Results 1  10
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29
Simple Timing Channels
 Proceedings 1994 IEEE Computer Society Symposium on Research in Security and Privacy
, 1994
"... the proof of Corollary 1.1 in the actual published paper. We havechanged the bottom index of the second sum from a0toa1. As of Sept. 21, 1994 another typo has been xed. page 60, column 2, beginning of line 9 should read C T(a;a+d) instead of T (a; a + d). ..."
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Cited by 31 (9 self)
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the proof of Corollary 1.1 in the actual published paper. We havechanged the bottom index of the second sum from a0toa1. As of Sept. 21, 1994 another typo has been xed. page 60, column 2, beginning of line 9 should read C T(a;a+d) instead of T (a; a + d).
Natural halting probabilities, partial randomness, and zeta functions
 Inform. and Comput
, 2006
"... We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin’s Omega number, halting probability, and programsize complexity. A classification of Turing machines according to their zeta numbers is proposed: divergent, convergent ..."
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Cited by 17 (8 self)
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We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin’s Omega number, halting probability, and programsize complexity. A classification of Turing machines according to their zeta numbers is proposed: divergent, convergent and tuatara. We prove the existence of universal convergent and tuatara machines. Various results on (algorithmic) randomness and partial randomness are proved. For example, we show that the zeta number of a universal tuatara machine is c.e. and random. A new type of partial randomness, asymptotic randomness, is introduced. Finally we show that in contrast to classical (algorithmic) randomness—which cannot be naturally characterised in terms of plain complexity—asymptotic randomness admits such a characterisation. 1
Entropy rates and finitestate dimension
 THEORETICAL COMPUTER SCIENCE
, 2005
"... The effective fractal dimensions at the polynomialspace level and above can all be equivalently defined as the Centropy rate where C is the class of languages corresponding to the level of effectivization. For example, pspacedimension is equivalent to the PSPACEentropy rate. At lower levels of c ..."
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Cited by 14 (0 self)
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The effective fractal dimensions at the polynomialspace level and above can all be equivalently defined as the Centropy rate where C is the class of languages corresponding to the level of effectivization. For example, pspacedimension is equivalent to the PSPACEentropy rate. At lower levels of complexity the equivalence proofs break down. In the polynomialtime case, the Pentropy rate is a lower bound on the pdimension. Equality seems unlikely, but separating the Pentropy rate from pdimension would require proving P != NP. We show that at the finitestate level, the opposite of the polynomialtime case happens: the REGentropy rate is an upper bound on the finitestate dimension. We also use the finitestate genericity of AmbosSpies and Busse (2003) to separate finitestate dimension from the REGentropy rate. However, we point out that a blockentropy rate characterization of finitestate dimension follows from the work of Ziv and Lempel (1978) on finitestate compressibility and the compressibility characterization of finitestate dimension by Dai, Lathrop, Lutz, and Mayordomo (2004). As applications of the REGentropy rate upper bound and the blockentropy rate characterization, we prove that every regular language has finitestate dimension 0 and that normality is equivalent to finitestate dimension 1.
Growth and ergodicity of contextfree languages
 Trans. Amer. Math. Soc
, 2002
"... Abstract. A language L over a finite alphabet Σ is called growthsensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every ergodic unambiguous, nonlinear contextfree language is growthsensitive. “Ergodic ” ..."
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Cited by 11 (7 self)
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Abstract. A language L over a finite alphabet Σ is called growthsensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every ergodic unambiguous, nonlinear contextfree language is growthsensitive. “Ergodic ” means for a contextfree grammar and language that its dependency digraph is strongly connected. The same result as above holds for the larger class of essentially ergodic contextfree languages, and if growth is considered with respect to the ambiguity degrees, then the assumption of unambiguity may be dropped. The methods combine a construction of grammars for 2block languages with a generating function technique regarding systems of algebraic equations. 1. Introduction and
Reduction Of A Class Of FoxWright PSI Functions For Certain Rational Parameters
, 1995
"... The FoxWright Psi function is a special case of Fox's Hfunction and a generalization of the generalized hypergeometric function. In the present paper we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite su ..."
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Cited by 9 (8 self)
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The FoxWright Psi function is a special case of Fox's Hfunction and a generalization of the generalized hypergeometric function. In the present paper we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite sum of generalized hypergeometric functions when these parameters are rational numbers. Applications to the solution of algebraic trinomial equations and to a problem in information theory are provided. A connection with Meijer's Gfunction is also discussed. KEYWORDS: FoxWright Psi function, zeros of trinomials, special functions, information theory. 1 PREPRINTTo appear: Computers & Mathematics with Applications, rev:3/29/95 2 Present address: 1616 Eighteenth Street NW, Washington DC 200092530 3 Author for correspondence 1. INTRODUCTION The FoxWright Psi function p \Psi q [z] and its normalization p \Psi q [z] are hypergeometric functions whose series representations are give...
