Theory of wire addition and removal in combinational Boolean networks

  • Authors:
  • Chih-Wei(Jim) Chang;Malgorzata Marek-Sadowska

  • Affiliations:
  • Extreme DA Corporation, Palo Alto, CA 94301, United States;Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, United States

  • Venue:
  • Microelectronic Engineering
  • Year:
  • 2007

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Abstract

Let w"t be a wire in a combinational Boolean network. There may exist a wire w"a such that when w"a is added and w"t is removed, the overall circuit functionality is unchanged. Redundancy-addition-and-removal (RAR) is an efficient technique to find such a w"a. The idea is to add a redundant alternative wire w"a to make the target wire w"t redundant. However, as long as the addition of w"a together with the removal of w"t does not change the overall functionality of the circuit, wires that are added and removed do not necessarily need to be redundant. This raises a question about the existence of alternative wires. Why can one wire replace another wire in a combinational Boolean network? In this paper, we analyze theoretically the existence of alternative wires and model it as an error-cancellation problem. The two existing rewiring techniques, the redundancy-addition-and-removal and the global flow optimization, are unified under the proposed generalized model.