We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture". Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and storage complexity of the proposed procedure are both linear in the source sequence length. We derive a natural upper bound on the cumulative redundancy of our method for individual sequences. The three terms in this bound can be identified as coding, parameter and model redundancy. The bound holds for all source sequence lengths, not only for asymptotically large lengths. The analysis that leads to this bound is based on standard techniques and turns out to be extremely simple. Our upper bound on the redundancy shows that the proposed context tree weighting procedure is optimal in the sense that i...

CONTENTS Table of Contents i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Figures iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Tables viii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary ix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of abbreviations x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary xi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statement of originality xii . . . . . . . . . . . . . . . .

: We note the main points of history, as a framework on which to hang many background remarks concerning the nature and motivation of Bayesian/Maximum Entropy methods. Experience has shown that these are needed in order to understand recent work and problems. A more complete account of the history, with many more details and references, is given in Jaynes (1978). The following discussion is essentially nontechnical; the aim is only to convey a little introductory "feel" for our outlook, purpose, and terminology, and to alert newcomers to common pitfalls of misunderstanding. HERODOTUS 2 BERNOULLI 2 BAYES 4 LAPLACE 5 JEFFREYS 6 COX 8 SHANNON 9 COMMUNICATION DIFFICULTIES 10 IS OUR LOGIC OPEN OR CLOSED? 13 DOWNWARD ANALYSIS IN STATISTICAL MECHANICS 14 CURRENT PROBLEMS 15 REFERENCES 17 ? Presented at the Fourth Annual Workshop on Bayesian/Maximum Entropy Methods, University of Calgary, August 1984. In the Proceedings Volume, Maximum Entropy and Bayesian Methods in Applied Statistics, J. H....

We show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class AM \ co AM. Thus, if the polynomial time hierarchy does not collapse, then NP-complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict NP languages being proven with even one bit of knowledge. Our result is a common generalization of two previous results: The rst asserts that statistical zero knowledge is contained in AM \ co AM [F-89, AH-91], while the second asserts that the languages recognizable in logarithmic statistical knowledge complexity are in BPP NP [GOP-94]. Next, we consider the relation between the error probability and the knowledge complexity of an interactive proof. Note that reducing the error probability via repetition is not free: it may increase the knowledge complexity. We show that if the negligible error probability (n) is less than 2 3k(n) (where k(n) is the knowledge complexity) then the language proven is in the third level of the polynomial time hierarchy (specically, it is in AM NP . In the standard setting of negligible error probability, there exist PSPACE-complete languages which have sub-linear knowledge complexity. However, if we insist, for example, that the error probability is less than 2 n 2 , then PSPACE-complete languages do not have sub-quadratic knowledge complexity, unless PSPACE= P 3 . In order to prove our main result, we develop an AM protocol for checking that a samplable distribution D has a given entropy h. For any fractions ; , the verier runs in time polynomial in 1= and log(1=) and fails with probability at most to detect an additive error in the entropy. We believe that this ...

Abstract not found

Database systems for real-time applications must satisfy timing constraints associated with transactions, in addition to maintaining data consistency. In addition to real-time requirements, security is usually required in many applications. Multilevel security requirements introduce a new dimension to transaction processing in real-time database systems. In this paper, we argue that due to the conflicting goals of each requirement, trade-offs need to be made between security and timeliness. We first define capacity, a measure of the degree to which security is being satisfied by a system. A secure two-phase locking protocol is then described and a scheme is proposed to allow partial violations of security for improved timeliness. The capacity of the resultant covert channel is derived and a feedback control scheme is proposed that does not allow the capacity to exceed a specified upper bound. 1 Introduction Database security is concerned with the ability of a database management syst...

Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like l-calculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its object-oriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.

Abstract. Using the past-future mutual information as a measure of complexity, the relation between the complexity and the Shannon entropy is determined analytically for sequences generated by Markov chains and regular languages. It is emphasized that, given an entropy value, there are many possible complexity values, and vice versa; that is, the relationship between complexity and entropy is not one-toone, but rather many-to-one or one-to-many. It is also emphasized that there are structures in the complexity-versus-entropy plots, and these structures depend on the details of a Markov chain or a regular language grammar. 1.

We extend the work of Sherwood and Zeger [1, 2] to progressive video coding for noisy channels. By utilizing a three-dimensional (3-D) extension of the set partitioning in hierarchical trees (SPIHT) algorithm [3], we cascade the resulting 3-D SPIHT video coder [4, 5] with the ratecompatible punctured convolutional (RCPC) channel coder [6] for transmission of video over a binary symmetric channel (BSC). Progressive coding is achieved by increasing the target rate of the 3-D embedded SPIHT video coder as the channel condition improves. The performance of our proposed coding system is acceptable at low transmission rate and bad channel conditions. 1 Introduction Transmission of compressed images/video over a noisy channel may su#er from disturbance or channel noise. The result is usually uncontrolled degradation in reproduction quality, especially when variable-length coding (VLC) is used for high performance compression. Therefore, a major concern of the designer is the control o...

Summary discovery is one of the major components of knowledge discovery in databases, which provides the user with comprehensive information for grasping the essence from a large amount of information in a database. In this paper, we propose an interactive top-down summary discovery process which utilizes fuzzy ISA hierarchies as domain knowledge. We define a generalized tuple as a representational form of a database summary including fuzzy concepts. By virtue of fuzzy ISA hierarchies where fuzzy ISA relationships common in actual domains are naturally expressed, the discovery process comes up with more accurate database summaries. We also present an informativeness measure for distinguishing generalized tuples that delivers much information to users, based on Shannon's information theory. Keywords--- data mining, summary discovery, fuzzy set application I. Introduction A S the rapid growth of database volumes has deepened the gap between data generation and data understanding, kn...