Vaughan R. Pratt

Fast Pattern Matching in Strings

An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings. The constant of proportionality is low enough to make this algorithm of practical use, and the procedure can also be extended to deal with some more general pattern-matching problems. A theoretical application of the algorithm shows that the set of concatenations of even palindromes, i.e., the language

Stanley: The Robot That Won the DARPA Grand Challenge

\{\alpha \alpha ^R\}^*

Time bounds for selection

, can be recognized in linear time. Other algorithms which run even faster on the average are also considered.

Modeling concurrency with partial orders

This article describes the robot Stanley, which won the 2005 DARPA Grand Challenge. Stanley was developed for high-speed desert driving without human intervention. The robot’s software system relied predominately on state-of-the-art AI technologies, such as machine learning and probabilistic reasoning. This article describes the major components of this architecture, and discusses the results of the Grand Challenge race.

Direct least-squares fitting of algebraic surfaces

The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK. Specifically, no more than 5.4305 n comparisons are ever required. This bound is improved for extreme values of i, and a new lower bound on the requisite number of comparisons is also proved.

Towards fully autonomous driving: Systems and algorithms

Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic,inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets orpomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. The general benefits of the approach are that it is conceptually straightforward, involves fewer artificial constructs than many competing models of concurrency, yet is applicable to a considerably wider range of types of systems, including systems with buses and ethernets, analog systems, and real-time systems.

Linear Algorithm for Data Compression via String Matching

In the course of developing a system for fitting smooth curves to camera input we have developed several direct (i.e. noniterative) methods for fitting a shape (line, circle, conic, cubic, plane, sphere, quadric, etc.) to a set of points, namely exact fit, simple fit, spherical fit, and blend fit. These methods are all dimension-independent, being just as suitable for 3D surfaces as for the 2D curves they were originally developed for.Exact fit generalizes to arbitrary shapes (in the sense of the term defined in this paper) the well-known determinant method for planar exact fit. Simple fit is a naive reduction of the general overconstrained case to the exact case. Spherical fit takes advantage of a special property of circles and spheres that permits robust fitting; no prior direct circle fitters have been as robust, and there have been no previous sphere fitters. Blend fit finds the best fit to a set of points of a useful generalization of Middleditch-Sears blending curves and surfaces, via a nonpolynomial generalization of planar fit.These methods all require (am+bn)n2 operations for fitting a surface of order n to m points, with a = 2 and b = 1/3 typically, except for spherical fit where b is larger due to the need to extract eigenvectors. All these methods save simple fit achieve a robustness previously attained by direct algorithms only for fitting planes. All admit incremental batched addition and deletion of points at cost an2 per point and bn3 per batch.

Every Prime Has a Succinct Certificate

In order to achieve autonomous operation of a vehicle in urban situations with unpredictable traffic, several realtime systems must interoperate, including environment perception, localization, planning, and control. In addition, a robust vehicle platform with appropriate sensors, computational hardware, networking, and software infrastructure is essential.

Models of program logics

A linear implementation of the optimal universal data compression methods of Lempel and Ziv is described. The main tool is McCreights algorithm for constructing suffix trees. Both bounded and unbounded memory are considered.

A near-optimal method for reasoning about action☆

To prove that a number n is composite, it suffices to exhibit the working for the multiplication of a pair of factors. This working, represented as af string, is of length bounded by a polynomial in