Valuations of Languages, with Applications to Fractal Geometry
, 1994
"... Valuations  morphisms from (\Sigma ; \Delta; ) to ((0; 1); \Delta; 1)  are a simple generalization of Bernoulli morphisms (distributions, measures) as introduced in [28, 41, 11, 9, 10, 42]. This paper shows that valuations are useful not only within the theory of codes, but also when dealing wit ..."
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Cited by 8 (4 self)
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Valuations  morphisms from (\Sigma ; \Delta; ) to ((0; 1); \Delta; 1)  are a simple generalization of Bernoulli morphisms (distributions, measures) as introduced in [28, 41, 11, 9, 10, 42]. This paper shows that valuations are useful not only within the theory of codes, but also when dealing with ambiguity, especially in contextfree grammars, or for defining outer measures on the space of omegawords which are of some importance to the theory of fractals. These connections yield new formulae to determine the Hausdorff dimension of fractal sets (especially in Euclidean spaces) defined via formal languages. The class of fractals describable with contextfree languages strictly includes that of MRFSfractals introduced in [58, 18]. Some of the results of this paper also appear as part of the author's PhD thesis [36] and in [30, 31].
Fractals, Dimension, And Formal Languages
"... We consider classes of sets of radic expansions of reals specified by means of the theory of formal languages or automata theory. It is shown how these specifications are used to calculate the Hausdorff dimension and Hausdorff measure of such sets. Since the appearence of Mandelbrot's 11 book ..."
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Cited by 6 (4 self)
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We consider classes of sets of radic expansions of reals specified by means of the theory of formal languages or automata theory. It is shown how these specifications are used to calculate the Hausdorff dimension and Hausdorff measure of such sets. Since the appearence of Mandelbrot's 11 book "Fractals, Form, Chance and Dimension " Fractal Geometry as a means providing a theory describing many of the seemingly complex patterns in nature and the sciences has become popular not only in the sciences (cf. Peitgen and Saupe 13 ), but also in computer science. Here Barnsley's 3 "Computational Fractal Geometry" aims at a practical description of fractal patterns by socalled Iterative Function Systems (IFS). Besides IFS several other computational methods for the description (generation) of fractal images involving concepts of Automata or Formal Language Theory have been developed (see e.g. Berstel and Morcrette 4 , Berstel and NaitAbdallah 5 , Culik and Dube 6; 7 , Prusinki...
Growthsensitivity of contextfree languages
, 2003
"... A language L over a finite alphabet is called growthsensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every (essentially) ergodic nonlinear contextfree language of convergent type is growthsensitive. ..."
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Cited by 5 (2 self)
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A language L over a finite alphabet is called growthsensitive if forbidding any set of subwords F yields a sublanguage L F whose exponential growth rate is smaller than that of L. It is shown that every (essentially) ergodic nonlinear contextfree language of convergent type is growthsensitive. “Ergodic” means that the dependency digraph of the generating contextfree grammar is strongly connected, and “essentially ergodic” means that there is only one nonregular strong component in that graph. The methods combine (1) an algorithm for constructing from a given grammar one that generates the associated 2block language and (2) a generating function technique regarding systems of algebraic equations. Furthermore, the algorithm of (1) preserves unambiguity as well as the number of nonregular strong components of the dependency digraph.
Infinite iterated function systems in Cantor space and the Hausdorff measure of ωpower languages
 Intern. J. Found. Comput. Sci
, 2005
"... We use means of formal language theory to estimate the Hausdorff measure of sets of a certain shape in Cantor space. These sets are closely related to infinite iterated function systems in fractal geometry. Our results are used to provide a series of simple examples for the noncoincidence of limit ..."
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Cited by 4 (3 self)
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We use means of formal language theory to estimate the Hausdorff measure of sets of a certain shape in Cantor space. These sets are closely related to infinite iterated function systems in fractal geometry. Our results are used to provide a series of simple examples for the noncoincidence of limit sets and attractors for infinite iterated function systems.
Dimension characterizations of complexity classes
 In Proceedings of the Thirtieth International Symposium on Mathematical Foundations of Computer Science
, 2006
"... We use derandomization to show that sequences of positive pspacedimension – in fact, even positive ∆ p kdimension for suitable k – have, for many purposes, the full power of random oracles. For example, we show that, if S is any binary sequence whose ∆ p 3dimension is positive, then BPP ⊆ PS and, ..."
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Cited by 4 (0 self)
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We use derandomization to show that sequences of positive pspacedimension – in fact, even positive ∆ p kdimension for suitable k – have, for many purposes, the full power of random oracles. For example, we show that, if S is any binary sequence whose ∆ p 3dimension is positive, then BPP ⊆ PS and, moreover, every BPP promise problem is PSseparable. We prove analogous results at higher levels of the polynomialtime hierarchy. The dimensionalmostclass of a complexity class C, denoted by dimalmostC, is the class consisting of all problems A such that A ∈ CS for all but a Hausdorff dimension 0 set of oracles S. Our results yield several characterizations of complexity classes, such as BPP = dimalmostP, PromiseBPP = dimalmostPSep, and AM = dimalmostNP, that refine previously known results on almostclasses. 1