SNR 2015:Editor's Preface

This volume contains the papers presented at SNR 2015: 1st International Workshop on Symbolic and Numerical Methods for Reachability Analysis 2015 held on July 19, 2015 in San Francisco, CA, USA as part of the 27th International Conference on Computer Aided Verification (CAV 2015).

Hybrid systems model complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into certain subset of its state space, stand at the core of verification and synthesis problems for hybrid systems.

Successful reachability analysis methods for hybrid systems requires the unification of techniques from at least two traditions:

  • Symbolic methods that operate on exact and discrete representations of systems, in the form of various model checking and theorem proving algorithms,

  • Numerical methods that operate on various forms of numerical approximations and continuous transformations of the systems, as developed in the area of continuous dynamical systems and control theory.

As concrete examples, one can observe how the two types of techniques interact in the existing approaches towards reachability analysis. Reachable set computation methods explicitly construct flow-pipes that overapproximate the reachable states over time, while efficient computation of such overapproximations requires symbolic representations such as support functions. Constraint solving methods symbolically encode reachability properties as logic formulas, while solving such formulas requires numerically-driven decision procedures. The goal of the workshop was to seek further synergies among these approaches.

The submitted papers were refereed by the Program Committee consisting of Matthias Althoff (TUM, Germany), Sergiy Bogomolov (IST Austria, Austria) - chair, Parasara Sridhar Duggirala  (University of Illinois at Urbana Champaign, USA), Martin Fränzle (University of Oldenburg, Germany), Goran Frehse (Verimag, France), Sicun Gao (Massachusetts Institute of Technology, USA), Daniele Magazzeni (King’s College, UK), Sayan Mitra (University of Illinois at Urbana Champaign, USA), Erion Plaku (CUA, USA), Stefan Ratschan  (Academy of Sciences, Czech Republic), Ashish Tiwari (SRI, USA) - chair, Stavros Tripakis  (Aalto University, Finnland), Paolo Zuliani (University of Newcastle, UK). The Program Committee decided to accept 5 papers. The program also includes an invited talk “Symbolic-Numeric Reachability Analysis of Hybrid Systems” by Sriram Sankaranarayanan (University of Colorado Boulder, USA).        

We would like to thank all authors for their contributions, the members of the Program Committee for their excellent work during the reviewing process and the invited speaker for kindly accepting the invitation. Finally, we gratefully acknowledge the support of EasyChair.


Sergiy Bogomolov
Ashish Tiwari
June 22, 2015