Recognizing Decomposition of a Partial Boolean Function

A hard combinatorial problem is investigated which has useful application in design of discrete devices: the two-block decomposition of a partial Boolean function. The key task is regarded: finding such a weak partition on the set of arguments, at which the considered function can be decomposed. Solving that task is essentially speeded up by the way of preliminary discovering traces of the sought-for partition. Efficient combinatorial operations are used by that, based on parallel execution of operations above adjacent units in the Boolean space.

Using the Business Process Execution Language for Managing Scientific Processes

This paper describes the use of the Business Process Execution Language for Web Services (BPEL4WS/BPEL) for managing scientific workflows. This work is result of our attempt to adopt Service Oriented Architecture in order to perform Web services – based simulation of metal vapor lasers. Scientific workflows can be more demanding in their requirements than business processes. In the context of addressing these requirements, the features of the BPEL4WS specification are discussed, which is widely regarded as the de-facto standard for orchestrating Web services for business workflows. A typical use case of calculation the electric field potential and intensity distributions is discussed as an example of building a BPEL process to perform distributed simulation constructed by loosely-coupled services.

Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Along the Traces of the Conic Sections

Based on a geometry problem by Ivan Salabashev we demonstrate an exploratory process leading to conic sections as a locus of points. We work for the purpose with the GeoGebra dynamic software making use of different objects’ representations for explorations related with conic sections.