Towards efficient inductive synthesis of expressions from input/output examples

Abstract

Our goal through several years has been the development of efficient search algorithm for inductive inference of expressions using only input/output examples. The idea is to avoid exhaustive search by means of taking full advantage of semantic equality of many considered expressions. This might be the way that people avoid too big search when finding proof strategies for theorems, etc. As a formal model for the development of the method we use arithmetic expressions over the domain of natural numbers. A new approach for using weights associated with the functional symbols for restricting search space is considered. This allows adding constraints like the frequency of particular symbols in the expression. Additionally the current state of the art of computer experiments using this methodology is described. An example that is considered is the inductive inference of the formula for solving quadratic equations, the finding of which by pure exhaustive search would be unrealistic.