24,603 research outputs found
The effect of the distributed test architecture on the power of testing
Copyright @ 2008 Oxford University PressThere has been much interest in testing from finite-state machines (FSMs). If the system under test can be modelled by the (minimal) FSM N then testing from an (minimal) FSM M is testing to check that N is isomorphic to M. In the distributed test architecture, there are multiple interfaces/ports and there is a tester at each port. This can introduce controllability/synchronization and observability problems. This paper shows that the restriction to test sequences that do not cause controllability problems and the inability to observe the global behaviour in the distributed test architecture, and thus relying only on the local behaviour at remote testers, introduces fundamental limitations into testing. There exist minimal FSMs that are not equivalent, and so are not isomorphic, and yet cannot be distinguished by testing in this architecture without introducing controllability problems. Similarly, an FSM may have non-equivalent states that cannot be distinguished in the distributed test architecture without causing controllability problems: these are said to be locally s-equivalent and otherwise they are locally s-distinguishable. This paper introduces the notion of two states or FSMs being locally s-equivalent and formalizes the power of testing in the distributed test architecture in terms of local s-equivalence. It introduces a polynomial time algorithm that, given an FSM M, determines which states of M are locally s-equivalent and produces minimal length input sequences that locally s-distinguish states that are not locally s-equivalent. An FSM is locally s-minimal if it has no pair of locally s-equivalent states. This paper gives an algorithm that takes an FSM M and returns a locally s-minimal FSM M′ that is locally s-equivalent to M.This work was supported in part by Leverhulme
Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research
Council grant number GR/R43150, Formal Methods and Testing (FORTEST)
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Overcoming controllability problems with fewest channels between testers
When testing a system that has multiple physically distributed
ports/interfaces it is normal to place a tester at each port. Each
tester observes only the events at its port and it is known that
this can lead to additional controllability problems. While such
controllability problems can be overcome by the exchange of
external coordination messages between the testers, this requires
the deployment of an external network and may thus increase the
costs of testing. The problem studied in this paper is finding a
minimum number of coordination channels to overcome
controllability problems in distributed testing. Three instances
of this problem are considered. The first problem is to find a
minimum number of channels between testers in order to overcome
the controllability problems in a given test sequence to be
applied in testing. The second problem is finding a minimal set of
channels that allow us to overcome controllability problems in any
test sequence that may be selected from the specification of the
system under test. The last problem is to find a test sequence
that achieves a particular test objective and in doing so allows
fewest channels to be used
Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems
This paper investigates the link between the null controllability property for some abstract parabolic problems and an inequality that can be seen as a quantified Fattorini-Hautus test. Depending on the hypotheses made on the abstract setting considered we prove that this inequality either gives the exact minimal null control time or at least gives the qualitative property of existence of such a minimal time. We also prove that for many known examples of minimal time in the parabolic setting, this inequality recovers the value of this minimal time.Dans cet article nous Ă©tudions le lien entre la contrĂ´labilitĂ© Ă zĂ©ro d'un problème parabolique abstrait et la validitĂ© d'une inĂ©galitĂ© qui est une version quantifiĂ©e du test de Fattorini–Hautus. Nous prouvons que cette inĂ©galitĂ© permet de caractĂ©riser l'existence d'un temps minimal pour le problème de contrĂ´labilitĂ© Ă zĂ©ro et, selon les hypothèses considĂ©rĂ©es, d'obtenir la valeur de ce temps minimal. Nous prouvons aussi que dans la plupart des exemples connus de problèmes paraboliques ayant un temps minimal de contrĂ´le Ă zĂ©ro, cette inĂ©galitĂ© est une condition nĂ©cessaire et suffisante de contrĂ´labilitĂ©.Ministerio de EconomĂa y Competitivida
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