Search for: All records

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to generateallpolynomial invariants for a restricted class of programs, but cannot be applied to programs outside of this class—for instance, programs with nested loops, conditional branching, unstructured control flow, etc. There currently lacks approaches to apply these prior methods to the case of general programs. This paper bridges that gap. Instead of restricting the kinds of programs we can handle, our methodabstractsevery loop into a model that can be solved with prior techniques, bringing to bear prior work on solvable polynomial maps to general programs. While no method can generate all polynomial invariants for arbitrary programs, our method establishes its merit through amonotonictyresult. We have implemented our techniques, and tested them on a suite of benchmarks from the literature. Our experiments indicate our techniques show promise on challenging verification tasks requiring non-linear reasoning. 

This paper is a tutorial on algebraic program analysis. It explains the foundations of algebraic program analysis, its strengths and limitations, and gives examples of algebraic program analyses for numerical invariant generation and termination analysis.