Gerard Berry and Ravi Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....O(2 j j) if the classical Thompson s NFA construction algorithm [Tho68] is used. Thompson s construction produces up to 2m states, but it has interesting properties, such as ensuring a linear number of edges, constant indegree and outdegree, etc. An alternative NFA construction is Glushkov s [Glu61, BS86]. Although it does not provide the same regularities of Thompson s, this construction has other interesting properties, such as producing the minimum number of states (m 1) and that all the edges arriving at a node are labeled by the same character. The corresponding DFA needs only O(2 j j) ....

....represent the states of a DFA (i.e. the sets of states of an NFA) is a bit mask of O(m) bits. The bit mask has in 1 the bits that belong to the set. We use set notation or bit mask notation indistinctly. The description of Glushkov s NFA construction algorithm is outside the scope of this paper [Glu61, BS86]. We just remark some of its properties. Given a regular expression of m characters (not counting operator symbols) the algorithm de nes m 1 positions numbered 0 to m (one per position of a character of in the regular expression, plus an initial position 0) Then, the NFA has exactly one ....

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117-126, 1986.

....techniques to build an NFA from a regular expression R. The most classical one is Thompson s construction [31] which builds an NFA with at most 2m states (where m is counted as the number of letters and s in the RE) A second one is Glushkov s construction, popularized by Berry and Sethi in [4]. The NFA resulting of this construction has the advantage of having just m 1 states (where m is counted as the number of letters in the RE) A lot of research on Glushkov s construction has been pursued, like [6] where it is shown that the resulting NFA is quadratic in the number of edges in ....

G. Berry and R. Sethi. From regular expression to deterministic automata. Theor. Comput. Sci., 48(1):117-126, 1986.

....this method produces an NFA of at most 2m states and 4m edges. A less popular one is Glushkov s [9] which produces an NFA of exactly m 1 states but O(m ) edges. To x ideas we will assume in this paper that we build NFAs using the version of Glushkov s algorithm popularized by Berry and Sethi [6]. The problem of searching for a regular expression E in a given text string T is that of nding all the text substrings that belong to L(E) These are called occurrences. For simplicity, we report the text positions where the occurrences nish in the text, that is, fjxyj; T = xyz; y 2 L(E)g. ....

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117-126, 1986.

....to skip characters under a Shift Or approach, for example [10] 3.4 Regular Expression Searching Bit parallelism has been successfully used to deal with regular expressions. Shift Or was extended in two ways [30, 24, 25] to deal with this case, first using the Thompson [28] and later Glushkov s [5] constructions of NFAs from the regular expression. Figure 4 shows both constructions for the pattern abcd(d ) e f)de . a b c d 1 2 3 0 e e e e d e 13 14 15 16 10 11 12 7 9 8 6 5 4 a 4 5 9 d b c d d e 1 2 3 8 7 0 6 d e f f e Figure 4: Thompson s (top) and ....

....can be applied. Therefore, we use the bit parallel simulation of Glushkov s automaton for nrgrep. After the update operation and we check whether a final state of D is reached (this means just an and operation with the mask of final states) Describing Glushkov s NFA construction algorithm [5] is outside the scope of this paper, but it takes O(m ) time. The result of the construction can be represented as a table B[c] which yields the states reached by character c (no matter from where) and a table F ollow[i] which yields the bitmask of states activated from state i, no matter by ....

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.

....to its small size. However, we need a final confirmation step to find the actual matching strings. It will be interesting to compare the performance of these two approaches. Finite automata There is a large body of literature studying how to match a regex to a string (see the textbook [17] and [22, 9, 25, 6] for instance) The approach is to first convert a regex into an equivalent deterministic finite automaton (DFA) and then use the DFA to match the regex. To expedite the matching, most systems allow the user to save the constructed DFA, so that the user can reuse it when she wants to match the ....

....below. 5 Algorithm 3. 1 Multigram index Input: database Output: index: multigram index [1] k =1,expand = is a zero length string [2] While (expand is not empty) 3] k grams : all k grams in database whose (k 1) prefix expand [4] expand : 5] For each gram x in k grams [6] If sel(x) c Then check selectivity [7] insert(x, index) the gram is useful [8] Else [9] expand : expand # x [10] k : k 1 Figure 4. Construction of a multigram index Theorem 3.9 Let X be the set of grams indexed by algorithm 3.1. 1. If x X , then x is useful. 2. ....

[Article contains additional citation context not shown here]

Gerard Berry and Ravi Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1986.

....issue in practice. We are currently working on techniques that can avoid unbounded growth by restricting the class of patterns permitted in ASL. The starting points for our algorithm for generating EFSA from ASL patterns are the seminal papers by Brzozowski [Brzozowski64] and Berry and Sethi [Berry86]. However, these papers address regular expressions and classical FSA, whereas we must address conditions on event arguments and state variables that can be complex data structures. Our earlier work on first order term matching [Sekar95] provides the starting point for addressing this aspect. By ....

