Parallel Recursion

Role of recursion and induction in parallel computations We in computer science are extremely fortunate that recursion is applicable for descriptions and induc­ tion for analysis of sequential programs. In fact, they are indispensable tools in programming. Sequentiality is inherent in mathematics. The Peano axioms define natural numbers in a sequential fashion, starting with 0 and defining each num­ ber as the successor of the previous one. One can see its counterpart in Haskell; the fundamental data structure, list, is either empty, corresponding to 0, or one formed by appending a single element to a smaller list. Naturally, induction is the major tool for analyzing programs on lists. There is no counterpart of parallelism in classical mathematics because tradi­ tional mathematics is not concerned about mechanisms of computations, sequen­ tial or parallel. Any possible parallel structure is sequentialized (or serialized) so that traditional mathematical tools, including induction, can be used for its analy­ sis. Therefore, most parallel recursive algorithms are typically described iteratively, one parallel step at a time. The mathematical properties of the algorithms are rarely evident from these descriptions. Parallel Recursion