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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an <italic>n</italic>-node graph, the names of the nodes (i.e. integers from 1 to <italic>n</italic>) betray nothing about the graph itself. Indeed, the names (or labels) on the <italic>n</italic> nodes are just log<italic>n</italic> bit place… (More)

We formalize a potentially rich new streaming model, the semi-streaming model, that we believe is necessary for the fruitful study of efficient algorithms for solving problems on massive graphs whose edge sets cannot be stored in memory. In this model, the input graph, G = (V, E), is presented as a stream of edges (in adversarial order), and the storage… (More)

We extend the notion of program checking to include programs which alter their environment. In particular, we consider programs which store and retrieve data from memory. The model we consider allows the checker a small amount of reliable memory. The checker is presented with a sequence of requests (on-line) to a data structure which must reside in a large… (More)

A <italic>program correctness checker</italic> is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It designs program checkers for a few specific… (More)

We investigate the importance of space when solving problems based on graph distance in the streaming model. In this model, the input graph is presented as a stream of edges in an arbitrary order. The main computational restriction of the model is that we have limited space and therefore cannot store all the streamed data; we are forced to make… (More)

- Fei Xia, Aravind Joshi, Vijay Shanker, Hiyan Alshawi, Christy Doran, Beth Ann Hockey +74 others

We give a space-efficient, one-pass algorithm for approximating the L 1 difference P i ja i , b i j between two functions , when the function values a i and b i are given as data streams, and their order is chosen by an adversary. Our main technical innovation is a method of constructing families fV j g of limited-independence random variables that are… (More)

We show that the class of all circuits is exactly learnable in randomized expected polynomial time using subset and superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected polynomial time with equivalence queries and the aid of an NP-oracle. We… (More)

We describe a procedure which may be helpful to any disorganized carpenter who has a mixed pile of bolts and nuts and wants to nd the corresponding pairs of bolts and nuts. The procedure uses our (and the carpenter's) ability to construct eeciently highly expanding graphs. The problem considered is given a collection of n bolts of distinct widths and n nuts… (More)

We describe the Monitoring and Checking (MaC) framework which assures the correctness of the current execution at run-time. Monitoring is performed based on a formal specification of system requirements. MaC bridges the gap between formal specification and verification, which ensures the correctness of a design rather than an implementation, and testing,… (More)