Model Checking Software with First Order Logic Specifications Using AIG Solvers

Abstract

Static verification techniques leverage Boolean formula satisfiability solvers such as SAT and SMT solvers that operate on conjunctive normal form and first order logic formulae, respectively, to validate programs. They force bounds on variable ranges and execution time and translate the program and its specifications into a Boolean formula. They are limited to programs of relatively low complexity for the following reasons. (1) A small increase in the bounds can cause a large increase in the size of the translated formula. (2) Boolean satisfiability solvers are restricted to using optimizations that apply at the level of the formula. Finally, (3) the Boolean formulae often need to be regenerated with higher bounds to ensure the correctness of the translation. We present a method that uses And-Inverter-Graph (AIG) sequential circuits, and AIG synthesis and verification frameworks to validate programs. An AIG is a Boolean formula with memory elements, logically complete negated conjunction gates, and a hierarchical structure. Encoding the validation problem of a program as an AIG (1) typically provides a more succinct representation than a Boolean formulae encoding with no memory elements, (2) preserves the high-level structure of the program, and (3) enables the use of a number of powerful automated analysis techniques that have no counterparts for other Boolean formulae such as CNF. Our method takes an imperative program with a first order logic specification consisting of a precondition and a postcondition pair, and a bound on the program variable ranges, and produces an AIG with a designated output that is ${true}$ when the program violates the specification. Our method uses AIG synthesis reduction techniques to reduce the AIG, and then uses AIG verification techniques to check the satisfiability of the designated output. The results show that our method can validate designs that are not possible with other state of the art techniques, and with bounds that are an order of magnitude larger.