Written by a leading Haskell researcher and instructor, well-known for his teaching skills, this clear-cut text will enable students to write simpler and cleaner code, and to learn how to structure and reason about programs.

/pdf/programming-in-haskell-3o0wiwae3r.pdf

A first course in formal language theory

Programming in Haskell

Motif statistics

A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more completemechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a low-degree-of-freedom robot can control more degrees-of-freedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for nonprehensile manipulation. The rst problem is to determine whether the goal state of the object is reachable by nonprehensile manipulation, and the second is to nd a manipulator motion to bring the object to the goal state. Part I studies these problems for quasistatic nonprehensile manipulation by pushing. I elucidate the controllability properties of objects pushed with point and line contact, and I describe a planner that nds stable pushing paths among obstacles. Pushing can also be used to simplify the hardware of a parts feeder; a one-degree-of-freedom robot, positioned over a conveyor, can position and orient any polygonal part on the conveyor by a series of pushes. Part II of the thesis studies dynamic nonprehensile manipulation. By considering dynamics, I show that even a one-degree-of-freedom robot can take a planar object to a full six-dimensional subset of its state space. Then I describe a planner that nds manipulator trajectories to perform dynamic tasks such as snatching an object from a table, rolling an object on the surface of the arm, and throwing and catching. To demonstrate the feasibility of nonprehensile manipulation, all planners have been implemented on actual robot systems.

Nonprehensile robotic manipulation: controllability and planning

We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers "motifs" widely used in computational biology. Our approach is based on: (i) classical constructive results in theoretical computer science (automata and formal language theory); (ii) analytic combinatorics to compute asymptotic properties from generating functions; (iii) computer algebra to determine generating functions explicitly, analyse generating functions and extract coefficients efficiently. We provide constructions for overlapping or non-overlapping matches of a regular expression. A companion implementation produces: multivariate generating functions for the statistics under study; a fast computation of their Taylor coefficients which yields exact values of the moments with typical application to random texts of size 30,000; precise asymptotic formulae that allow predictions in texts of arbitrarily large sizes. Our implementation was tested by comparing predictions of the number of occurrences of motifs against the 7 megabytes aminoacid database Prodom. We handled more than 88% of the standard collection of Prosite motifs with our programs. Such comparisons help detect which motifs are observed in real biological data more or less frequently than theoretically predicted.

Motif Statistics

We introduce a family of multiplicative distributions {μs|s∈(0,1)} on a free group F and study it as a whole. In this approach, the measure of a given set R⊆F is a function μ(R) : s → μs(R), rather then just a number. This allows one to evaluate sizes of sets using analytical properties of their measure functions μ(R). We suggest a new hierarchy of subsets R in F with respect to their size, which is based on linear approximations of the function μ(R). This hierarchy is quite sensitive, for example, it allows one to differentiate between sets with the same asymptotic density. Estimates of sizes of various subsets of F are given.

A first course in formal language theory

Citations

Programming in Haskell

Motif statistics

Nonprehensile robotic manipulation: controllability and planning

Motif Statistics

Multiplicative measures on free groups

Related Papers (5)

Formal languages and group theory

Jewels of formal language theory

An Introduction to Formal Languages and Automata

Formal methods in the study of language

Introduction to Algorithms, Data Structures and Formal Languages