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Issue No.02 - February (2009 vol.58)
pp: 287
Published by the IEEE Computer Society
R. M. Hierons , Brunel University, Uxbridge, Middlesex
H. Ural , University of Ottawa, Ottawa
ABSTRACT
This paper describes corrections to a previous paper, Reduced Length Checking Sequecnes, that appeared in IEEE Transactions on Computers in 2002 (51 9, pp.1111-1117).
The paper [ 1] describes improvements on the algorithm from [ 2], which produces a checking sequence from a finite state machine $M$ that has a known distinguishing sequence $D$ . However, while the improvements described in [ 1] are valid, the final step of the checking sequence generation algorithm was not included and we outline this step here.
The algorithm in [ 1] produces a directed graph $G$ and then generates a tour $\cal T$ of $G$ such that $\cal T$ contains certain edges. Checking sequence generation is thus represented in terms of the rural Chinese postman problem. The checking sequence is produced by starting $\cal T$ at vertex $v_1$ . However, in contrast to [ 2], in doing this we may fail to check the final transition in the tour and, if this is the case, then we need to add a distinguishing sequence to the end of the sequence produced by [ 1]. We can thus produce a checking sequence from $\cal T$ in the following way: We choose an edge $e$ from $\cal T$ such that $e$ represents a transition test for a transition $\tau$ that ends at the initial state $s_1$ of $M$ . We replace $e$ by the corresponding sequence $e_1, \ldots, e_k$ of edges from $G$ to form a tour ${\cal T}'$ . Let $P$ denote a walk produced by starting ${\cal T}'$ with $e_2$ and let $Q$ be the label of $P$ . We return the input/output sequence $QD/\lambda(s_1,D)$ that forms our checking sequence.
Although both [ 1] and [ 2] correctly state that the algorithm of [ 2] should start a tour at the vertex $v_1$ , instead, in the examples, [ 1] started it at $v'_1$ . As a result, [ 1] did not apply the algorithm of [ 2] correctly to the example and should have given the checking sequence


$$\eqalign{&a/x, a/x, \alpha_1, L_{452}, L_{212}, L_{252}, a/x, b/y, \alpha_2, T_2, L_{441}, L_{124}, b/x, L_{531}, L_{112},\cr& T_2, b/x, L_{512}, T_2, b/x, b/y, L_{352}, T_2, b/x, b/y, L_{341}.}$$

The corrected algorithm of [ 1] returns the checking sequence


$$\eqalign{&D/\lambda(s_1,D), b/y, D/\lambda(s_1,D), a/x, \alpha'_1, a/x, D/\lambda(s_4,D), a/x,\cr& D/\lambda(s_2,D), b/x, D/\lambda(s_5,D), a/x, b/y, \alpha'_2, a/x, a/y, D/\lambda(s_1,D),\cr& a/x, b/y, b/x, D/\lambda(s_5,D), a/x, b/y, a/y, D/\lambda(s_4,D), b/y, D/\lambda(s_1,D)}$$

of length 64 (rather than one of length 61 reported).

    R.M. Hierons is with the School of Information Systems, Computing, and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK.

    E-mail: rob.hierons@brunel.ac.uk.

    H. Ural is with the School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada.

    E-mail: ural@site.uottawa.ca, ural@sci.uottawa.ca.

Manuscript received 13 Nov. 2006; accepted 23 Jan. 2007; published online 15 Sept. 2008.

Recommended for acceptance by B. Bose.

For information on obtaining reprints of this article, please send e-mail to: tc@computer.org, and reference IEEECS Log Number TC-0432-1106.

Digital Object Identifier no. 10.1109/TC.2008.173.

REFERENCES

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