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Logic circuits from zero forcing.

Burgarth D, Giovannetti V, Hogben L, Severini S, Young M - Nat Comput (2015)

Bottom Line: Finally, we show 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.It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ UK.

ABSTRACT

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 show 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. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

No MeSH data available.


A circuit computing the Boolean function  AND  OR  AND . The circuit exhibits the phenomenon of back forcing
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Fig6: A circuit computing the Boolean function AND OR AND . The circuit exhibits the phenomenon of back forcing

Mentions: If each Boolean variable in the input of a circuit is set to , then the vertices of the circuit that are initially colored black form a zero forcing set. However, this is not the only situation in which we have a zero forcing set. Figure 6 gives an example.Fig. 6


Logic circuits from zero forcing.

Burgarth D, Giovannetti V, Hogben L, Severini S, Young M - Nat Comput (2015)

A circuit computing the Boolean function  AND  OR  AND . The circuit exhibits the phenomenon of back forcing
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4541710&req=5

Fig6: A circuit computing the Boolean function AND OR AND . The circuit exhibits the phenomenon of back forcing
Mentions: If each Boolean variable in the input of a circuit is set to , then the vertices of the circuit that are initially colored black form a zero forcing set. However, this is not the only situation in which we have a zero forcing set. Figure 6 gives an example.Fig. 6

Bottom Line: Finally, we show 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.It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ UK.

ABSTRACT

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 show 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. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

No MeSH data available.