Generating Random Values Using Binary Decision Diagrams and Convex Polyhedra

Abstract

This article describes algorithms to solve Boolean and numerical constraints, and to randomly select values among the set of solutions. Those algorithms were first designed to generate inputs for testing and simulating reactive real-time programs. As a consequence, the chose a solving technology that allow a fine control in the way solutions are elected. Indeed, a fair selection is sometimes required, while favoring limit cases is often interesting for testing. Moreover, simulating a single reactive execution means generating several hundreds or even several thousands of atomic steps, and thus as many solving steps. Hence, the emphasis is put on efficiency, sometimes sacrificing precision or fairness.

Lutin: A Language for Specifying and Executing Reactive Scenarios

“…Actually, we use the solver [15] that have been developed for the testing tool Lurette [16,17]. This solver is quite powerful, since it covers Boolean algebra and linear arithmetics.…”

“…Concretely, constraints are solved by generating a normalized representation mixing binary decision diagrams and convex polyhedra. This constraint solver is sketched below and fully described in [15] First of all, each atomic numeric constraint (e.g., x + y > 1) is replaced by a fresh Boolean variable. Then, the resulting constraint is translated into a BDD.…”

“…In order to chose a Boolean monomial that is valid with respect to numerics, a (inefficient) method would be to select at random a path in the BDD until that selection corresponds to a satisfiable problem for the numeric constraints. The actual algorithm is more sophisticated [15], but the resulting solution is the same.…”

Environment-Model Based Testing of Control Systems: Case Studies

“…This chosen point defines the output for the current reaction. The solver of the current Lutin interpreter uses Binary Decision Diagrams (BDD) and convex polyhedron libraries [6]. It is thus able to deal with any combination of logical operators and linear constraints.…”