Politeness and Stable Infiniteness: Stronger Together

TL;DR

This paper explores the relationship between politeness and strong politeness in satisfiability modulo theories, introduces an optimization for polite combination leveraging stable infiniteness, and demonstrates potential performance improvements in smart contract verification.

Contribution

It distinguishes politeness from strong politeness and proposes an optimized polite combination method that reduces variable arrangements, improving efficiency in SMT solving.

Findings

Separation between politeness and strong politeness established.

Optimization reduces variable arrangements needed, enhancing performance.

Preliminary results show speed-up in smart contract verification.

Abstract

We make two contributions to the study of polite combination in satisfiability modulo theories. The first contribution is a separation between politeness and strong politeness, by presenting a polite theory that is not strongly polite. This result shows that proving strong politeness (which is often harder than proving politeness) is sometimes needed in order to use polite combination. The second contribution is an optimization to the polite combination method, obtained by borrowing from the Nelson-Oppen method. In its non-deterministic form, the Nelson-Oppen method is based on guessing arrangements over shared variables. In contrast, polite combination requires an arrangement over \emph{all} variables of the shared sort (not just the shared variables). We show that when using polite combination, if the other theory is stably infinite with respect to a shared sort, only the shared variables of that sort need be considered in arrangements, as in the Nelson-Oppen method. Reasoning about arrangements of variables is exponential in the worst case, so reducing the number of variables that are considered has the potential to improve performance significantly. We show preliminary evidence for this in practice by demonstrating a speed-up on a smart contract verification benchmark.