The main goal of this paper is to study the behaviour of a particular type of hybrid cellular automata, as cryptographically secure pseudorandom bit generators. The hybrid cellular automata considered have been passed the statistical tests de…ned in the cryptographic literature to study the security of the sequences generated for cryptographic purposes: frequency test, serial test, poker test, ...

Hybrid systems combine continuous and discrete behavior. Hybrid Automata are a powerful formalism for the modeling and verification of such systems. A common problem in hybrid system verification is the good parameters problem, which consists in identifying a set of parameter valuations which guarantee a certain behavior of a system. Recently, a method has been presented for attacking this prob...

We define a new class of hybrid automata for which reachability is decidable—a proper superclass of the initialized rectangular hybrid automata—by taking parallel compositions of simple components. Attempting to generalize, we encounter timed automata with algebraic constants. We show that reachability is undecidable for these algebraic timed automata by simulating two-counter Minsky machines. ...

We use linear hybrid automata to deene linear approximations of the phase portraits of nonlinear hybrid systems. The approximating automata can be analyzed automatically using the symbolic model checker HyTech. We demonstrate the technique through the study of predator-prey systems, where we compute population bounds for both species. We also identify a class of nonlinear hybrid automata for wh...

We consider systems composed of an unbounded number of uniformly designed linear hybrid automata, whose dynamic behavior is determined by their relation to neighboring systems. We present a class of such systems and a class of safety properties whose verification can be reduced to the verification of (small) families of “neighboring” systems of bounded size, and identify situations in which suc...

We devise and analyze vertex-based schemes on polyhedral meshes to approximate advection-reaction equations. Error estimates of order O(h) are established in the discrete inf-sup stability norm which includes the mesh-dependent weighted advective derivative. The two key ingredients are a local polyhedral reconstruction map leaving affine polynomials invariant, and a local design of stabilizatio...

We show that the presentation of affine T-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine G-varieties of complexi...

We present some new decidability results on the veri cation of hybrid automata by symbolic analysis (abstract interpretation using polyhedra). The results include de ning a class of hybrid automata for which all properties expressed in the real-time temporal logic Tctl are decidable. The obtained class of automata is shown powerful enough to model reactive applications in which every task event...

This paper discusses the use of hybrid automata to specify and verify embedded distributed systems that consist of both discrete and continuous components The basis of the evaluation is an automotive control system which controls the height of an automobile by pneumatic suspension It has been proposed by BMW AG as a case study taken from a current industrial development Essential parts of the s...

The paper shows the decidability of the reachability problem for planar, monotonic, linear hybrid automata without resets. These automata are a special class of linear hybrid automata with only two variables, whose flows in all states is monotonic along some direction in the plane, and in which the continuous variables are not reset on a discrete transition.