415 research outputs found
On Empirical Entropy
We propose a compression-based version of the empirical entropy of a finite
string over a finite alphabet. Whereas previously one considers the naked
entropy of (possibly higher order) Markov processes, we consider the sum of the
description of the random variable involved plus the entropy it induces. We
assume only that the distribution involved is computable. To test the new
notion we compare the Normalized Information Distance (the similarity metric)
with a related measure based on Mutual Information in Shannon's framework. This
way the similarities and differences of the last two concepts are exposed.Comment: 14 pages, LaTe
On the power of real-time turing machines under varying specifications
We investigate the relative computing power of Turing machines with differences in the number of work tapes, heads pro work tape, instruction repertoire etc. We concentrate on the k-tape, k-head and k-head jump models as well as the 2-way multihead finite automata with and without jumps. Differences in computing power between machines of unlike specifications emerge under the real-time restriction. In particular it is shown that k+1 heads are more powerful than k heads for re
Forgetful maps between Deligne-Mostow ball quotients
We study forgetful maps between Deligne-Mostow moduli spaces of weighted
points on P^1, and classify the forgetful maps that extend to a map of
orbifolds between the stable completions. The cases where this happens include
the Livn\'e fibrations and the Mostow/Toledo maps between complex hyperbolic
surfaces. They also include a retraction of a 3-dimensional ball quotient onto
one of its 1-dimensional totally geodesic complex submanifolds
On efficient simulations of multicounter machines
An oblivious 1-tape Turing machine can simulate a multicounter machine on-line in linear time and logarithmic space. This leads to a linear cost combinational logic network implementing the first n steps of a multicounter machine and also to a linear time/logarithmic space on-line simulation by an oblivious logarithmic cost RAM. An oblivious log*n-head tape unit can simulate the first n steps of a multicounter machine in real-time, which leads to a linear cost combinational logic network with a constant data rate
Logical depth for reversible Turing machines with an application to the rate of decrease in logical depth for general Turing machines
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