Using Whales to Complete a Boolean Algebra

Quantifier-Free Boolean Algebra with Presburger Arithmetic is NP-Complete

Boolean Algebra with Presburger Arithmetic (BAPA) combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded finite sets and can be used to express verification conditions in verification of data structure consistency properties. In this report I cons...

A Complete Boolean Algebra That Has No Proper Atomless Complete Sublagebra

There exists a complete atomless Boolean algebra that has no proper atomless complete subalgebra. An atomless complete Boolean algebra B is simple [5] if it has no atomless complete subalgebra A such that A 6= B. The question whether such an algebra B exists was first raised in [8] where it was proved that B has no proper atomless complete subalgebra if and only if B is rigid andminimal. For mo...

Fast Vertical Mining Using Boolean Algebra

The vertical association rules mining algorithm is an efficient mining method, which makes use of support sets of frequent itemsets to calculate the support of candidate itemsets. It overcomes the disadvantage of scanning database many times like Apriori algorithm. In vertical mining, frequent itemsets can be represented as a set of bit vectors in memory, which enables for fast computation. The...

An Enhanced Approach To Network Reliability Using Boolean Algebra

1 Abstract The network reliability analysis problem consists of evaluating a measure of the reliability of a network. A more general context than the network reliability analysis is the stochastic coherent binary system (SCBS) analysis. One approach used in determining the reliability of a system involves Boolean algebra, and in particular a sum of disjoint products (SDP) technique. This paper ...

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