2011/06/30 by Daniel Burgarth, Vittorio Giovannetti, Leslie Hogben +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #cs.DM #cs.ET #math.CO #quant-ph
paper · pdf · doi:10.1007/s11047-014-9438-5
published as Nat Comput 14, 485 (2015) · 5 pages, 10 EPS figures
arxiv created 2011/12/01 · arxiv updated 2017/01/12
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of "back forcing" as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we point out that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity.