Results 1  10
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35
Simple timing channels
 in Proceedings 1994 IEEE Computer Society Symposium on Research in Security and Privacy
, 1994
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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 19 (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
Growth and ergodicity of contextfree languages
 Trans. Amer. Math. Soc
"... Abstract. A language L over a finite alphabet Σ is called growthsensitive if forbidding any set of subwords F yields a sublanguage LF 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 13 (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 LF 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
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 12 (1 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.
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 fini ..."
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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...
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 ..."
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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...
Contextfree pairs of groups. II  cuts, tree sets, and random walks
"... This is a continuation of the study, begun by CeccheriniSilberstein and Woess [5], of contextfree pairs of groups and the related contextfree graphs in the sense of Muller and Schupp [20]. Instead of the cones (connected components with respect to deletion of finite balls with respect to the gra ..."
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Cited by 5 (2 self)
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This is a continuation of the study, begun by CeccheriniSilberstein and Woess [5], of contextfree pairs of groups and the related contextfree graphs in the sense of Muller and Schupp [20]. Instead of the cones (connected components with respect to deletion of finite balls with respect to the graph metric), a more general approach to contextfree graphs is proposed via tree sets consisting of cuts of the graph, and associated structure trees. The existence of tree sets with certain “good” properties is studied. With a tree set, a natural contextfree grammar is associated. These investigations of the structure of context free pairs, resp. graphs are then applied to study random walk asymptotics via complex analysis.
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.
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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Cited by 5 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
Infinite Iterated Function Systems in Cantor Space and the Hausdorff Measure of ωPower Languages
 Int. J. of Foundations of Computer Science
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