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15
Fast and Flexible String Matching by Combining Bitparallelism and Suffix Automata
 ACM JOURNAL OF EXPERIMENTAL ALGORITHMICS (JEA
, 1998
"... ... In this paper we merge bitparallelism and suffix automata, so that a nondeterministic suffix automaton is simulated using bitparallelism. The resulting algorithm, called BNDM, obtains the best from both worlds. It is much simpler to implement than BDM and nearly as simple as ShiftOr. It inher ..."
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Cited by 74 (10 self)
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... In this paper we merge bitparallelism and suffix automata, so that a nondeterministic suffix automaton is simulated using bitparallelism. The resulting algorithm, called BNDM, obtains the best from both worlds. It is much simpler to implement than BDM and nearly as simple as ShiftOr. It inherits from ShiftOr the ability to handle flexible patterns and from BDM the ability to skip characters. BNDM is 30%40% faster than BDM and up to 7 times faster than ShiftOr. When compared to the fastest existing algorithms on exact patterns (which belong to the BM family), BNDM is from 20% slower to 3 times faster, depending on the alphabet size. With respect to flexible pattern searching, BNDM is by far the fastest technique to deal with classes of characters and is competitive to search allowing errors. In particular, BNDM seems very adequate for computational biology applications, since it is the fastest algorithm to search on DNA sequences and flexible searching is an important problem in that
NRgrep: A Fast and Flexible Pattern Matching Tool
 Software Practice and Experience (SPE
, 2000
"... We present nrgrep ("nondeterministic reverse grep"), a new pattern matching tool designed for efficient search of complex patterns. Unlike previous tools of the grep family, such as agrep and Gnu grep, nrgrep is based on a single and uniform concept: the bitparallel simulation of a non ..."
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Cited by 46 (7 self)
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We present nrgrep ("nondeterministic reverse grep"), a new pattern matching tool designed for efficient search of complex patterns. Unlike previous tools of the grep family, such as agrep and Gnu grep, nrgrep is based on a single and uniform concept: the bitparallel simulation of a nondeterministic suffix automaton. As a result, nrgrep can find from simple patterns to regular expressions, exactly or allowing errors in the matches, with an efficiency that degrades smoothly as the complexity of the searched pattern increases. Another concept fully integrated into nrgrep and that contributes to this smoothness is the selection of adequate subpatterns for fast scanning, which is also absent in many current tools. We show that the efficiency of nrgrep is similar to that of the fastest existing string matching tools for the simplest patterns, and by far unpaired for more complex patterns.
Fast and simple character classes and bounded gaps pattern matching, with application to protein searching
 Journal of Computational Biology
, 2001
"... The problem of fast exact and approximate searching for a pattern that contains classes of characters and bounded size gaps (CBG) in a text has a wide range of applications, among which a very important one is protein pattern matching (for instance, one PROSITE protein site is associated with the CB ..."
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Cited by 35 (3 self)
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The problem of fast exact and approximate searching for a pattern that contains classes of characters and bounded size gaps (CBG) in a text has a wide range of applications, among which a very important one is protein pattern matching (for instance, one PROSITE protein site is associated with the CBG [RK]  x(2,3)  [DE]  x(2,3)  Y, where the brackets match any of the letters inside, and x(2,3) a gap of length between 2 and 3). Currently, the only way to search for a CBG in a text is to convert it into a full regular expression (RE). However, a RE is more sophisticated than a CBG, and searching for it with a RE pattern matching algorithm complicates the search and makes it slow. This is the reason why we design in this article two new practical CBG matching algorithms that are much simpler and faster than all the RE search techniques. The first one looks exactly once at each text character. The second one does not need to consider all the text characters, and hence it is usually faster than the first one, but in bad cases may have to read the same text character more than once. We then propose a criterion based on the form of the CBG to choose a priori the fastest between both. We also show how to search permitting a few mistakes in the occurrences. We performed many practical experiments using the PROSITE database, and all of them show that our algorithms are the fastest in virtually all cases.
Compact DFA Representation for Fast Regular Expression Search
, 2001
"... . We present a new technique to encode a deterministic finite automaton (DFA). Based on the specific properties of Glushkov's nondeterministic finite automaton (NFA) construction algorithm, we are able to encode the DFA using (m + 1)(2 m+1 + j\Sigma j) bits, where m is the number of charact ..."
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Cited by 13 (6 self)
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. We present a new technique to encode a deterministic finite automaton (DFA). Based on the specific properties of Glushkov's nondeterministic finite automaton (NFA) construction algorithm, we are able to encode the DFA using (m + 1)(2 m+1 + j\Sigma j) bits, where m is the number of characters (excluding operator symbols) in the regular expression and \Sigma is the alphabet. This compares favorably against the worst case of (m+1)2 m+1 j\Sigma j bits needed by a classical DFA representation and m(2 2m+1 + j\Sigma j) bits needed by the Wu and Manber approach implemented in Agrep. Our approach is practical and simple to implement, and it permits searching regular expressions of moderate size (which include most cases of interest) faster than with any previously existing algorithm, as we show experimentally. 1
Regular Expression Searching on Compressed Text
 Journal of Discrete Algorithms
, 2003
"... We present a solution to the problem of regular expression searching on compressed text. ..."
