C.-H. Chang and R. Paige. From regular expressions to DFA's using compressed NFA's. Theoret. Comput. Sci., 178(1-2):1-36, May 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a constant [5] Therefore, we can just convert the regular expression to a DFA and then use our derived algorithm. We have skipped the step that converts a regular expression to a DFA, since there are standard algorithms. Those who are interested in this may nd an algorithm by Chang and Paige [4], also derived using Paige s methods, that improves over previous algorithms for this. Variables in regular expression patterns. For applications in program analysis and model checking, it is often desirable to include variables in regularexpression patterns. Such a variable can match any labels ....

C.-H. Chang and R. Paige. From regular expressions to DFA's using compressed NFA's. Theoret. Comput. Sci., 178(1-2):1-36, May 1997.

....small and considered a constant [5] Therefore, we can just convert it to a DFA and then use our derived algorithm. We have skipped the step that converts a regular expression to a DFA, since there are standard algorithms. Those who are interested in this may nd an algorithm by Chang and Paige [4], also derived using Paige s methods, that improves over previous algorithms for this. 7 Related work and conclusion The regular path query problem was introduced by de Moor et al. recently for program analysis and compiler optimization [5] where the problem was speci ed, and a high level ....

C.-H. Chang and R. Paige. From regular expressions to DFA's using compressed NFA's. Theoret. Comput. Sci., 178(1-2):1-36, May 1997.

....can be expressed as follows: build a system of language equations of the form X = t 1 : t n , where each t i is a language term of a special form. The various known methods for building grep machines can be related to the form of the terms. This classification is largely inspired by [5, 6]. In this paper, we use the following notations: let be a system of equations, we note V( the set of language identifiers defined in , A( 2 V( the main language (the axiom) and for each X 2 V( X) the set of terms t i defining X in . We note L( the solution (if it exists) of , ....

C. H. Chang and R. Paige. From regular expressions to DFA's using compressed NFA's. In Apostolico, Crochemore, Galil, and Manber, editors, Combinatorial Pattern Matching. Proceedings, pages 88--108. LNCS 644, Springer Verlag, 1992.

....by McNaughton and Yamada s algorithm [14] and by its improvement due to Berry and Sethi [4] However, in many cases our NFA have actually fewer states than this upper bound. Moreover, there are examples when our NFA turn out to be smaller than those produced by a tricky Chang and Paige s algorithm [7] (which involves several non trivial optimizations of the representation of NFA) The second procedure in this section provides several improvements to Brzozowski s algorithm [5] due to the use of partial derivatives. We have implemented our algorithm turning regular expressions into NFA as an ....

....of partial derivatives corresponding to the states of the automaton. Below we present some examples obtained with the help of this program. We consider regular terms on the alphabet A = fa; b; c; g. The concatenation sign is omitted from the terms. Example 3. This is a working example from [7]: the regular expression t = a b) abb: Our algorithm turns it into the following NFA with 4 states and 5 edges: State equations Partial derivatives S 1 : a Delta S 1 b Delta S 1 a Delta S 2 (a b) abb S 2 : b Delta S 3 bb S 3 : b Delta S 4 b S 4 : In [7] the expression ....

[Article contains additional citation context not shown here]

C.-H. Chang and R. Paige. From regular expressions to DFA's using compressed NFA's. In A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, editors, Combinatorial Pattern Matching. Proceedings., volume 644 of Lecture Notes in Computer Science, pages 88--108. Springer-Verlag, 1992.

....can be expressed as follows: build a system of language equations of the form: X = t 1 : t n where each t i is a language term of a special form. The various known methods for building grep machines can be related to the form of the terms. This classification is largely inspired by [5, 6]. In this paper, we use the following notations: let be a system of equations, we note V( the set of language identifiers defined in , A( 2 V( the main language (the axiom) and for each X 2 V( X) the set of terms t i defining X in . We note L( the solution (if it exists) of , ....

C. H. Chang and R. Paige. From regular expressions to dfa's using compressed nfa's. In Apostolico, Crochemore, Galil, and Manber, editors, LNCS 644: Combinatorial Pattern Matching. Proceedings, pages 88--108. Springer Verlag, 1992.

