Non-cancellative Boolean circuits: A generalization of monotone boolean circuits

Non-cancellative Boolean Circuits: A Generalization of Monotone Boolean Circuits

Cancellations are known to be helpful in e cient algebraic computation of polynomials over elds. We de ne a notion of cancellation in Boolean circuits and de ne Boolean circuits that do not use cancellation to be non-cancellative. Non-cancellative Boolean circuits are a natural generalization of monotone Boolean circuits. We show that in the absence of cancellation, Boolean circuits require sup...

Cyclic Boolean circuits

A Boolean circuit is a collection of gates and wires that performs a mapping from Boolean inputs to Boolean outputs. The accepted wisdom is that such circuits must have acyclic (i.e., loop-free or feed-forward) topologies. In fact, the model is often defined this way – as a directed acyclic graph (DAG). And yet simple examples suggest that this is incorrect. We advocate that Boolean circuits sh...

Graphene-Based Non-Boolean Logic Circuits

Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. Here we show that the negative differential resistance ex...

Lecture Notes: Boolean Circuits

Goals in the Propositional Horn Language Are Monotone Boolean Circuits

Horn⊃ is a logic programming language which extends usual Horn clauses by adding intuitionistic implication in goals and clause bodies. This extension can be seen as a form of structuring programs in logic programming. Restricted to the propositional setting of this language, we prove that any goal in Horn⊃ can be translated into a monotone Boolean circuit which is linear in the size of the goal.