Decidability of 3-Dimensional Piecewise Constant Derivative Systems Revised⋆

Piecewise-constant derivative systems and their algorithmic properties

E. Asarin deals with simple diierential systems: dynamical systems with piecewise-constant derivative|in short, PCD systems. Recently, it has been proved that the reach-ability problem is decidable in a 2-dimensional space 2]. Asarin and Maler proved in 1] that every Turing machine can be simulated by a 3-dimensional PCD system. Thus, the reachability problem is proved to be undecidable in more...

Piecewise Constant Controlled Linear Fuzzy Systems

On the decidability and complexity of problems for restricted hierarchical hybrid systems

We study variants of a recently introduced hybrid system model, called a Hierarchical Piecewise Constant Derivative (HPCD). These variants (loosely called Restricted HPCDs) form a class of natural models with similarities to many other well known hybrid system models in the literature such as Stopwatch Automata, Rectangular Automata and PCDs. We study the complexity of reachability and mortalit...

The Intractability of Face Reachability in 3D Visit-Once Piecewise-Constant Derivative Systems

We consider a class of three-dimensional dynamical systems whose state spaces are defined by piecewise constant vector fields and whose trajectories never return to a state-space region once they exit the region. We demonstrate that the reachability problem for this class of systems is decidable while the computation is provably intractable. We prove the intractability (i.e., PSPACE-completenes...

Reachability for Continuous and Hybrid Systems

In this talk I present some past, present and future work concerning reachability computation for continuous and hybrid systems. The problem of what may happen in the future is very naturally phrased as a reachability problem in a dynamical system. Starting from an initial state or a set of states, following some dynamic rules, possibly with some dose of uncertainty, we would like to know wheth...