Definability of Accelerated Relations in a Theory of Arrays and Its Applications

ion and Acceleration in SMT-based Model-Checking for Array Programs Francesco Alberti1, Silvio Ghilardi2, Natasha Sharygina1 1 Faculty of Informatics, University of Lugano, Switzerland 2 Università degli Studi di Milano, Milan, Italy Abstract Abstraction (in its various forms) is a powerful established technique in modelchecking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an approach which is widely used to avoid divergence, but it has been applied mostly to integer programs. This paper addresses the problem of accelerating transition relations for unbounded arrays with the ultimate goal of avoiding divergence during reachability analysis of abstract programs. For this, we first design a format to compute accelerations in this domain; then we show how to adapt the so-called ‘monotonic abstraction’ technique to efficiently handle complex formulæ with nested quantifiers generated by the acceleration preprocessing. Notably, our technique can be easily plugged-in into abstraction/refinement loops, and strongly contributes to avoid divergence: experiments conducted with the MCMT model checker attest the effectiveness of our approach on programs with unbounded arrays, where acceleration and abstraction/refinement technologies fail if applied alone. Report Info Published October 2012 Revised April 2013 Number USI-INF-TR-2012-1 Institution Faculty of Informatics University of Lugano Lugano, Switzerland Online Access www.inf.usi.ch/techreportsAbstraction (in its various forms) is a powerful established technique in modelchecking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an approach which is widely used to avoid divergence, but it has been applied mostly to integer programs. This paper addresses the problem of accelerating transition relations for unbounded arrays with the ultimate goal of avoiding divergence during reachability analysis of abstract programs. For this, we first design a format to compute accelerations in this domain; then we show how to adapt the so-called ‘monotonic abstraction’ technique to efficiently handle complex formulæ with nested quantifiers generated by the acceleration preprocessing. Notably, our technique can be easily plugged-in into abstraction/refinement loops, and strongly contributes to avoid divergence: experiments conducted with the MCMT model checker attest the effectiveness of our approach on programs with unbounded arrays, where acceleration and abstraction/refinement technologies fail if applied alone. Report Info Published October 2012 Revised April 2013 Number USI-INF-TR-2012-1 Institution Faculty of Informatics University of Lugano Lugano, Switzerland Online Access www.inf.usi.ch/techreports