Decision Procedures - An Algorithmic Point of View

A decision procedure is an algorithm that, given a decision problem, terminates with a correct yes/no answer. Here, the authors focus on theories that are expressive enough to model real problems, but are still decidable. Specifically, the book concentrates on decision procedures for first-order theories that are commonly used in automated verification and reasoning, theorem-proving, compiler optimization and operations research. The techniques described in the book draw from fields such as graph theory and logic, and are routinely used in industry. The authors introduce the basic terminology of SAT, Satisfiability Modulo Theories (SMT) and the DPLL(T) framework. Then, in separate chapters, they study decision procedures for propositional logic

Implement a simple version of this procedure in which each variable has ceiling(log n) bits, where n is the number of variables, via a reduction to a propositional formula. Chapter 6 has relevant information about encoding such bitvector formulas. As a more advanced project, do the same for a nonuniform range, as explained in Sects. 4.5.2 - 4.5.3.