Algebra-Dynamic Models for CPU- and GPU-Parallel Program Design and the Model of Auto-Tuning

This chapter considers algebra-dynamic models of parallel programs, which are based on concepts of transition systems theory and algebra of algorithms. The models of sequential and parallel multithreaded programs for multicore processors and program models for graphics processing units are constructed. The authors describe transformations of programs aimed at transition from sequential to parallel versions (parallelization) and improving performance of parallel programs in respect to execution time (optimization). The transformations are based on using rewriting rules technique. The formal model of program auto-tuning as an evolutional extension of transition systems is proposed, and some properties of programs are considered.