ABSTRACT
A rule-based programming paradigm is described as a formal basis for biological, chemical and physical computations. In this paradigm, the computations are interpreted as the outcome arising out of interaction of elements in an object space. The interactions can create new elements (or same elements with modified attributes) or annihilate old elements according to specific rules. Since the interaction rules are inherently parallel, any number of actions can be performed cooperatively or competitively among the subsets of elements, so that the elements evolve toward an equilibrium or unstable or chaotic state. Such an evolution may retain certain invariant properties of the attributes of the elements. The object space resembles Gibbsian ensemble that corresponds to a distribution of points in the space of positions and momenta (called phase space). It permits the introduction of probabilities in rule applications. As each element of the ensemble changes over time, its phase point is carried into a new phase point. The evolution of this probability cloud in phase space corresponds to a distributed probabilistic computation. Thus, this paradigm can handle tor deterministic exact computation when the initial conditions are exactly specified and the trajectory of evolution is deterministic. Also, it can handle probabilistic mode of computation if we want to derive macroscopic or bulk properties of matter. We also explain how to support this rule-based paradigm using relational-database like query processing and transactions.
Subject(s)
Software , Algorithms , Biological Evolution , Classification , Computer Simulation , DNA/genetics , Databases, Factual , Models, Chemical , Models, Genetic , Models, Molecular , Models, Statistical , Monte Carlo MethodABSTRACT
An error-free carry-free (parallel) rational arithmetic system based on residue and p-adic representation is introduced. In this system, Farey rational numbers, whose numerators and denominators are bounded, are encoded into Para-Hensel codes (parallel rational Hensel code), and the parallel element-wise arithmetic is performed using these codes. The algorithms for encoding into and decoding from the Para-Hensel code and the arithmetic algorithms are described. This system will have extensive applications in massively parallel processors.
