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Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
In this paper we describe an experimental system called d/dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use anExpand
Effective synthesis of switching controllers for linear systems
In this paper, we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate theExpand
Proving Positive Almost-Sure Termination
This work provides several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules, including classical ones for non-probabilistic systems. Expand
Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs
The strong (uniform computability) Turing completeness of chemical reaction networks over a finite set of molecular species under the differential semantics is derived, solving a long standing open problem. Expand
Recursive Analysis Characterized as a Class of Real Recursive Functions
It is proved that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimalization and limit schema. Expand
Orthogonal Polyhedra: Representation and Computation
This paper defines representation schemes for orthogonal polyhedra based on their vertices, and shows that these compact representation schemes are canonical for all (convex and non- Convex)polyhedra in any dimension. Expand
Probabilistic Rewrite Strategies. Applications to ELAN
An extension of the ELAN strategy language to deal with randomized systems is proposed, and it is argued through several examples that a natural setting to model systems with randomized choices is proposed. Expand
The Mortality Problem for Matrices of Low Dimensions
The problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices is proved and some NP-completeness results are state. Expand
On the Representation of Timed Polyhedra
This paper defines a representation scheme for timed polyhedra based on their extreme vertices, and shows that this compact representation scheme is canonical for all (convex and non- Convex)polyhedra in any dimension. Expand
The Stability of Saturated Linear Dynamical Systems Is Undecidable
We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. SuchExpand