An Extension of ERODE to Reduce Boolean Networks By Backward Boolean Equivalence

Asynchronous Simulation of Boolean Networks by Monotone Boolean Networks

We prove that the fully asynchronous dynamics of a Boolean network f : {0, 1} → {0, 1} without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network f : {0, 1} → {0, 1}, an initial configuration x and a fixed point y of f such that: (i) y can be re...

The Extension of an Arbitrary Boolean Algebra to an Implicative Boolean Algebra

Quasi-Boolean Equivalence

which ought to have the value true despite the fact that the second disjunct is undefined. Such expressions, sometimes called quasi-boolean [7], are traditionally handled by the conditional connectives cand and cor [6] [9]. However, these do not satisfy pleasant algebraic laws and their use tends to complicate calculations to an unacceptable degree. In the present paper, we show that the proble...

Omega-almost Boolean rings

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Confluence of an Extension of Combinatory Logic by Boolean Constants

We show confluence of a conditional term rewriting system CLC, which is an extension of Combinatory Logic by Boolean constants. This solves problem 15 from the RTA list of open problems.