Boolean circuits versus arithmetic 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...

Minimally Unsatisfiable Boolean Circuits

Automated reasoning tasks in many real-world domains involve analysis of redundancies in unsatisfiable instances of SAT. In CNF-based instances, some of the redundancies can be captured by computing a minimally unsatisfiable subset of clauses (MUS). However, the notion of MUS does not apply directly to non-clausal instances of SAT, particularly those that are represented as Boolean circuits. In...

Using Boolean Circuits

Alloy is a automatically analyzable modelling language based on first-order logic. An Alloy model can be translated into a Boolean formula whose satisfying assignments correspond to instances in the model. Currently, the translation procedure mechanically converts each piece of the Alloy model individually into its most straightforward Boolean representation. This thesis proposes a more efficie...

Lecture Notes: Boolean Circuits