6,177 research outputs found
Dynamic Shannon Coding
We present a new algorithm for dynamic prefix-free coding, based on Shannon
coding. We give a simple analysis and prove a better upper bound on the length
of the encoding produced than the corresponding bound for dynamic Huffman
coding. We show how our algorithm can be modified for efficient
length-restricted coding, alphabetic coding and coding with unequal letter
costs.Comment: 6 pages; conference version presented at ESA 2004; journal version
submitted to IEEE Transactions on Information Theor
Prefix Codes for Power Laws with Countable Support
In prefix coding over an infinite alphabet, methods that consider specific
distributions generally consider those that decline more quickly than a power
law (e.g., Golomb coding). Particular power-law distributions, however, model
many random variables encountered in practice. For such random variables,
compression performance is judged via estimates of expected bits per input
symbol. This correspondence introduces a family of prefix codes with an eye
towards near-optimal coding of known distributions. Compression performance is
precisely estimated for well-known probability distributions using these codes
and using previously known prefix codes. One application of these near-optimal
codes is an improved representation of rational numbers.Comment: 5 pages, 2 tables, submitted to Transactions on Information Theor
Turchin's Relation for Call-by-Name Computations: A Formal Approach
Supercompilation is a program transformation technique that was first
described by V. F. Turchin in the 1970s. In supercompilation, Turchin's
relation as a similarity relation on call-stack configurations is used both for
call-by-value and call-by-name semantics to terminate unfolding of the program
being transformed. In this paper, we give a formal grammar model of
call-by-name stack behaviour. We classify the model in terms of the Chomsky
hierarchy and then formally prove that Turchin's relation can terminate all
computations generated by the model.Comment: In Proceedings VPT 2016, arXiv:1607.0183
Fragments of first-order logic over infinite words
We give topological and algebraic characterizations as well as language
theoretic descriptions of the following subclasses of first-order logic FO[<]
for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and
Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). These
descriptions extend the respective results for finite words. In particular, we
relate the above fragments to language classes of certain (unambiguous)
polynomials. An immediate consequence is the decidability of the membership
problem of these classes, but this was shown before by Wilke and Bojanczyk and
is therefore not our main focus. The paper is about the interplay of algebraic,
topological, and language theoretic properties.Comment: Conference version presented at 26th International Symposium on
Theoretical Aspects of Computer Science, STACS 200
Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs
Let be a measure of strictly positive probabilities on the set
of nonnegative integers. Although the countable number of inputs prevents usage
of the Huffman algorithm, there are nontrivial for which known methods find
a source code that is optimal in the sense of minimizing expected codeword
length. For some applications, however, a source code should instead minimize
one of a family of nonlinear objective functions, -exponential means,
those of the form , where is the length of
the th codeword and is a positive constant. Applications of such
minimizations include a novel problem of maximizing the chance of message
receipt in single-shot communications () and a previously known problem of
minimizing the chance of buffer overflow in a queueing system (). This
paper introduces methods for finding codes optimal for such exponential means.
One method applies to geometric distributions, while another applies to
distributions with lighter tails. The latter algorithm is applied to Poisson
distributions and both are extended to alphabetic codes, as well as to
minimizing maximum pointwise redundancy. The aforementioned application of
minimizing the chance of buffer overflow is also considered.Comment: 14 pages, 6 figures, accepted to IEEE Trans. Inform. Theor
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