Synthesis for Polynomial Lasso Programs

Abstract

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions conjunctions of polynomial equalities. Central to this approach is the discovery of non-linear algebraic loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion. We perform program synthesis by generating a constraint whose solution is a synthesized program together with a loop invariant that proves the program's correctness. This constraint is non-linear and is passed to an SMT solver. Moreover, we can enforce the termination of the synthesized program with the support of test cases.