Counting the Number of Solutions to Constraints

TL;DR

This paper surveys methods and tools for counting solutions to various types of constraints, highlighting their applications in automated reasoning, verification, and security.

Contribution

It provides a comprehensive overview of existing techniques for counting solutions to constraints across different domains and constraint forms.

Findings

Various techniques for counting solutions are summarized.

Applications include automated reasoning, program analysis, and security.

The survey highlights gaps and future directions in the field.

Abstract

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various forms, including, formulas in the propositional logic, linear inequalities over the reals or integers, Boolean combination of linear constraints. We describe some techniques and tools for solving the counting problems, as well as some applications (e.g., applications to automated reasoning, program analysis, formal verification and information security).