Etude on Recursion Elimination

Transformation-based program verification was a very important topic in early years of theory of programming. Great computer scientists contributed to these studies: John McCarthy, Amir Pnueli, Donald Knuth ... Many fascinating examples were examined and resulted in recursion elimination techniques known as tail-recursion and co-recursion. In the paper, we examine just a single example (but new we hope) of recursion elimination via program manipulations and problem analysis. The recursion pattern of the example matches descending dynamic programming but is neither tail-recursion nor corecursion pattern. Also, the example may be considered from different perspectives: as a transformation of a descending dynamic programming to ascending one (with a fixed-size static memory), or as a proof of the functional equivalence between recursive and iterative programs (that can later serve as a casestudy for automatic theorem proving), or just as a fascinating algorithmic puzzle for fun and exercising in algorithm design, analysis, and verification. The article is published in the author’s wording.

Tail Recursion Transformation in Functional Dataflow Parallel Programs

The peculiarities of transforming functional dataflow parallel programs into programs with finite resources are analysed. It is considered how these transformations are affected by the usage of asynchronous lists, the return of delayed lists and the variation of the data arrival pace relative to the time of its processing. These transformations allow us to generate multiple programs with static parallelism based on one and the some functional dataflow parallel program.