Testing a distributed system: Generating minimal synchronised test sequences that detect output-shifting faults

A distributed system may have a number of separate interfaces called ports and in testing it may be necessary to have a separate tester at each port. This introduces a number of issues, including the necessity to use synchronised test sequences and the possibility that output-shifting faults go undetected. This paper considers the problem of generating a minimal synchronised test sequence that detects output-shifting faults when the system is specified using a finite state machine with multiple ports. The set of synchronised test sequences that detect output-shifting faults is represented by a directed graph G and test generation involves finding appropriate tours of G. This approach is illustrated using the test criterion that the test sequence contains a test segment for each transition

Implementation relations for testing through asynchronous channels

This paper concerns testing from an input output transition system (IOTS) model of a system under test that interacts with its environment through asynchronous first in first out (FIFO) channels. It explores methods for analysing an IOTS without modelling the channels. If IOTS M produces sequence $\sigma$ then, since communications are asynchronous, output can be delayed and so a different sequence might be observed. Thus M defines a language Tr(M) of sequences that can be observed when interacting with M through FIFO channels. We define implementation relations and equivalences in terms of Tr(M): an implementation relation says how IOTS N must relate to IOTS M in order for N to be a correct implementation of M. It is important to use an appropriate implementation relation since otherwise the verdict from a test run might be incorrect and because it influences test generation. It is undecidable whether IOTS N conforms to IOTS M and so also whether there is a test case that can distinguish between two IOTSs. We also investigate the situation in which we have a finite automaton P and either wish to know whether $Tr(M) \cap L(P)$ is empty or whether Tr(M) \cap \tr(P) is empty and prove that these are undecidable. In addition, we give conditions under which conformance and intersection are decidable.This work was partially supported by EPSRC grant EP/G04354X/1:The Birth, Life and Death of Semantic Mutants

Testing from a finite state machine: Extending invertibility to sequences

When testing a system modelled as a finite state machine it is desirable to minimize the effort required. It has been demonstrated that it is possible to utilize test sequence overlap in order to reduce the test effort and this overlap has been represented by using invertible transitions. In this paper invertibility will be extended to sequences in order to reduce the test effort further and encapsulate a more general type of test sequence overlap. It will also be shown that certain properties of invertible sequences can be used in the generation of state identification sequences

Applying adaptive test cases to nondeterministic implementations

The testing of a state-based system involves the application of sequences of inputs and the observation of the resultant input/output sequences (traces). These traces can result from preset input sequences or adaptive test cases in which the choice of the next input depends on the trace that has observed up to that input. Adaptive test cases are used in a number of areas including protocol conformance testing and adaptivity forms the basis of the standardised test language TTCN. Suppose that we apply adaptive test case ° to the system under test (SUT) and observe the trace ¯¾. If the SUT is deterministic and we apply ° again, after resetting the SUT, then we will observe ¯¾ again. Further, if we have another adaptive test case °0 where a prefix ¯¾0 of ¯¾ is a possible response to °0 then we know that the application of °0 must lead to ¯¾0. Thus, for a deterministic SUT the response of the SUT to an adaptive test case °0 might be deduced from the response of the SUT to another adaptive test case. This observation can be used to reduce the cost of testing: we only apply adaptive test case °0 if we cannot deduce the response to °0 from the set of observations. While many systems are deterministic, nondeterminism is becoming increasingly common. Nondeterminism in the SUT is typically a consequence of limits in the ability to observe the SUT. For example, it could be a result of information hiding, real time properties, or of different possible interleavings in a concurrent system (see, for example. This paper investigates the case where the SUT is nondeterministic. We consider the situation in which a set O of traces has been observed in testing and we are considering applying an adaptive test case °. In general we cannot expect to be able to deduce the response of a nondeterministic SUT to an adaptive test case ° since there may be more than one possible response. Instead we consider the question of how we can decide whether the application of ° could lead to a trace that has not been observed. A solution to this would allow us to reduce the cost of testing: if all possible responses of the SUT to ° have already been observed then we do not have to apply ° in testing and thus reduce the cost of test execution. This paper considers three cases. Section 3 considers the case where we can apply a fairness assumption. Section 4 weakens this assumption to us having a lower bound p on the probability of observing alternative responses of the SUT to any input and in any state. Section 5 then considers the general case

The Evolution of the European Central Bank

This is Queen Mary School of Law Legal Studies Research Paper No. 99/2012, which was later published at Fordham International Law Journal, Spring 2012

Controllable testing from nondeterministic finite state machines with multiple ports

Copyright @ 2011 IEEESome systems have physically distributed interfaces, called ports, at which they interact with their environment. We place a tester at each port and if the testers cannot directly communicate and there is no global clock then we are using the distributed test architecture. It is known that this test architecture introduces controllability problems when testing from a deterministic finite state machine. This paper investigates the problem of testing from a nondeterministic finite state machine in the distributed test architecture and explores controllability. It shows how we can decide in polynomial time whether an input sequence is controllable. It also gives an algorithm for generating such an input sequence bar{x} and shows how we can produce testers that implement bar{x}

The numerical solution of two-dimensional moving boundary problems using curvilinear co-ordinate transformations

A numerical method is described for the solution of two-dimensional moving boundary problems by tansforming the curved, fixed and moving boundaries in the originalco-ordinate system (x,y) into an orthogonal or, in general, nonorthogonal curvilinear system (ξ,η) such that the curved boundaries become (ξ,η) co-ordinate lines. All computations are then carried out in the transformed region using a fixed, rectangular (ξ,η) mesh which corresponds to a moving, non-rectangular (x,y) mesh. A one-phase, two-dimensional problem is solved by using two different such transformations and the results are compared with those from finite-element, enthalpy and isotherm migration methods

Comparing test sets and criteria in the presence of test hypotheses and fault domains

A number of authors have considered the problem of comparing test sets and criteria. Ideally test sets are compared using a preorder with the property that test set T1 is at least as strong as T2 if whenever T2 determines that an implementation p is faulty, T1 will also determine that p is faulty. This notion can be extended to test criteria. However, it has been noted that very few test sets and criteria are comparable under such an ordering; instead orderings are based on weaker properties such as subsumes. This paper explores an alternative approach, in which comparisons are made in the presence of a test hypothesis or fault domain. This approach allows strong statements about fault detecting ability to be made and yet for a number of test sets and criteria to be comparable. It may also drive incremental test generation

Avoiding coincidental correctness in boundary value analysis

In partition analysis we divide the input domain to form subdomains on which the system's behaviour should be uniform. Boundary value analysis produces test inputs near each subdomain's boundaries to find failures caused by incorrect implementation of the boundaries. However, boundary value analysis can be adversely affected by coincidental correctness---the system produces the expected output, but for the wrong reason. This article shows how boundary value analysis can be adapted in order to reduce the likelihood of coincidental correctness. The main contribution is to cases of automated test data generation in which we cannot rely on the expertise of a tester