ALGORITHM INVENTION AND VERIFICATION BY LAZY THINKING Presented at the 5 International Workshop on Symbolic and Numeric Algorithms for Scientific Computation

In this paper, we study algorithm invention and verification as a specific variant of systematic theory exploration and propose the ”lazy thinking paradigm” for inventing and verifying algorithms automatically; i.e., for a given predicate logic specification of the problem in terms of a set of operations (functions and predicates), the method produces an algorithm that solves the problem together with a correctness proof for the algorithm. In the ideal case, the only information that has to be provided by the user consists of the formal problem specification and a complete knowledge base for the operations that occur in the problem specification. The ”lazy thinking paradigm” is characterized • by using a library of algorithm schemes • and by using the information contained in failing attempts to prove the correctness theorem for an algorithm scheme in order to invent sufficient requirements on the auxiliary functions in the algorithm scheme.