Solving contest problems via formal program verification

Abstract

The interface between mathematics and computer science is many-sided. In particular, E.W. Dijkstra promoted a special “computer science” approach to mathematics problem solving. The approach combines a heuristic algorithm design and rigorous mathematical proof of algorithm correctness (in style of A. Hoare and R. Floyd). The paper sketches two problems of this kind in a form of tutorials for undergraduate students that are interested in different programming contests (like ACM International Collegiate Programming Contests). These tutorials took place at Novosibirsk State University in years 2005–2008. The paper also dioceses some direction for further research that emerge from the problems.