This paper studies the mathematical properties of collectively canalizing Boolean functions, a class functions that has arisen from applications in systems biology. networks are an increasingly popular modeling framework for regulatory networks, and studied here captures key feature biological network dynamics, namely subset one or more variables, under certain conditions, can dominate value fu...

A new class of partial order-types, class G bqo is defined and investigated here. A poset P is in the class G bqo iff the poset algebra F (P ) is generated by a better quasi-order G that is included in L(P ). The free Boolean algebra F (P ) and its free distrivutive lattice L(P ) were defined in [ABKR]. The free Boolean algebra F (P ) contains the partial order P and is generated by it: F (P ) ...

Stochastic Boolean Satisfiability (SSAT) is a powerful representation for the concise encoding of quantified decision problems with uncertainty. While it shares commonalities formula (QBF) satisfiability and has same PSPACE-complete complexity, SSAT solving tends to be more challenging as involves expensive model counting, a.k.a. Sharp-SAT. To date, solvers, especially those imposing no restric...

We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise Boolean domains equipped with an orientation, or as full structure sheaves on piecewise Boolean domains.