Uniform Random Sampling Product Configurations of Feature Models That Have Numerical Features

Abstract

Analyses of Software Product Lines (SPLs) rely on automated solvers to navigate complex dependencies among features and find legal configurations. Often these analyses do not support numerical features with constraints because propositional formulas use only Boolean variables. Some automated solvers can represent numerical features natively, but are limited in their ability to count and Uniform Random Sample (URS) conigurations, which are key operations to derive unbiased statistics on configuration spaces. Bit-blasting is a technique to encode numerical constraints as propositional formulas. We use bit-blasting to encode Boolean and numerical constraints so that we can exploit existing #SAT solvers to count and URS conigurations. Compared to state-of-art Satisfiability Modulo Theory and Constraint Programming solvers, our approach has two advantages: 1) faster and more scalable coniguration counting and 2) reliable URS of SPL configurations. We also show that our work can be used to extend prior SAT-based SPL analyses to support numerical features and constraints.