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Diagnosis of three types of constant faults in read-once contact networks over finite bases.pdf

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Diagnosis of three types of constant faults in read-once contact networks over finite bases.pdf

Theoretical Computer Science 630 (2016) 26–42 Contents lists available at ScienceDirect Theoretical Computer Science /locate/tcs Diagnosis of three types of constant faults in read-once contact networks over ?nite bases Monther Busbait, Mikhail Moshkov ? Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia article info Article history: Received 13 September 2015 Received in revised form 16 January 2016 Accepted 18 March 2016 Available online 24 March 2016 Communicated by S.-Y. Hsieh Keywords: Read-once contact networks Constant faults Decision trees abstract We study the depth of decision trees for diagnosis of three types of constant faults in readonce contact networks over ?nite bases containing only indecomposable networks. For each basis and each type of faults, we obtain a linear upper bound on the minimum depth of decision trees depending on the number of edges in networks. For bases containing networks with at most 10 edges, we ?nd sharp coe?cients for linear bounds. ? 2016 Elsevier B.V. All rights reserved. 1. Introduction In this paper, we study read-once contact networks representing Boolean functions. A read-once contact network is an undirected graph with two poles in which pairwise different Boolean variables are assigned to edges. For a given tuple of variable values, the value of the function corresponding to the network is equal to 1 if and only if there exists a path between poles such that the value of each variable assigned to the edges in this path is equal to 1. Note that the contact networks are also known as contact schemes, contact circuits, and switching circuits [5,10,19]. We study read-once networks over a ?nite set B of networks which is called basis. These networks can be obtained by replacing some edges in a network from B with recursively constructed networks (including networks from B). We assume that all networks from B are indecom