🤖 AI Summary
This work addresses the inefficiency of directly handling quantified formulas in SMT solving and the absence of a general-purpose automated grounder supporting aggregation operations, which often compels users to resort to error-prone manual grounding. To overcome these limitations, the paper introduces relational algebra into the SMT grounding process for the first time, establishing a theoretical grounding framework that supports first-order logic with aggregation and enables finite equivalent transformations of certain quantified formulas over infinite domains. Building on an embedded SQLite engine for efficient relational algebra evaluation, the authors develop xmt-lib, an SMT-LIB-compliant grounder. Empirical evaluation on public benchmarks demonstrates that xmt-lib substantially enhances the performance of the Z3 solver, outperforming purely declarative approaches.
📝 Abstract
Satisfiability Modulo Theories (SMT) specifications often rely on quantifiers to remain concise and declarative. However, checking the satisfiability of such specifications directly can be inefficient. A common optimization is to ground the specification - that is, to expand quantified formulas into equivalent variable-free formulas. While dedicated tools known as grounders are a cornerstone of Answer Set Programming (ASP) solvers, they are are largely absent from SMT solving workflows. As a result, users frequently resort to writing ad-hoc, error-prone code to perform this transformation.
In this work, I propose a theoretical framework for grounding first order logic formulas with aggregates, based on relational algebra. Within this framework, I formulate a method for efficiently grounding such formulas. Remarkably, the method allows certain formulas that quantify over infinite domains to be transformed into equivalent formulas of finite size.
I have implemented this method in a new SMT-LIB grounder, called xmt-lib. It leverages an embedded relational database (SQLite) to execute relational operations efficiently. An evaluation on a public benchmark for grounders demonstrates that xmt-lib significantly improves the performance of the Z3 SMT solver compared to its purely declarative use, and makes it com