12,086 research outputs found
Hardware Based Projection onto The Parity Polytope and Probability Simplex
This paper is concerned with the adaptation to hardware of methods for
Euclidean norm projections onto the parity polytope and probability simplex. We
first refine recent efforts to develop efficient methods of projection onto the
parity polytope. Our resulting algorithm can be configured to have either
average computational complexity or worst case
complexity on a serial processor where
is the dimension of projection space. We show how to adapt our projection
routine to hardware. Our projection method uses a sub-routine that involves
another Euclidean projection; onto the probability simplex. We therefore
explain how to adapt to hardware a well know simplex projection algorithm. The
hardware implementations of both projection algorithms achieve area scalings of
at a delay of
. Finally, we present numerical results in
which we evaluate the fixed-point accuracy and resource scaling of these
algorithms when targeting a modern FPGA
On one-way cellular automata with a fixed number of cells
We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA
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