The notion of the maximal number of mind changes for a Boolean function was defined and applied in several contexts. An application in complexity theory is the result of Wagner and Wechsung that the classes of the Boolean closure of NP are exactly the classes of the Boolean hierarchy over NP. The aim of this paper is to study the complexity of determining the maximal number of mind changes of a...

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

We show that the isomorphism relation for countable Boolean algebras is Borel complete, i.e., the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Boolean algebras. This implies that Ketonen’s classification of countable Boolean algebras is optimal in the sense that the kind of objects used for the complete invariants cannot be improved in an esse...

Following the introduction of an algebraic K-theory of special groups in [6], generalizing Milnor’s mod 2 K-theory for fields, the aim of this paper is to compute the K-theory of Boolean algebras, inductive limits, finite products, extensions, SG-sums and (finitely) filtered Boolean powers of special groups. A parallel theme is the preservation by these constructions of property [SMC], an analo...

The theory of hierarchical Boolean satisfiability (SAT) solving proposed in this paper is based on a strict axiomatic system and introduces a new important notion of implicativity. The theory makes evident that increasing implicativity is the core of SAT-solving. We provide a theoretical basis for increasing the implicativity of a given SAT instance and for organizing SAT-solving in a hierarchi...

Abductive reasoning involves determining a parsimonious set of explanations that can account for a set of observations. In the Boolean minimization problem, the designer attempts to express a Boolean formula as a sum of products or product of sums expression of the smallest size that satisfies the desired function. In this paper, we show that independent abduction problem can be encoded as an i...

In this paper, we introduce Interpolative Boolean algebra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a generalization of the traditional fuzzy set theory. We propose a realization...

where (~xn) ∈ B and B is a Boolean algebra. Only finite Boolean algebras are considered. The Boolean logic presented is based on the abstract Boolean algebra given by Huntington’s [14] postulates and on a special canonical form for a Boolean function given by Archie Blake [2]. The theory of reasoning is divided into functional and general parts, both of which seek antecedents or consequents of ...

theory atoms LTL(Th) formula φ φabs pseudo-Boolean input variables Xabs Input variables X Output variables Y pseudo-Boolean LTL LTL controller check whether the input formula is realizable synthesis