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18
Computing on an Anonymous Ring
 Journal of the ACM
, 1988
"... Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is s ..."
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Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is shown that any of these functions can be computed in O(r?) messages in the asynchronous model. This is also proved to be a lower bound for such elementary functions as AND, SUM, and Orientation. In the synchronous model any computable function can be computed in O(n log n) messages. A ring can be oriented and start synchronized within the same bounds. The main contribution of this paper is a new technique for proving lower bounds in the synchronous model. With this technique tight lower bounds of O(nlogn) (for particular n) are proved for XOR, SUM, Orientation, and Start Synchronization. The technique is based on a stringproducing mechanism from formal language theory, first introduced by Thue to study squarefree words. Two methods for generalizing the synchronous lower bounds to arbitrary ring sizes are presented.
Subword Complexity of Profinite Words and Subgroups of Free Profinite Semigroups
 Internat. J. Algebra Comput
, 2003
"... We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy. ..."
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Cited by 17 (9 self)
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We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.
Complexity of sequences and dynamical systems
 Discr. Math
, 1999
"... In recent years, there has been a number of papers about the combinatorial notion of symbolic complexity: this is the function counting the number of factors of length n for a sequence. The complexity is an indication of the degree of randomness of the sequence: a periodic sequence has a bounded com ..."
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Cited by 16 (0 self)
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In recent years, there has been a number of papers about the combinatorial notion of symbolic complexity: this is the function counting the number of factors of length n for a sequence. The complexity is an indication of the degree of randomness of the sequence: a periodic sequence has a bounded complexity, the expansion of a normal number has an exponential complexity. For a given sequence, the complexity function is generally not of easy access, and it is a rich and instructive work to compute it; a survey of this kind of results can be found in [ALL]. We are interested here in further results in the theory of symbolic complexity, somewhat beyond the simple question of computing the complexity of various sequences. These lie mainly in two directions; first, we give a survey of an open question which is still very much in progress, namely: to determine which functions can be the symbolic complexity function of a sequence. Then, we investigate the links between the complexity of a sequence and its associated dynamical system, and insist on the cases where the knowledge of
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.
Second Preimage Attacks on Dithered Hash Functions
"... Abstract. We develop a new generic longmessage second preimage attack, based on combining the techniques in the second preimage attacks of Dean [8] and Kelsey and Schneier [16] with the herding attack of Kelsey and Kohno [15]. We show that these generic attacks apply to hash functions using the Mer ..."
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Cited by 9 (1 self)
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Abstract. We develop a new generic longmessage second preimage attack, based on combining the techniques in the second preimage attacks of Dean [8] and Kelsey and Schneier [16] with the herding attack of Kelsey and Kohno [15]. We show that these generic attacks apply to hash functions using the MerkleDamgård construction with only slightly more work than the previously known attack, but allow enormously more control of the contents of the second preimage found. Additionally, we show that our new attack applies to several hash function constructions which are not vulnerable to the previously known attack, including the dithered hash proposal of Rivest [25], Shoup’s UOWHF[26] and the ROX hash construction [2]. We analyze the properties of the dithering sequence used in [25], and develop a timememory tradeoff which allows us to apply our second preimage attack to a wide range of dithering sequences, including sequences which are much stronger than those in Rivest’s proposals. Finally, we show that both the existing second preimage attacks [8,16] and our new attack can be applied even more efficiently to multiple target messages; in general, given a set of many target messages with a total of 2 R message blocks, these second preimage attacks can find a second preimage for one of those target messages with no more work than would be necessary to find a second preimage for a single target message of 2 R message blocks.
Palindrome complexity
 To appear, Theoret. Comput. Sci
, 2002
"... We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some sequences, in particular for Rote sequences and for fixed points o ..."
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Cited by 8 (2 self)
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We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some sequences, in particular for Rote sequences and for fixed points of primitive morphisms of constant length belonging to “class P ” of HofKnillSimon. We also give an upper bound for the palindrome complexity of a sequence in terms of its (block)complexity. 1
Toeplitz Words, Generalized Periodicity and Periodically Iterated Morphisms
 European J. of Combinatorics
, 1997
"... We consider socalled Toeplitz words which can be viewed as generalizations of oneway infinite periodic words. We compute their subword complexity, and show that they can always be generated by iterating periodically a finite number of morphisms. Moreover, we define a structural classification of T ..."
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Cited by 7 (2 self)
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We consider socalled Toeplitz words which can be viewed as generalizations of oneway infinite periodic words. We compute their subword complexity, and show that they can always be generated by iterating periodically a finite number of morphisms. Moreover, we define a structural classification of Toeplitz words which is reflected in the way how they can be generated by iterated morphisms.