E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, pages 7--37, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by Navarro in Nrgrep, by combining Shift And and BNDM with the row wise simulation of the NFA that recognizes P . Each row of the NFA now recognizes a complex pattern P . Finally, approximate searching of regular expressions can be done in O(mn) time and O(m) space, as shown by Myers and Miller [49], and in general in O(mn= log s) time using O(s) space, as shown by Wu et al. and Navarro [75, 53] 17 4 Indexed Text Searching In this section we review the main techniques to maintain an index over the text, to speed up searches. As explained, the text must be suciently static (few or no ....

E. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5-37, 1989.

....needed to match the text (0 to k, or more than k) If one applies the classical DFA construction algorithm, the space requirement raises to O( k 2) using Thompson s NFA and O( k 2) using Glushkov s NFA. A dynamic programming based solution with O(mn) time and O(m) space exists [MM89]. Although this is an achievement because it retains the time complexity of the exact search version and handles real valued weights, it is still slow. The Four Russians technique has been gracefully extended to this problem [WMM95] obtaining O(mn= log k s) time using O(s) space. Again, this ....

....(insertions in the text) we have a potential dependence problem, because in order to compute C for state i we need to have already computed C for states that precede i, in an automaton that can perfectly contain cycles. There are good previous solutions to this circular dependence problem [MM89], but these are not easy to apply in a bit parallel context. We present a new solution now. We will use the form i in minimization arguments, whose range is as follows: i (0) i and i (r 1) 2 F ollow (i ) Also, we will denote S i (r) S i (r) T j ) and D = D(T j ) Let us now ....

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E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:7-37, 1989.

.... a cost that depends on the characters inserted deleted and on the number of consecutive insertions deletions made (usually inserting deleting a group costs less than the sum of the individual operations) There exist good algorithms to deal with regular expression searching allowing k di erences [20, 19]. In particular, the latter focuses on the so called network expressions , which are regular expressions without cycles. Although the worst case search cost is O(mn) 20] somewhat improved average time search algorithms are possible [19] These algorithms are rather slow in comparison to those ....

....of the individual operations) There exist good algorithms to deal with regular expression searching allowing k di erences [20, 19] In particular, the latter focuses on the so called network expressions , which are regular expressions without cycles. Although the worst case search cost is O(mn) [20], somewhat improved average time search algorithms are possible [19] These algorithms are rather slow in comparison to those for exact searching, but they permit using the complex cost functions that are of interest in computational biology. Since CBG patterns can be translated into network ....

E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:7-37, 1989.

....(see Table 3) The meaning of this signal is: the rst position is either a C or a T in all the tRNA sequences of the test alignment, the second position can be anything except a T , etc. Such signals are network expressions (regular expressions not containing a Kleene closure) Myers and Miller [11] developed an O(np) algorithm for approximately matching a sequence G of size n to a regular expression R of size p. This algorithm is based on an alignment graph obtained by concatenating n 1 copies of a non deterministic nite automaton recognizing R. An optimization running in O(kp) time, ....

....A secondary expression representing a signature for the T C region of tRNAs; b) An occurrence of the secondary expression (a) We present an algorithm that allows to search for a secondary expression S in a exible and ecient way. We have developed a method inspired by that of Myers and Miller [11], but which is more complex since we need to control the di erent paths leading to an acceptance. In order to do so, we use pushdown automata instead of non deterministic nite automata. The worst time complexity of our new algorithm is O(rpn) where n is the genome size , p the size of the ....

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E.W. Myers and W. Miller. Approximate matching of regular expressions. Bull. of Mathematical Biology, 51(1):5-37, 1989.

....previous work on approximate regular expression matching. In [38] Mutko presents nondeterministic automata for approximate regular expression matching, but concludes that simulation of a nondeterministic automaton is of a high time complexity without doing any concrete complexity analysis. In [39] Myers and Miller give an algorithm to solve the problem in O(MP ) time, given a string of length M and a regular expression of length P . This is asymptotically no worse than for the simpler problem of approximate matching of simple keywords. The paper also gives an O(MP (M P ) N 2 log N) ....

E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:537, 1989.

....for sets of strings or regular expressions. 3.8. Regular Expressions The algorithm can be extended to allow any regular expression as a pattern. We describe the method here only briefly. Algorithms for matching regular expressions with errors, based on the dynamic programming approach, appear in [MM89]. First, we illustrate the algorithm with a simple example. We do not try to optimize the algorithm at this stage; we try to make it as simple as possible (a more detailed discussion and more efficient algorithms will be presented elsewhere) Let the pattern be P = ab (cd e) fg (i.e. ....

