Computer Journal, 55(11), 1270-1287] is available online at: http://comjnl.oxfordjournals.org/content/55/11/1270. Copyright @ The Authors 2011.In testing systems with distributed interfaces/ports, we may place a separate tester at each port. It is known that this approach can introduce controllability problems which have received much attention in testing from finite state machines. Message sequence charts (MSCs) form an alternative, commonly used, language for modelling distributed systems. However, controllability problems in testing from MSCs have not been thoroughly investigated. In this paper, controllability problems in MSC test cases are analysed with three notions of observability: local, tester and global. We identify two types of controllability problem in MSC-based testing. It transpires that each type of controllability problem is related to a type of MSC pathology. Controllability problems of timing are caused by races but not every race causes controllability problems; controllability problems of choice are caused by non-local choices and not every non-local choice causes controllability problems. We show that some controllability problems of timing are avoidable and some controllability problems of choice can be overcome when testers have better observational power. Algorithms are provided to tackle both types of controllability problems. Finally, we show how one can overcome controllability problems using a coordination service with status messages based on algorithms developed in this paper.EPSR

Relative controllability of linear difference equations

In this paper, we study the relative controllability of linear difference equations with multiple delays in the state by using a suitable formula for the solutions of such systems in terms of their initial conditions, their control inputs, and some matrix-valued coefficients obtained recursively from the matrices defining the system. Thanks to such formula, we characterize relative controllability in time $T$ in terms of an algebraic property of the matrix-valued coefficients, which reduces to the usual Kalman controllability criterion in the case of a single delay. Relative controllability is studied for solutions in the set of all functions and in the function spaces $L^p$ and $\mathcal C^k$. We also compare the relative controllability of the system for different delays in terms of their rational dependence structure, proving that relative controllability for some delays implies relative controllability for all delays that are "less rationally dependent" than the original ones, in a sense that we make precise. Finally, we provide an upper bound on the minimal controllability time for a system depending only on its dimension and on its largest delay