Optimizing the length of checking sequences

A checking sequence, generated from a finite state machine, is a test sequence that is guaranteed to lead to a failure if the system under test is faulty and has no more states than the specification. The problem of generating a checking sequence for a finite state machine M is simplified if M has a distinguishing sequence: an input sequence D~ with the property that the output sequence produced by M in response to D is different for the different states of M. Previous work has shown that, where a distinguishing sequence is known, an efficient checking sequence can be produced from the elements of a set A of sequences that verify the distinguishing sequence used and the elements of a set /spl gamma/ of subsequences that test the individual transitions by following each transition t by the distinguishing sequence that verifies the final state of t. In this previous work, A is a predefined set and /spl gamma/ is defined in terms of A. The checking sequence is produced by connecting the elements of /spl gamma/ and A to form a single sequence, using a predefined acyclic set E/sub c/ of transitions. An optimization algorithm is used in order to produce the shortest such checking sequence that can be generated on the basis of the given A and E/sub c/. However, this previous work did not state how the sets A and E/sub c/ should be chosen. This paper investigates the problem of finding appropriate A and E/sub c/ to be used in checking sequence generation. We show how a set A may be chosen so that it minimizes the sum of the lengths of the sequences to be combined. Further, we show that the optimization step, in the checking sequence generation algorithm, may be adapted so that it generates the optimal E/sub c/. Experiments are used to evaluate the proposed method

Checking sequences for distributed test architectures

Controllability and observability problems may manifest themselves during the application of a checking sequence in a test architecture where there are multiple remote testers. These problems often require the use of external coordination message exchanges among testers during testing. However, the use of coordination messages requires the existence of an external network that can increase the cost of testing and can be difficult to implement. In addition, the use of coordination messages introduces delays and this can cause problems where there are timing constraints. Thus, sometimes it is desired to construct a checking sequence from the specification of the system under test that will be free from controllability and observability problems without requiring the use of external coordination message exchanges. This paper gives conditions under which it is possible to produce such a checking sequence, using multiple distinguishing sequences, and an algorithm that achieves this

Generating a checking sequence with a minimum number of reset transitions

Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.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)

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

Minimizing the cost of fault location when testing from a finite state machine

If a test does not produce the expected output, the incorrect output may have been caused by an earlier state transfer failure. Ghedamsi and coworkers generate a set of candidates and then produce further tests to locate the failures within this set. We consider a special case where there is a state identification process that is known to be correct. A number of preset and adaptive approaches to fault location are described and the problem of minimizing the cost is explored. Some of the approaches lead to NP-hard optimization problems for which possible heuristics are suggested

Using distinguishing and UIO sequences together in a checking sequence

If a finite state machine M does not have a distinguishing sequence, but has UIO sequences for its states, there are methods to produce a checking sequence for M. However, if M has a distinguishing sequence D, then there are methods that make use of D to construct checking sequences that are much shorter than the ones that would be constructed by using only the UIO sequences for M. The methods to applied when a distinguishing sequence exists, only make use of the distinguishing sequences. In this paper we show that, even if M has a distinguishing sequence D, the UIO sequences can still be used together with D to construct shorter checking sequences

Adaptive testing of a deterministic implementation against a nondeterministic finite state machine

A number of authors have looked at the problem of deriving a checking experiment from a nondeterministic finite state machine that models the required behaviour of a system. We show that these methods can be extended if it is known that the implementation is equivalent to some (unknown) deterministic finite state machine. When testing a deterministic implementation, the test output provides information about the implementation under test and can thus guide future testing. The use of an adaptive test process is thus proposed

UIO sequence based checking sequences for distributed test architectures

This study addresses the construction of a preset checking sequence that will not pose controllability (synchronization) and observability (undetectable output shift) problems when applied in distributed test architectures that utilize remote testers. The controllability problem manifests itself when a tester is required to send the current input and because it did not send the previous input nor did it receive the previous output it cannot determine when to send the input. The observability problem manifests itself when a tester is expecting an output in response to either the previous input or the current input and because it is not the one to send the current input, it cannot determine when to start and stop waiting for the output. Based on UIO sequences, a checking sequence construction method is proposed to yield a sequence that is free from controllability and observability problems

Checking sequence construction using adaptive and preset distinguishing sequences

Methods for testing from finite state machine-based specifications often require the existence of a preset distinguishing sequence for constructing checking sequences. It has been shown that an adaptive distinguishing sequence is sufficient for these methods. This result is significant because adaptive distinguishing sequences are strictly more common and up to exponentially shorter than preset ones. However, there has been no study on the actual effect of using adaptive distinguishing sequences on the length of checking sequences. This paper describes experiments that show that checking sequences constructed using adaptive distinguishing sequences are almost consistently shorter than those based on preset distinguishing sequences. This is investigated for three different checking sequence generation methods and the results obtained from an extensive experimental study are given