....the same line; a is the regular expression union operation; and a is the Kleene closure. The results are given in Table 3 (the file was the same bibliographic file used in Table 1) The best algorithm we know for approximate matching to arbitrary regular expressions is by Myers and Miller [MM89]. Its running times for the cases we tested were more than an order of magnitude slower than our algorithm, but this is not a fair test, because Myers and Miller s algorithm can handle arbitrary costs (which we cannot handle) and its running time is independent of the number of errors (which makes ....

Myers, E. W., and W. Miller, "Approximate matching of regular expressions," Bull. of Mathematical Biology, 51 (1989), pp. 5-37.

....to select a candidate pattern, in particular the basic operations in the analysis component are: Select form the nucleotide sequence a candidate pattern consisting of positions j 1; i. Align the pattern with the surrounding sequence using wraparound dynamic programming (WDP) see [9] and [6] Report the tandem repeat if at least two copies of the pattern are aligned. Some other implementing details are reported below: Several pattern sizes are possible when a single tandem repeat contains many copies. The author choice, in this case, is to limit this redundancy in the ....

E.W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:5--37, 1989.

....: 68R15. Keywords : free monoid, word, factor, period, morphism, equation, solution, pattern, algorithm, complexity. Bull. Belg. Math. Soc. 1 (1994) 253 283 254 J. Neraud Approximate pattern matching is also concerned, and led to a lot of challenging combinatorical algorithms (e.g. 26] [21], 18] Languages described by generalized regular expression (GRE for short) a more general class of languages, are also concerned. Practically, this notion of GRE is illustrated in the commands of the text editors of the UNIX system. Formally, given two finite disjoint sets, say #, the ....

E. Myers, W. Miller, Approximate matching of regular expressions, Bulletin of Mathematical Biology 51 (1) (1989) 5--37.

....foundation of the method described in Section 3. We will restrict ourselves to regular languages as this is sufficient for the considered application. The algorithm presented in this section is a restricted version of the parser introduced in [10] Similar algorithms have been described in [11,12]. The following definitions are taken from [13] We consider a finite alphabet X = fx 1 ; x n g of symbols. The set of all words over X, including the empty word ffl, is denoted by X . A (deterministic) finite state automaton (fsa) over X is a 5 tuple A = Q; X; ffi; q 0 ; F ) where Q is ....

Myers, E. and Miller, W.: Approximate matching of regular expressions, Bulletin of Math. Biology, Vol. 51, No. 1, 1989, 5-37

....1 Throughout the paper, we shall refer to ordered trees simply as trees when no ambiguity occurs. 2 This problem has been studied by Sellers [16] and Ukkonen [22] Landau and Vishkin [9] and Galil and Park [6] improved their algorithms and gave fast parallel algorithms. Myers and Miller [12] investigated similar problems in the context of regular expression matching. Specifically, they develop algorithms to find (1) the sequence in a pattern that is most similar to the data string, and (2) substrings of a data string that strongly align with a sequence in the pattern. One interesting ....

E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5--37, 1989.

....in several ways. One of them is to reduce the number of ffl transitions based on states with out degree greater than 1. This leads to an interesting optimization problem which is being studied. This algorithm can be extended to consider errors as is mentioned also in [WM92, WMM95] see also [MM89]) 7 Concluding Remarks In this paper we have unified several algorithms using a single technique: bitwise simulation of NFAs. We have also shown that many algorithms for approximate string matching, including dynamic programming, can be seen as specialized bitwise simulations. An additional ....

E. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5--37, 1989.

....including regular expressions. Agrep does not yet use any Boyer Moore type filtering for these patterns. As a result, the running times are slower than they are for simpler patterns. The best algorithm we know for approximate matching to arbitrary regular expressions is by Myers and Miller [MM89]. Its running times for the cases we tested were more than an order of magnitude slower than our algorithm, but this is not a fair test, because Myers and Miller s algorithm can handle arbitrary costs (which we cannot handle) and its running time is independent of the number of errors (which makes ....

Myers, E. W., and W. Miller, "Approximate matching of regular expressions," Bull. of Mathematical Biology 51 (1989), pp. 5-37.

.... very different from the standard definition in which two strings are an approximate match if they are within a specified edit distance (number of insertions, deletions, or substitutions) from each other, as studied, for example, in [CL,GG] Even exact or approximate matches to regular expressions [Aho,MM,WM] do not involve any notion of relating repeated occurrences of corresponding (but different) symbols. The UNIX grep pattern matching program and ed editor [KP] allow a pattern to be a restricted regular expression with backreferencing to refer to parts of the text matching earlier parts of the ....

Eugene W. Myers and Webb Miller, Approximate matching of regular expressions, Bulletin of Mathematical Biology 51 (1989), pp. 5-37.

