This paper presents a program analysis method that generates program summaries
involving polynomial arithmetic. Our approach builds on prior techniques that use solvable …

This paper presents a technique for summarizing recursive procedures operating on integer
variables. The motivation of our work is to create more predictable program analyzers, and …

The theory of arithmetic is integral to many uses of SMT solvers. Z3 has implemented native
solvers for arithmetic reasoning since its first release. We present a full re-implementation of …

We introduce a calculus for incremental pre-processing for SMT and instantiate it in the
context of z3. It identifies when powerful formula simplifications can be retained when …

We show that computing the strongest polynomial invariant for single-path loops with
polynomial assignments is at least as hard as the Skolem problem, a famous problem …

Automatic static cost analysis infers information about the resources used by programs
without actually running them with concrete data and presents such information as functions …

This paper studies the problem of synthesizing (lexicographic) polynomial ranking functions
for loops that can be described in polynomial arithmetic over integers and reals. While the …

Loops are inductive constructs, which make them difficult to analyze and verify in general.
One approach is to represent the inductive behaviors of the program variables in a loop by …

We show that computing the strongest polynomial invariant for single-path loops with
polynomial assignments is at least as hard as the Skolem problem, a famous problem …

The presence of bugs in deployed software can lead to great economic and or human cost.
One strategy for mitigating these losses is to prove the functional correctness of programs …