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22
A complexity theoretic approach to randomness, in
 Proceedings of the 15th Annual ACM Symposium on Theory of Computing
, 1983
"... Abstract: We study a time bounded variant of Kolmogorov complexity. This motion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the the ..."
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Abstract: We study a time bounded variant of Kolmogorov complexity. This motion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the theory of probabilistic constructions. I.
A New Challenge for Compression Algorithms: Genetic Sequences
 Information Processing & Management
, 1994
"... Universal data compression algorithms fail to compress genetic sequences. It is due to the specificity of this particular kind of "text". We analyze in some details the properties of the sequences, which cause the failure of classical algorithms. We then present a lossless algorithm, bioco ..."
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Cited by 88 (0 self)
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Universal data compression algorithms fail to compress genetic sequences. It is due to the specificity of this particular kind of "text". We analyze in some details the properties of the sequences, which cause the failure of classical algorithms. We then present a lossless algorithm, biocompress2, to compress the information contained in DNA and RNA sequences, based on the detection of regularities, such as the presence of palindromes. The algorithm combines substitutional and statistical methods, and to the best of our knowledge, lead to the highest compression of DNA. The results, although not satisfactory, gives insight to the necessary correlation between compression and comprehension of genetic sequences. 1 Introduction There are plenty of specific types of data which need to be compressed, for ease of storage and communication. Among them are texts (such as natural language and programs), images, sounds, etc. In this paper, we focus on the compression of a specific kin...
A Natural Law of Succession
, 1995
"... Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we presen ..."
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Cited by 40 (3 self)
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Consider the following problem. You are given an alphabet of k distinct symbols and are told that the i th symbol occurred exactly ni times in the past. On the basis of this information alone, you must now estimate the conditional probability that the next symbol will be i. In this report, we present a new solution to this fundamental problem in statistics and demonstrate that our solution outperforms standard approaches, both in theory and in practice.
Measuring Sets in Infinite Groups
, 2002
"... We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like "a random element (or a tuple of elements) of a group G has a property P with probability p". The validi ..."
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Cited by 22 (6 self)
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We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like "a random element (or a tuple of elements) of a group G has a property P with probability p". The validity of a statement like that does, of course, heavily depend on how one defines probability on groups, or, equivalently, how one measures sets in a group (in particular, in a free group). We hope that new approaches to defining probabilities on groups as outlined in this paper create, among other things, an appropriate framework for the study of the "average case" complexity of algorithms on groups.
Language Acquisition in the MDL Framework
 In Eric Sven Ristad, Language Computation. American Mathemtatical Society, Philedelphia
, 1994
"... The Minimum Description Length (MDL) principle provides guidance to the fundamental question of determining what a given set of observed data tells us about the underlying data generating machinery. Hence, in the broadest sense the MDL principle relates to the central question of all science, al ..."
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The Minimum Description Length (MDL) principle provides guidance to the fundamental question of determining what a given set of observed data tells us about the underlying data generating machinery. Hence, in the broadest sense the MDL principle relates to the central question of all science, although its most useful applications have been to the more practical problem of fitting statistical models to data. In this article, we review the MDL principle and demonstrate how it may be profitably applied to the logical problem of language acquisition.
Unsupervised Lexical Learning as Inductive Inference
, 2000
"... To learn a language, the learners must first learn its words, the essential building blocks for utterances. The difficulty in learning words lies in the unavailability of explicit word boundaries in speech input. The learners have to infer lexical items with some innately endowed learning mechanism( ..."
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To learn a language, the learners must first learn its words, the essential building blocks for utterances. The difficulty in learning words lies in the unavailability of explicit word boundaries in speech input. The learners have to infer lexical items with some innately endowed learning mechanism(s) for regularity detection regularities in the speech normally indicate word patterns. With respect to Zipf's leasteffort principle and Chomsky's thoughts on the minimality of grammar for human language, we hypothesise a cognitive mechanism underlying language learning that seeks for the leasteffort representation for input data. Accordingly, lexical learning is to infer the minimalcost representation for the input under the constraint of permissible representation for lexical items. The main theme of this thesis is to examine how far this learning mechanism can go in unsupervised lexical learning from real language data without any predefined (e.g., prosodic and phonotactic) cues, but entirely resting on statistical induction of structural patterns for the most economic representation for the data. We first review
Easy sets and hard certificate schemes
 Acta Informatica
, 1997
"... Can easy sets only have easy certificate schemes? In this paper, we study the class of sets that, for all NP certificate schemes (i.e., NP machines), always have easy acceptance certificates (i.e., accepting paths) that can be computed in polynomial time. We also study the class of sets that, for al ..."
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Can easy sets only have easy certificate schemes? In this paper, we study the class of sets that, for all NP certificate schemes (i.e., NP machines), always have easy acceptance certificates (i.e., accepting paths) that can be computed in polynomial time. We also study the class of sets that, for all NP certificate schemes, infinitely often have easy acceptance certificates. In particular, we provide equivalent characterizations of these classes in terms of relative generalized Kolmogorov complexity, showing that they are robust. We also provide structural conditions—regarding immunity and class collapses—that put upper and lower bounds on the sizes of these two classes. Finally, we provide negative results showing that some of our positive claims are optimal with regard to being relativizable. Our negative results are proven using a novel observation: we show that the classical “wide spacing ” oracle construction technique yields instant nonbiimmunity results. Furthermore, we establish a result that improves upon Baker, Gill, and Solovay’s classical result that NP = P = NP ∩ coNP holds in some relativized world.
Enumerations of the Kolmogorov Function
"... We consider the hardness of enumerating k possible values for the Kolmogorov complexity function C(x) so that one of them is correct. We show several results including Any computable enumerator for C(x) must enumerate n) possibilities. If a kenumerator (fixed k) for C is reducible to an r.e. ..."
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We consider the hardness of enumerating k possible values for the Kolmogorov complexity function C(x) so that one of them is correct. We show several results including Any computable enumerator for C(x) must enumerate n) possibilities. If a kenumerator (fixed k) for C is reducible to an r.e. set A then A is Turingequivalent to the halting problem. Every nonrecursive set is not weaktruthtable reducible to some 2enumerator for C(x) or any other recursivelybounded function. The timebounded enumeration question gives a new characterization of the class symP dened by Russell and Sundaram. Enumerating O(log n) values of the spacebounded Kolmogorov function remains hard for PSPACE.