Work

Checking δ-Satisfiability of Reals with Integrals

Year: 2025

Type: article

Abstract: Many synthesis and verification problems can be reduced to determining the truth of formulas over the real numbers. These formulas often involve constraints with integrals in them. To this end, we extend the framework of δ -decision procedures with techniques for handling integrals of user-specified real functions. We implement this decision procedure in the tool ∫dReal, which is built on top of dReal. We evaluate ∫dReal on a suite of problems that include formulas verifying the fairness of algorithms and the privacy and the utility of privacy mechanisms and formulas that synthesize parameters for the desired utility of privacy mechanisms. The performance of the tool in these experiments demonstrates the effectiveness of ∫dReal.

Source: Proceedings of the ACM on Programming Languages

DOI: 10.1145/3720446

Authors: Cody Rivera, Bishnu Bhusal, Rohit Chadha, A. Prasad Sistla, Mahesh Viswanathan

Institutions: University of Illinois Urbana-Champaign, University of Missouri, University of Illinois Chicago

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: SHF: Medium: Collaborative Research: Verification of Differential Privacy Mechanisms, SHF: Small: New Algorithmic Paradigms in Dynamic Analysis of Multithreaded Software, SHF: Medium: Collaborative Research: Verification of Differential Privacy Mechanisms