G. Berry and R. Sethi, From Regular Expressions to Deterministic Automata, Theoretical Computer Science 48 pp. 117-126, 1986.

....regular expressions should not take long. A lazy TDFA generating algorithm might also be acceptable, but would be much more complex and use a lot more memory, so I decided to go ahead with a TNFA implementation. There are numerous methods for converting regular expressions to nite automata [8, 9, 10, 46, 36], making an NFA matcher run faster [2, 41] reducing the space requirements for the transition tables [4, 5, 12, 17, 52] and other useful methods and tricks [18, 42, 53] Most of these are probably applicable to TNFAs and TDFAs perhaps with slight modi cations. 4.1 Sacri cing Complexity Any NFA ....

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Comput. Sci., 48(1):117126, 1986.

....LIAFA, Universit e Paris VII. Address: 2, pl. Jussieu, case 7014, F 75251 Paris Cedex 05. time. A well known method for constructing ffl free NFA from regular expressions is based on position automata (Glushkov automata) This classical construction yields NFA of quadratic size (see [5, 10] or [1, 3, 2] for more recent expositions) A substantial improvement on this construction was achieved in [8] where a nondeterministic version of the position automata construction was shown to yield ffl free NFA with O(n log 2 (n) transitions. This is optimal up to a possible log(n) factor, as shown also ....

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1986.

....can be thought of as an alternative decomposition scheme, instead of Myers modules. All the approaches mentioned are based on the Thompson construction of the NFA, whose properties have been exploited in different ways. An alternative, much less known, NFA construction algorithm is Glushkov s [6, 3]. A good point of this construction is that, for a regular expression of m characters, the NFA obtained has exactly m 1 states and is free of transitions. Thompson s construction, instead, produces between m 1 and 2m states. This means that Wu and Manber s table may need a table of size 2 ....

.... transitions leaving each node) that have been extensively exploited in several regular expression search algorithm such as that of Thompson [10] Myers [7] and Wu and Manber [13, 12] Another particularly interesting NFA construction algorithm is by Glushkov [6] popularized by Berry and Sethi in [3]. The NFA resulting from this construction has the advantage of having just m 1 states (one per position in the regular expression) Its number of transitions is worst case quadratic, but this is unimportant under our bit parallel representation (it just means denser bit masks) We present this ....

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.

No context found.

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1987.

No context found.

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1987.

....compiling algorithms. While the Esterel v2 compiler strictly used Brzozowski s original derivative algorithm in which automaton states are program texts, which is unreasonably memory consuming, Gonthier s technique uses simple bit sets as states, which is orders of magnitude more efficient (see [15] for the same kind of optimization for regular expressions) Finally, Gonthier designed the overall architecture of the Esterel v3 compiler, which was written in 1987 88 by Raphael Bernhard, the author, Fr ed eric Boussinot, Annie Ressouche, JeanPaul Rigault, and Jean Marc Tanzi. The architecture ....

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1987.

....and compiling algorithms. While the Esterel v2 compiler strictly used Brzozowski s original derivative algorithm in which automaton states are program texts, which is unreasonably memory consuming, Gonthier s technique uses simple bit sets as states, which is orders of magnitude more eOEcient (see [15] for the same kind of optimization for regular expressions) Finally, Gonthier designed the overall architecture of the Esterel v3 compiler, which was written in 1987 88 by Rapha#l Bernhard, the author, Fr#d#ric Boussinot, Annie Ressouche, Jean Paul Rigault, and JeanMarc Tanzi. The architecture ....

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117126, 1987.

No context found.

Gerard Berry and Ravi Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.

No context found.

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.

No context found.

G. Berry and R. Sethi. From regular expression to deterministic automata. Theoretical Computer Science, 48(1):117--126, 1986.

No context found.

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1986.

No context found.

G. Berry and R. Sethi. From regular expression to deterministic automata. Theor. Comp. Sci., 48(1):117-126, 1986.

No context found.

Berry, G., Sethi, R.: From regular expressions to deterministic automata, Theoretical Computer Science, 48, 1986, 117--126.

No context found.

G. Berry and R. Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117--126, 1986.

No context found.

G. Berry and R. Sethi, From regular expressions to deterministic automata, Theoretical Computer Science, 48, 1986, 117-126.

No context found.

Gerard Berry and Ravi Sethi. From Regular Expressions to Deterministic Automata. Theoretical Computer Science, 48:117-126, 1986.

No context found.

Gerard Berry and Ravi Sethi. From Regular Expressions to Deterministic Automata. Theoretical Computer Science, 48, pages 117-126, 1986

No context found.

G. Berry and R. Sethi, `From regular expressions to deterministic automata', Theoretical Computer Science, 48, 117--126 (1986).

No context found.

G. Berry and R. Sethi. From regular expression to deterministic automata. Theor. Comput. Sci., 48(1):117-126, 1986.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC