John W. Havlicek

Reasoning with Temporal Logic on Truncated Paths

We consider the problem of reasoning with linear temporal logic on truncated paths. A truncated path is a path that is finite, but not necessarily maximal. Truncated paths arise naturally in several areas, among which are incomplete verification methods (such as simulation or bounded model checking) and hardware resets. We present a formalism for reasoning about truncated paths, and analyze its characteristics.

The analytic image

We introduce a novel directional multidimensional Hilbert transform and use it to define the complex-valued analytic image associated with a real-valued image. The analytic image associates a unique pair of instantaneous amplitude and frequency functions with an image, and also admits many of the other important properties of the one-dimensional analytic signal.

Skewed 2D Hilbert transforms and computed AM-FM models

Computed AM-FM models represent images in terms of instantaneous amplitude and frequency modulations. However, the instantaneous amplitude and frequency of a real valued image are ambiguous. We apply the directional 2D Hilbert transform to compute a complex extension for a real image. This extension, called the analytic image, admits most of the attractive properties of the 1D analytic signal. However, the analytic image is not unique: for a given real image, taking the Hilbert transform in the horizontal and vertical directions yields different complex extensions and differing computed AM-FM models. We show that these two differing models are essentially equivalent and develop explicit formulations relating them.

The definition of a temporal clock operator

Modern hardware designs are typically based on multiple clocks. While a singly-clocked hardware design is easily described in standard temporal logics, describing a multiply-clocked design is cumbersome. Thus it is desirable to have an easier way to formulate properties related to clocks in a temporal logic. We present a relatively simple solution built on top of the traditional LTL-based semantics, study the properties of the resulting logic, and compare it with previous solutions.

A Note on the Homotopy Type of Wait-Free Atomic Snapshot Protocol Complexes

In the atomic snapshot system model, the processes of an asynchronous distributed system communicate by atomic write and atomic snapshot read operations on a shared memory consisting of single-writer multiple-reader registers. The processes may fail by crashing. It is shown that in this model, a wait-free full-information protocol complex is homotopy equivalent to the underlying input complex. A span in the sense of Herlihy and Shavit provides the homotopy equivalence. It follows that the protocol and input complexes are indistinguishable by ordinary homology or homotopy groups.

Multidimensional orthogonal FM transforms

The present a novel class of multidimensional orthogonal FM transforms. The analysis suggests a novel signal-adaptive FM transform possessing interesting energy compaction properties. We show that the proposed signal-adaptive FM transform produces point spectra for multidimensional signals with uniformly distributed samples. This suggests that the proposed transform is suitable for energy compaction and subsequent coding of broadband signals and images that locally exhibit significant level diversity. We illustrate these concepts with simulation experiments.

On the representation of wideband images using permutations for lossless coding

We introduce a novel method for representing and coding wideband signals using permutations. The signal samples are first sorted, and then encoded using differential pulse code modulation. We show that our method is optimal for DPCM coding and develop a novel algorithm for encoding the permutation information efficiently. We show that the new algorithm achieves coding gains over Huffman coding.

Formal Verification Successes at Motorola

Formal tools are either too labor intensive or are completely impractical for industrial-size problems. This paper describes two formal verification tools used within Motorola, Versys2 and CBV, that challenge this assertion. The two tools are being used in current design verification flows and have shown that it is possible to seamlessly integrate formal tools into existing design flows.

Generically sufficient conditions for exact multichannel blind image restoration

We have previously developed an algorithm and sufficient conditions for exact multichannel blind image restoration. In this paper, we use the resultant matrix theorem and techniques of algebraic geometry to prove that the sufficient conditions hold generically given three blurred versions of the same image and some restrictions on the size of the original image. Moreover, the extension to multichannel blind n-dimensional signal restoration is described.