Counting the Number of Solutions to Constraints
This survey provides a comprehensive overview of counting problems for researchers and practitioners in automated reasoning, program analysis, formal verification, and information security.
This paper surveys research on counting the number of solutions to various constraint types, including propositional logic formulas, linear inequalities over reals or integers, and Boolean combinations of linear constraints. It describes techniques, tools, and applications in automated reasoning, program analysis, formal verification, and information security.
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).