Correction to "Reduced Length Checking Sequences"
FEBRUARY 2009 (Vol. 58, No. 2) pp. 287-287
0018-9340/09/$31.00 © 2009 IEEE

Published by the IEEE Computer Society
Correction to "Reduced Length Checking Sequences"
R.M. Hierons, IEEE Member

H. Ural
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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.

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