Explicit model checking algorithms explore the full state space of a system. We have gathered a large collection of state spaces and performed an extensive study of their structural properties. The results show that state spaces have several typical properties and that they differ significantly from both random graphs and regular graphs. We point out how to exploit these typical properties in p...

A very powerful and very general, mathematical model of a system is the state-space representation. Intuitively speaking, the state of a system is a collection of variables that tell us how much ”energy” is currently in the system. Taking this intuition further, this means that the outputs of the system are completely characterized by both its states and inputs; the same input, but with differe...

Dynamic state-space models [24], consisting of a latent Markov process X0, X1, . . . and noisy observations Y1, Y2, . . . that are conditionally independent, are used in a wide variety of applications e.g. wireless networks [8], object tracking [21], econometrics [7] etc. The model is specified by an initial distribution p(x0|✓), a transition kernel p(xt|xt 1, ✓) and an observation distribution...

Synthesis of correct by design systems from specification has recently attracted much attention. The theoretical results imply that this problem is highly intractable, e.g., synthesizing a system is 2EXPTIMEcomplete for an LTL specification and EXPTIME-complete for CTL. An argument in favor of synthesis is that the temporal specification is highly compact, and the complexity reflects the large ...

We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories defined as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively...

An ongoing challenge in Markovian analysis is the so-called “state-space explosion,” which is the exponential growth of the size of the state space of a model as the model size increases. We introduce a partial order on the states of a model to facilitate aggregation of states in order to reduce model size while bounding the error introduced by the aggregation. The partial order implies that th...

In this paper a novel tool BioDiVinE for parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions. Chemical reactions are transformed into a system of multi-affine differential equations. BioDiVinE employs techniques for finite discrete abstraction of the continuous state space. At that level, parallel a...

We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints...

In sensor data management, it is often useful to collect statistics about state changes of an observed phenomenon. The most basic case is to keep track of how often certain transitions, e.g. from state c to d, have occurred. In our research, we consider a discrete state space and timeline. For example, in the above figure, the state space corresponds to actual two-dimensional space and is divid...

We present a method for checking global conditions for object systems in a way that avoids state space explosion. The objects referred to in a global condition are checked step by step against local conditions and communication requirements derived from the global condition. The derivation is automatic, based on information about the system structure contained in the global condition. The appro...