A Logical Product Approach to Zonotope Intersection

We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather inexpensive and accurate even for interpreting non-linear computations, we are able to also interpret tests (i.e. intersections) efficiently. This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not always zonotopes, and there is not even a best zonotopic over-approximation of the intersection. We describe some examples and an im- plementation of our method in the APRON library, and discuss some further in- teresting combinations of zonotopes with non-linear or non-convex domains such as quadratic templates and maxplus polyhedra

Ice skate blade alignment mechanism

A blade alignment mechanism for an ice skate including a clamp for releasably securing the blade assembly to a skating boot in a trial position. The clamp includes a first member secured to the boot at a point remote from the screw apertures in the front or rear flanges, and a second member attached to the first member and disposed to contact one of the flanges to hold it in a trial position. The second member includes an enlarged adjustment opening that allows side-to-side and fore-and-aft adjustment of the second member with respect to the first member. The first and second members are locked into the selected trial position by tightening a threaded fastener that draws contacting serrated faces of the first and second members together. Thus, the blade assembly is releasably attached to the boot in a trial position for trial use by the skater

Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation

Microwave hydrology: A trilogy

Microwave hydrology, as the term in construed in this trilogy, deals with the investigation of important hydrological features on the Earth's surface as they are remotely, and passively, sensed by orbiting microwave receivers. Microwave wavelengths penetrate clouds, foliage, ground cover, and soil, in varying degrees, and reveal the occurrence of standing liquid water on and beneath the surface. The manifestation of liquid water appearing on or near the surface is reported by a microwave receiver as a signal with a low flux level, or, equivalently, a cold temperature. Actually, the surface of the liquid water reflects the low flux level from the cosmic background into the input terminals of the receiver. This trilogy describes and shows by microwave flux images: the hydrological features that sustain Lake Baykal as an extraordinary freshwater resource; manifestations of subsurface water in Iran; and the major water features of the Congo Basin, a rain forest

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster