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An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].

) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and Tel-Aviv University Summary of results Optimal concurrent-read concurrent-write 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 square-free. We present an optimal O(log log n) time algorithm for testing if a string is square-free, 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...

A string w covers another string z if every position of z is within some occurrence of in z.

Codes play an important role in the study of combinatorics on words. Recently, we introduced pcodes that play a role in the study of combinatorics on partial words. Partial words are strings over a finite alphabet that may contain a number of “do not know ” symbols. In this paper, the theory of codes of words is revisited starting from pcodes of partial words. We present some important properties of pcodes. We give several equivalent definitions of pcodes and the monoids they generate. We investigate in particular the Defect Theorem for partial words. We describe an algorithm to test whether or not a finite set of partial words is a pcode. We also discuss two-element pcodes, complete pcodes, maximal pcodes, and the class of circular pcodes. A World Wide Web server interface has been established at

An O(m)-work, O(m)-space, O(log m)-time CREW-PRAM algorithm for constructing the suffix tree of a string s of length m drawn from any fixed alphabet set is obtained. This is the first known work and space optimal parallel algorithm for this problem. It can be generalized to a string s drawn from any general alphabet set to perform in O(log m) time and O(m log j\Sigmaj) work and space, after the characters in s have been sorted alphabetically, where j\Sigmaj is the number of distinct characters in s. In this case too, the algorithm is work-optimal.

We establish a variety of combinatorial bounds on the tradeoffs inherent in reconstructing strings using few rounds of a given number of substring queries per round. These results lead us to propose a new approach to sequencing by hybridization (SBH), which uses interaction to dramatically reduce the number of oligonucleotides used for de novo sequencing of large DNA fragments, while preserving the parallelism which is the primary advantage of SBH. 1 Introduction Sequencing by hybridization (SBH) [4, 11] is a new and promising approach to DNA sequencing which offers the potential of reduced cost and higher throughput over traditional gel-based approaches. In this paper, we propose a new approach to sequencing by hybridization which permits the sequencing of arbitrarily large fragments without the inherently exponential chip area of SBH, while retaining the massive parallelism which is the primary advantage of the technique. We establish the potential of our technique through both ana...

this paper we characterize all the covers of x in terms of an easily computed normal form for x. The characterization theorem then gives rise to a simple recursive algorithm which computes all the covers of x in time \Theta(n). By avoiding unnecessary checks, this algorithm appears to execute more quickly than that given in [2]. Let x denote a string of length n = jxj 0; in particular, let ffl denote the empty string of zero length. For any nonempty string x, let k 1 be the greatest integer such that (1:1) x = (v

Abstract. We prove that the isomorphism problem for finitely generated fully residually free groups (or F-groups for short) is decidable. We also show that eachF-group G has a decomposition that is invariant under automorphisms of G, and obtain a structure theorem for the group of outer automorphisms Out(G).

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