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86
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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Cited by 86 (2 self)
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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.
The ubiquitous ProuhetThueMorse sequence
 Sequences and their applications, Proceedings of SETA’98
, 1999
"... We discuss a wellknown binary sequence called the ThueMorse sequence, or the ProuhetThueMorse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The ProuhetThueMorse sequence appears to be som ..."
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Cited by 55 (8 self)
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We discuss a wellknown binary sequence called the ThueMorse sequence, or the ProuhetThueMorse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The ProuhetThueMorse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences.
Optimal Parallel Algorithms for Periods, Palindromes and Squares (Extended Abstract)
, 1992
"... ) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and TelAviv University Summary of results Optimal concurrentread concurrentwrite parallel algorithms for two problems are presented: ffl Finding all the pe ..."
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Cited by 32 (13 self)
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) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and TelAviv University Summary of results Optimal concurrentread concurrentwrite parallel algorithms for two problems are presented: ffl Finding all the periods of a string. The period of a string can be computed by previous efficient parallel algorithms only if it is shorter than half of the length of the string. Our new algorithm computes all the periods in optimal O(log log n) time, even if they are longer. The algorithm can be used to compute all initial palindromes of a string within the same bounds. ffl Testing if a string is squarefree. We present an optimal O(log log n) time algorithm for testing if a string is squarefree, improving the previous bound of O(log n) given by Apostolico [1] and Crochemore and Rytter [12]. We show matching lower bounds for the optimal parallel algorithms that solve the problems above on a general alphab...
Generalizing Generalized Tries
, 1999
"... A trie is a search tree scheme that employs the structure of search keys to organize information. Tries were originally devised as a means to represent a collection of records indexed by strings over a fixed alphabet. Based on work by C.P. Wadsworth and others, R.H. Connelly and F.L. Morris generali ..."
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Cited by 31 (8 self)
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A trie is a search tree scheme that employs the structure of search keys to organize information. Tries were originally devised as a means to represent a collection of records indexed by strings over a fixed alphabet. Based on work by C.P. Wadsworth and others, R.H. Connelly and F.L. Morris generalized the concept to permit indexing by elements of an arbitrary monomorphic datatype. Here we go one step further and define tries and operations on tries generically for arbitrary firstorder polymorphic datatypes. The derivation is based on techniques recently developed in the context of polytypic programming. It is well known that for the implementation of generalized tries nested datatypes and polymorphic recursion are needed. Implementing tries for polymorphic datatypes places even greater demands on the type system: it requires rank2 type signatures and higherorder polymorphic nested datatypes. Despite these requirements the definition of generalized tries for polymorphic datatypes is...
Fast and lean selfstabilizing asynchronous protocols
 IN PROC. OF THE 35TH IEEE ANN. SYMP. ON FOUNDATION OF COMPUTER SCIENCE
, 1994
"... We consider asynchronous general topology dynamic networks of identical nameless nodes with worstcase transient faults. Starting from any faulty configuration, our protocols selfstabilize any computation in time polynomial in the (unknown) network diameter. This version sacrifices some diversity o ..."
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Cited by 31 (0 self)
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We consider asynchronous general topology dynamic networks of identical nameless nodes with worstcase transient faults. Starting from any faulty configuration, our protocols selfstabilize any computation in time polynomial in the (unknown) network diameter. This version sacrifices some diversity of tasks and efficiency for simplicity and clarity of details. Appendix gives more efficient procedures in less detail.
Generic Haskell: applications
 In Generic Programming, Advanced Lectures, volume 2793 of LNCS
, 2003
"... Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes discuss three advanced generic programming applications: generic dictionaries, compressing XML documents, and the zipper: a data structure used to represent a tree together with a s ..."
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Cited by 30 (16 self)
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Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes discuss three advanced generic programming applications: generic dictionaries, compressing XML documents, and the zipper: a data structure used to represent a tree together with a subtree that is the focus of attention, where that focus may move left, right, up or down the tree. When describing and implementing these examples, we will encounter some advanced features of Generic Haskell, such as typeindexed data types, dependencies between and generic abstractions of generic functions, adjusting a generic function using a default case, and generic functions with a special case for a particular constructor.
SelfAlignment in Words and their Applications
 J. Algorithms
, 1992
"... Some quantities associated with periodicities in words are analyzed within the Bernoulli probabilistic model. In particular, the following problem is addressed. Assume that a string X is given, with symbols emitted randomly but independently according to some known distribution of probabilities. T ..."
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Cited by 27 (8 self)
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Some quantities associated with periodicities in words are analyzed within the Bernoulli probabilistic model. In particular, the following problem is addressed. Assume that a string X is given, with symbols emitted randomly but independently according to some known distribution of probabilities. Then, for each pair (W , Z) of distinct suffixes of X, the expected length of the longest common prefix of W and Z is sought. The collection of these lengths, that are called here selfalignments, plays a crucial role in several algorithmic problems on words, such as building suffix trees or inverted files, detecting squares and other regularities, computing substring statistics, etc. The asymptotically best algorithms for these problems are quite complex and thus risk to be unpractical. The present analysis of selfalignments and related measures suggests that, in a variety of cases, more straightforward algorithmic solutions may yield comparable or even better performances. Key words and ph...
Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
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Cited by 22 (3 self)
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The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.