In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic probabili
ty measure on the positive real line. In particular, we study the problem of measuring the behavioral dissimilarity of two SMMs against linear real-time specifications expressed as Metric Temporal Logic (MTL) formulas or Deterministic Timed-Automata (DTA). The most natural choice for such a distance is the one that measures the maximal difference that can be observed comparing two SMMs with respect to their probability of satisfying an arbitrary specification. We show that computing this metric is NP-hard. In addition, we show that any algorithm that approximates the distance within a certain absolute error, depending on the size of the SMMs, is NP-hard. Nevertheless, we introduce an alternative distance, based on the Kantorovich metric, that is an over-approximation of the former and we show that, under mild assumptions on the residence time distributions, it can be computed in polynomial time.
This volume contains the proceedings of the first workshop on Advances in Systems of Systems (AISOS13), held in Roma, Italy, March 16. System-of-Systems describes the large scale integration of many independent self-contained systems to satisfy globa
l needs or multi-system requests. Examples are smart grid, intelligent buildings, smart cities, transport systems, etc. There is a need for new modeling formalisms, analysis methods and tools to help make trade-off decisions during design and evolution avoiding leading to sub-optimal design and rework during integration and in service. The workshop should focus on the modeling and analysis of System of Systems. AISOS13 aims to gather people from different communities in order to encourage exchange of methods and views.
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid sys
tems, and indicate the integration technique applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings.
