In his book The World is Flat, Thomas Friedman convincingly explains the challenges of a global marketplace [4]. One implication is that software development can be out-sourced, as can any narrow, skills-based occupation; however, as Friedman also points out, leadership, innovation, and insight are always in demand. We have recently created and are implementing threadstm, a new structuring principle for computing curricula. Threads provides one clear path for scientists seeking to reinvent and re-invigorate science degree programs. Threads form a cohesive, coordinated set of contexts for understanding computing. The union of all threads covers the breadth computer science. The union of any two threads is sufficient to cover a science degree. In this paper, we describe Threads, our process, the impact so far, and some of our future plans. We close with recommendations for other schools, especially schools with smaller programs.

We present new results, both positive and negative, on the well-studied problem of learning disjunctive normal form (DNF) expressions.We first prove that an algorithm due to Kushilevitz and Mansour ysis of a finite class of boolean functions 011 the hypercube.1

In a typical speech recognition system, computing the match between an incoming acoustic string and many competing models is computationally expensive. Once the highest ranking models are identified, all other match scores are discarded. The authors propose to make use of all computed scores by means of statistical inference. They view the match between an incoming acoustic string s and a model M/sub i/ as a random variable Y/sub i/. The class-conditioning distributions of (Y/sub 1/,. . .Y/sub N/) can be studied offline by sampling, and then used in a variety of ways. For example, the means of these distributions give rise to a natural measure of distance between models. One of the most useful applications of these distributions is as a basis for a new Bayesian classifier. The latter can be used to significantly reduce search effort in large vocabularies, and to quickly obtain a short list of candidate words. An example hidden Markov model (HMM)-based system shows promising results.>

We consider the problem of approximating a Boolean function f : f0; 1g n ! f0; 1g by the sign of an integer polynomial p of degree k. For us, a polynomial p(x) predicts the value of f(x) if, whenever p(x) 0, f(x) = 1, and whenever p(x) ! 0, f(x) = 0. A low-degree polynomial p is a good approximator for f if it predicts f at almost all points. Given a positive integer k, and a Boolean function f , we ask, "how good is the best degree k approximation to f?" We introduce a new lower bound technique which applies to any Boolean function. We show that the lower bound technique yields tight bounds in the case f is parity. Minsky and Papert [10] proved that a perceptron can not compute parity; our bounds indicate exactly how well Yale University, Dept. of Computer Science, P.O. Box 208285, New Haven CT 06520-8285. y Email: [email protected]. z Email: [email protected]. Supported in part by NSF grants CCR-8808949 and CCR-8958528. x Carnegie-Mellon University, Schoo...

Given n natural numbers $a_1 , \cdots ,a_n $ and a target integer b, the SubsetSum problem is to determine whether some subset of the $a_i $; sums to b. That is, to recognize members of the following set: \[ {\text{SubsetSum}} = \left\{ \left\langle {a_1 , \cdots ,a_n ;b} \right\rangle |a_i \in {\bf N} b \in {\bf Z},{\text{ and }}\exists x \in \{ 0,1\} ^n {\text{ such that }} a \cdot x = b \right\} . \] For a given vector $a = (a_1 , \cdots ,a_n )$ and integer b, if a subset of the $a_i $ sums to b, then listing which subset provides a short proof that $\langle {a;b} \rangle \in {\text{SubsetSum}}$. However, in general there are no short (polynomial-length) proofs of nonmembership unless NP equals coNP. The main result in this paper provides a proof system that contains polynomial-length nonmembership proofs for a vast majority of the problem instances that do not belong to SubsetSum.

The computational complexity of constructing the imbeddings of a given graph into surfaces of different genus is not well understood. In this paper, topological methods and a reduction to linear matroid parity are used to develop a polynomial-time algorithm to find a maximum-genus cellular imbedding. This seems to be the first imbedding algorithm for which the running time is not exponential in the genus of the imbedding surface.

Many different types of inter-process communication have been examined from a complexity point of view [SP, Y]. We study a new model, in which a collection of processes

We show that any group represented by generators that are cycles of bounded degree has O(n2) diameter, i.e., that the longest product of generators required to reach any permutation in the group is O(n2). We also show how such “short” products can be found in polynomial time. The techniques presented are applicable to generalizations of many permutation-group puzzles such as Alexander's Star and the Hungarian Rings.

A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function. Introducing the notion of polynomial-size, constant-depth reduction, similar results are shown for the majority, multiplication, and transitive closure functions. Connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.

A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n. We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testing are decidable in polynomial time. In addition, we demonstrate that the normal closure of a subgroup can be computed in polynomial time, and that this proceaure can be used to test a group for solvability. We also describe an approach to computing the intersection of two groups. The procedures and techniques have wide applicability and have recently been used to improve many graph isomorphism algorithms.