INTEGRATION, the VLSI journal 30 (2001) 157–168 Enumerating catastrophic fault patterns in VLSI arrays with both uni- and bidirectional links $ Soumen Maity a , Bimal K. Roy b , Amiya Nayak c, * a Stat-Math Unit, Indian Statistical Institute, Calcutta-35, India b Applied Statistics Unit, Indian Statistical Institute, Calcutta-35, India c School of Computer Science, Carleton University, Ottawa, Ont., Canada K1S 5B6 Received 30 January 2001 Abstract Characterization of catastrophic fault patterns (CFPs) and their enumeration have been studied by several authors. Given a linear array with a set of bypass links, an important problem is how to count the number of CFPs. Enumeration of CFPs for two link redundancy G ¼f1; gg has been solved for both unidirectional and bidirectional link cases. In this paper, we consider the more general case of link redundancy G ¼f1; 2; y; k; gg; 2pkog: Using random walk as a tool, we enumerate CFPs for both unidirectional and bidirectional cases. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Catastrophic fault patterns; Combinatorial problems; Random walk 1. Introduction A standard technique to lower the production costs of VLSI circuits is the provision of on-chip redundancy, and accompanying mechanisms to reconfigure the chip component at the occurrence of fabrication faults. Without the presence of reconfiguration capabilities, the yield of very large VLSI chips would be so poor to will make their production unacceptable. In the case of linear arrays of identical processing elements (PEs), redundant ones (called spares) are often placed on the chip to replace faulty PEs and, therefore, preserve the network connectivity. Besides the $ This work was supported in part by Natural Sciences and Engineering Research Council of Canada under Operating Grant 9167. *Corresponding author. E-mail addresses: res9716@isical.ac.in (S. Maity), bimal@isical.ac.in (B.K. Roy), nayak@scs.carleton.ca (A. Nayak). 0167-9260/01/$-see front matter r 2001 Elsevier Science B.V. All rights reserved. PII:S0167-9260(01)00016-5