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Cited by 13 (1 self)
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We present a solution to the problem of regular expression searching on compressed text.
New techniques for regular expression searching
 Algorithmica
, 2005
"... We present two new techniques for regular expression searching and use them to derive faster practical algorithms. Based on the specific properties of Glushkov’s nondeterministic finite automaton construction algorithm, we show how to encode a deterministic finite automaton (DFA) using O(m2 m) bits, ..."
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We present two new techniques for regular expression searching and use them to derive faster practical algorithms. Based on the specific properties of Glushkov’s nondeterministic finite automaton construction algorithm, we show how to encode a deterministic finite automaton (DFA) using O(m2 m) bits, where m is the number of characters, excluding operator symbols, in the regular expression. This compares favorably against the worst case of O(m2 m Σ) bits needed by a classical DFA representation (where Σ is the alphabet) and O(m2 2m) bits needed by the Wu and Manber approach implemented in Agrep. We also present a new way to search for regular expressions, which is able to skip text characters. The idea is to determine the minimum length ℓ of a string matching the regular expression, manipulate the original automaton so that it recognizes all the reverse prefixes of length up to ℓ of the strings originally accepted, and use it to skip text characters as done for exact string matching in previous work. We combine these techniques into two algorithms, one able and one unable to skip text characters. The algorithms are simple to implement, and our experiments show that they permit fast searching for regular expressions, normally faster than any existing algorithm. 1
A unified construction of the Glushkov, follow and Antimirov automata
 Lecture Notes in Computer Science 4162 (2006
"... Abstract. Many techniques have been introduced in the last few decades to create free automata representing regular expressions: Glushkov automata, the socalled follow automata, and Antimirov automata. This paper presents a simple and unified view of all these free automata both in the case of u ..."
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Cited by 12 (0 self)
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Abstract. Many techniques have been introduced in the last few decades to create free automata representing regular expressions: Glushkov automata, the socalled follow automata, and Antimirov automata. This paper presents a simple and unified view of all these free automata both in the case of unweighted and weighted regular expressions. It describes simple and general algorithms with running time complexities at least as good as that of the best previously known techniques, and provides concise proofs. The construction methods are all based on two standard automata algorithms: epsilonremoval and minimization. This contrasts with the multitude of complicated and specialpurpose techniques and proofs put forward by others to construct these automata. Our analysis provides a better understanding of free automata representing regular expressions: they are all the results of the application of some combinations of epsilonremoval and minimization to the classical Thompson automata. This makes it straightforward to generalize these algorithms to the weighted case, which also results in much simpler algorithms than existing ones. For weighted regular expressions over a closed semiring, we extend the notion of follow automata to the weighted case. We also present the first algorithm to compute the Antimirov automata in the weighted case. 1
On NFA reductions
 THEORY IS FOREVER
, 2004
"... We give faster algorithms for two methods of reducing the number of states in nondeterministic finite automata. The first uses equivalences and the second uses preorders. We develop restricted reduction algorithms that operate on position automata while preserving some of its properties. We show emp ..."
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Cited by 9 (2 self)
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We give faster algorithms for two methods of reducing the number of states in nondeterministic finite automata. The first uses equivalences and the second uses preorders. We develop restricted reduction algorithms that operate on position automata while preserving some of its properties. We show empirically that these reductions are effective in largely reducing the memory requirements of regular expression search algorithms, and compare the effectiveness of different reductions.
A fast algorithm for approximate string matching on gene sequences
 in Symposium. 16th Annu. Combinatorial Pattern Matching, LNCS, SpringerVerlag
, 2005
"... Abstract. Approximate string matching is a fundamental and challenging problem in computer science, for which a fast algorithm is highly demanded in many applications including text processing and DNA sequence analysis. In this paper, we present a fast algorithm for approximate string matching, call ..."
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Cited by 6 (0 self)
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Abstract. Approximate string matching is a fundamental and challenging problem in computer science, for which a fast algorithm is highly demanded in many applications including text processing and DNA sequence analysis. In this paper, we present a fast algorithm for approximate string matching, called FAAST. It aims at solving a popular variant of the approximate string matching problem, the kmismatch problem, whose objective is to find all occurrences of a short pattern in a long text string with at most k mismatches. FAAST generalizes the wellknown TarhioUkkonen algorithm by requiring two or more matches when calculating shift distances, which makes the approximate string matching process significantly faster than the TarhioUkkonen algorithm. Theoretically, we prove that FAAST on average skips more characters than the TarhioUkkonen algorithm in a single shift, and makes fewer character comparisons in an entire matching process. Experiments on both simulated data sets and real gene sequences also demonstrate that FAAST runs several times faster than the TarhioUkkonen algorithm in all the cases that we tested. 1