The preex problem is to compute all the products x 1 x 2 x k , for 1 k n, where is an associative binary operation. We start with an asynchronous circuit to solve this problem with O(log n) latency and O(n log n) circuit size, with O(n)-operations in the circuit. Our contributions are: (i) A modiication to the circuit that improves its average-case latency from O(log n) to O(log log n) time; an...

We are interested in solving the prefix problem of n inputs using p < n processors on completely connected distributed-memory multicomputers (CCDMMs). This paper improves a previous work in three respects. First, the communication time of the previous algorithm is reduced significantly. Second, we show that p(p + 1)/2 < n is required for the new algorithm and the original one to be applicable. ...

This paper introduces the concept of parallel distributed computation (PDC) in neural networks, whereby a neural network distributes a number of computations over a network such that the separate computations are not localized in any part of the network. This form of computation is analogous to distributed storage of information as found in distributed associative memories. The paper describes ...

Reverse-engineering the brain is one of the US National Academy of Engineering’s “Grand Challenges.” The structure of the brain can be examined at many different levels, spanning many disciplines from low-level biology through psychology and computer science. This thesis focusses on real-time computation of large neural networks using the Izhikevich spiking neuron model. Neural computation has ...

Parallel computing must meet seemingly contradictory goals: software development should be carried out in an architecture-and technology-independent environment, while both algorithms and system software should take full advantage of the features of the underlying parallel architecture. At the same time, application programmers cannot be expected to be parallel processing experts. Usability, sc...

There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their survival. In the current paper a formal definition of autonomous learning is proposed. From that definition we establish a Turing Machine model for learning, wh...

Results of Feynman and others have shown that the quantum formalism permits a closed, microscopic, and locally interacting system to perform deterministic serial computation. In this paper we show that this formalism can also describe deterministic parallel computation. Achieving full parallelism in more than one dimension remains an open problem.

Given inputs ~1,. . . , z,,, which are independent identically distributed random variables over a domain D, and an associative operation o, the probabilistic prej?x computation problem is to compute the product ~1 o x2 o . . . o xn and its n 1 prefixes. Instances of this problem are finite state transductions on random inputs, the addition or subtraction of two random n-bit binary numbers, and...