arXiv subjects

Stefan Ratschan

Publications and source records attributed to Stefan Ratschan.

23 records · Page 2Linked to original sources

arXiv2014

Combined Global and Local Search for the Falsification of Hybrid Systems

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length.

eess.SY↗

arXiv2014

Effective Topological Degree Computation Based on Interval Arithmetic

We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-valued continuous function given in the form of arithmetical expressions. The algorithm cleanly separates numerical from combinatorial computation. Based on this, the numerical part provably computes only the information that is strictly necessary for the following combinatorial part, and the combinatorial part may optimize its computation based on the numerical information computed before. We also present computational experiments based on an implementation of the algorithm. Also, in contrast to previous work, the algorithm does not assume knowledge of a Lipschitz constant of the function f, and works for arbitrary continuous functions for which some notion of interval arithmetic can be defined.

cs.CG↗

arXiv2007

Efficient Solving of Quantified Inequality Constraints over the Real Numbers

Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an undecidable problem when allowing function symbols such $\sin$ or $\cos$. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques.

cs.LO↗

arXiv2002

Convergent Approximate Solving of First-Order Constraints by Approximate Quantifiers

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate solutions instead of exact ones. However, the quantifiers of the first-order predicate language are an obstacle to allowing approximations to arbitrary small error bounds. In this paper we solve the problem by modifying the first-order language and replacing the classical quantifiers with approximate quantifiers. These also have two additional advantages: First, they are tunable, in the sense that they allow the user to decide on the trade-off between precision and efficiency. Second, they introduce additional expressivity into the first-order language by allowing reasoning over the size of solution sets.

cs.LO↗

arXiv2001

Solving Composed First-Order Constraints from Discrete-Time Robust Control

This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a (fictitious) constraint logic programming language with explicit quantifier notation. This allows us to clarify the special structure of the problem, and to extend an algorithm for computing approximate solution sets of first-order constraints over the reals to exploit this structure. As a result we can deal with inputs that are clearly out of reach for current symbolic solvers.

cs.LO↗