Being NP complete has been widely interpreted as being computationally intractable But NP completeness is a worst case concept Some NP complete problems are easy on average but some may not be How is one to know whether an NP complete problem is di cult on average The theory of average case computational complexity initiated by Levin about ten years ago is devoted to studying this problem This ...

Academic Interests Group theory and combinatorics (in particular groups acting on rooted trees, growth of groups, regular combings of groups, random walks on groups, and dynamical systems) Dynamical Systems (in particuliar iteration of holomorphic maps). Computer algebra and computational group theory

We develop a computational interpretation of guarded dependent type theory with clocks called CTT which enjoys a straightforward operational semantics and immediate canonicity result for base types. Our realizability-style presentation of guarded type theory is a computational and syntactic alternative to category-theoretic accounts of guarded recursion, emphasizing type theory’s role as the ul...

Computational type theory provides answers to questions such as: What is a type? What is a natural number? How do we compute with types? How are types related to sets? Can types be elements of types? How are data types for numbers, lists, trees, graphs, etc. related to the corresponding notions in mathematics? What is a real number? Are the integers a subtype of the reals? Can we form the type ...

Historically, computation has been a driving force in the development of mathematics. To help measure the sizes of their fields, the Egyptians invented geometry. To help predict the positions of the planets, the Greeks invented trigonometry. Algebra was invented to deal with equations that arose when mathematics was used to model the world. The list goes on, and it is not just historical. If an...

From the hospital, to the schoolroom, to the boardroom people nd that the actions they take aect and are aaected by v arious organizations, and the norms, procedures , culture, and members of those organizations. In order to navigate through an organizational world, agents (human and artiicial) need social and organizational intelligence. This organizational intelligence comprises many dimensio...

One of the goals of the study of music theory is to develop sets of rules to describe different styles of music. By formalising these rules so that their semantics are machine intelligible, it is possible to use computers to reason about and analyse these rules – computational music theory. ANTONis an automatic composition system based on this approach. It formalises the rules of Renaissance Co...

A linking theory explains how verbs’ semantic arguments are mapped to their syntactic arguments—the inverse of the semantic role labeling task from the shallow semantic parsing literature. In this paper, we develop the computational linking theory framework as a method for implementing and testing linking theories proposed in the theoretical literature. We deploy this framework to assess two cr...

XML must work. Here, we argue the construction of e-commerce. We describe a “fuzzy” tool for controlling checksums [114, 114, 188, 62, 70, 179, 70, 68, 95, 70, 54, 54, 68, 152, 191, 59, 168, 54, 148, 99], which we call SLIT.

Philosophy [nature] is written in that great book which ever lies before our eyes—I mean the universe—but we cannot understand it if we do not first learn the language.in which it is written. This book is written in the mathematical language.without which one wanders in vain through a dark labyrinth. —Galileo Galilei, The Assayer, 1623 (quoted in Burtt EA, The Metaphysical Foundations of Modern...