....facilitates the discovery of new algorithms. We believe that the success of this experiment hinges on the success of the first two experiments. Earlier forms of our methodology partly contributed to the discovery of improved solutions to DFA minimization[40,11] regular expression search[15], and bottom up multi pattern tree matching[13] A substantially narrower form of the transformational methodology presented here was used by Paige and Henglein[37] to develop a linear time program to solve the relational attribute closure problem using only list processing operations. An earlier ....

C.-H. Chang and R. Paige. From regular expressions to dfa's using compressed nfa's. In A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, editors, Proc. Combinatorial Pattern Matching '92, volume 644 of LNCS, pages 88--108. Springer-Verlag, 1992.

....bounds as Bruggemann Klein, but offers a practical improvement by computing the same NFA in a single left to right scan over the regular expression without producing a parse tree. That algorithm was discovered by Chang and Paige independently of Bruggemann Klein, and reported in the short form[10] of the current paper. 2. One disadvantage of McNaughton and Yamada s NFA is that its worst case number of edges is m = Theta(s 2 ) More specifically, its adjacency list representation takes up 3s s 2 space in the worst case. Thompson s NFA has between r and 2r states and between r and 4r ....

Chang, C. and Paige, R., "From Regular Expressions to DFA's Using Compressed NFA's," LNCS Num. 644, Springer-Verlag, eds. A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, 1992, pp. 88-108.

....and Theta(n) states in Theta(n 2 ) time for McNaughton and Yamada s NFA, Theta(kn) states and edges in Theta(kn) time for Thompson s machine, and Theta(n) states and edges in Theta(n) time for the CNNFA. We end this section with the following theoretical result, originally proved by Chang[9], which improves the auxiliary space given in Theorems 4.3 and 5.2. Theorem 5.6 Given any regular expression R with length r and with s occurrences of alphabet symbols, its equivalent CNNFA can be computed in time O(r) and auxiliary space O(s) Proof: See the Appendix. 2 6 Computational ....

....common parent w in I R Gammasucc , then these leaves can be replaced by a single leaf z. For i = 1; k, edge [q i ; z] is removed from FR Gammapred , and edge [w; q i ] is replaced by [w; z] within I R Gammasucc . We also need to assign the set fA(q i ) i = 1; kg of symbols to A(z) cf. [9] for details) Finally, if q 1 ; q k are all final states (they must be all final or none final) then they must be replaced in the set FR of final states by z. As an example, consider expression ( a 1 j) Delta Delta Delta ( a s Gamma1 j) a s j) Delta Delta Delta) once ....

[Article contains additional citation context not shown here]

Chang, C., Ph. D. Thesis, "From Regular Expressions to DFA's Using Compressed NFA's", 1992.

....improvements. This gives our work a potential for pragmatic as well as theoretical impact. Our transformational methodology has been used to invent new algorithms for propositional Horn Clause Satisfiability on a sequential pointer machine [32] transformation from regular expressions to DFA s [15], and ready simulation [6] We are currently working on transformational explanations and proofs of parallel algorithms. 3 Transformational System A meta transformational environment called APTS was built in order to implement the preceding transformations [34] APTS has meta tools for syntax, ....

C.-H. Chang and R. Paige. From Regular Expressions to DFA's Using Compressed NFA's. In Proc. CPM '92, A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, editors, SpringerVerlag, Lecture Notes in Computer Science number 644, pages 88 - 108, 1992.

....to test the viability and utility of our transformational methodology before launching into an implementation. The methodology has been used to invent new algorithms for propositional Horn Clause Satisfiability on a sequential pointer machine [48] transformation from regular expressions to DFA s [18], and ready simulation [8] We are currently working on transformational explanations and proofs of parallel algorithms. Recent algorithm inventions due to Jeuring [33] and Meertens [40] add credibility to the calculational approach to algorithm derivation due to Bird [7] and Meertens [39] Smith ....

C.-H. Chang and R. Paige. From Regular Expressions to DFA's Using Compressed NFA's. In Proc. CPM '92, A. Apostolico, M. Crochemore, Z. Galil, and U. Manber, editors, SpringerVerlag, Lecture Notes in Computer Science number 644, pages 88 - 108, 1992.

No context found.

Chang, Chia-Hsiang. Paige, Robert. From Regular Expressions to DFA's Using Compressed NFA's. Computer Science Department, Courant Institute of Mathematical Sciences, New York University, May 1996

No context found.

C Chang, From Regular Expressions to DFA's Using Compressed NFA's, PhD thesis, New York University, Oct 1992.

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