Etude on Recursion Elimination

Abstract

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.

Keywords

• рекурсивные и стандартные схемы программ
• рекурсивные и итеративные программы
• функциональная эквивалентность программ и схем программ
• восходящее и нисходящее динамическое программирование
• устранение рекурсии
• ассоциативные и стандартные массивы
• статическая и динамическая память