....to a number of reasons: e.g. abaaaba may be matched to abaaba correcting for a spurious a, or ababba may be matched to either abaaba correcting a b to an a, or to ababab correcting the reversal of the last two symbols. There have been a number of approaches to error tolerant recognition, e.g. [19, 12]. These are however suited for applications where the pattern or the regular expression is small, and the sequence to be matched is large which is typical in information retrieval applications. For example, Myers and Miller [12] present an O(MN ) algorithm with M being the length of the string ....

....been a number of approaches to error tolerant recognition, e.g. 19, 12] These are however suited for applications where the pattern or the regular expression is small, and the sequence to be matched is large which is typical in information retrieval applications. For example, Myers and Miller [12], present an O(MN ) algorithm with M being the length of the string and N , being the length of the regular expression. In the applications we are concerned with, the recognizers (and the corresponding regular expressions) are very large. The approach presented in this paper uses the finite state ....

Eugene W. Myers and Webb Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5--37, 1989.

....fl(M ) Lemma 2, 46] Hence, we have dist(T; T 0 ) min ffl(M ) j M is a mapping from T to T 0 g. 2.3 Approximate Tree Matching Operations In [37] Ukkonen discussed approximate string matching operations that allow prefixes of strings to be removed when comparing strings. Myers and Miller [21] discussed similar operations for regular expressions. We extend these operations to trees by considering prefixes as a collection of subtrees. The following two operations are introduced: ffl Cutting at node n from tree T means removing n and all its descendants (i.e. removing the subtree ....

E. W. Myers and W. Miller, "Approximate matching of regular expressions," Bulletin of Mathematical Biology, vol. 51, no. 1, pp. 5-37, 1989.

.... very different from the standard definition in which two strings are an approximate match if they are within a specified edit distance (number of insertions, deletions, or substitutions) from each other, as studied, for example, in [CL,GG] Even exact or approximate matches to regular expressions [Aho,MM,WM] do not involve any notion of relating repeated occurrences of corresponding (but different) symbols. A pattern p string can be 73 encoded as a regular expression by taking the union of patterns obtained by all possible renamings of parameters, but this gives a blowup in the size of the pattern ....

Eugene W. Myers and Webb Miller, Approximate matching of regular expressions, Bulletin of Mathematical Biology 51 (1989), pp. 5-37.

....Sequence O(mn) O(m) O(1) all endpts [WF74] Using dynamic programming. Sequence O(mn) O(mn) O(1) all [WF74] Using dynamic programming a . Sequence O(n) O(m) O(1) all endpts [BYG89, WM91] Pattern fits within a word of the computer. Small integer values of costs. RE O(mn) O(m) O(m) all endpts [MM89] Using dynamic programming. RE O(mn) O(mn) O(m) all [MM89] Using dynamic programming a . a Does not include the time for enumerating all matches which may be exponential While approximate pattern matching is useful in misuse intrusion detection, the general problem in misuse intrusion ....

....programming. Sequence O(mn) O(mn) O(1) all [WF74] Using dynamic programming a . Sequence O(n) O(m) O(1) all endpts [BYG89, WM91] Pattern fits within a word of the computer. Small integer values of costs. RE O(mn) O(m) O(m) all endpts [MM89] Using dynamic programming. RE O(mn) O(mn) O(m) all [MM89] Using dynamic programming a . a Does not include the time for enumerating all matches which may be exponential While approximate pattern matching is useful in misuse intrusion detection, the general problem in misuse intrusion detection cannot be reasonably solved by current pattern matching ....

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Eugene W. Myers and Webb Miller. Approximate Matching of Regular Expressions. In Bull. Math. Biol., volume 51, pages 5--37, 1989.

....to the fitness of its match to R, which we define as the best scoring alignment between (m) # and a substring of R under a user specified scoring scheme #. The e#cient comparison of the regular expression (m) # (matching zero or more repetitions of m) was introduced by Myers and Miller [14] for any regular expression, and a later reincarnation of their work for the case of this special pattern type became popularly known as wrap around 8 set of [0. n] R int I , J , Lmrk[0. n] Rmrk[0. n] procedure RMark(j) Mark j if j J then J # j for i # (Left(j) # (j GAP) # ....

E. W. Myers and W. Miller. Approximate matching of regular expressions. Bull. Math. Biol., 51:5--37, 1989.

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E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, pages 7--37, 1989.

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E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:7--37, 1989.

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E. Myers and W. Miller. Approximate matching of regular expressions. Bull. Math. Biol., 51:7-37, 1989.

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E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5--37, 1989.

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E. W. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51(1):5--37, 1989.

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G. Myers and W. Miller. Approximate matching of regular expressions. Bulletin of Mathematical Biology, 51:7--37, 1989. 22

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Myers, E., Miller W. "Approximate Matching of Regular Expressions", Bulletin of Mathematical Biology, vol.51, no.1, 1989, pp.5-37.

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