T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput, 12(4):645--655, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....objects by interpreting the enumeration recurrence relations. This generation e mail : dutour labri.u bordeaux.fr e mail : fedou unice.fr Figure 1: Complete binary trees. process have been formalized by Nijenhuis and Wilf [16] then by Hickey and Cohen in the case of context free languages [13] and by Greene within the framework of the labelled formal languages [12] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method concerning their specications of structures [11] The methods that they have examined enable to start from any hight level ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput., 12(4):645655, 1983.

....accurate measure for these algorithms, as discussed in [2] The above method applies obviously to rational languages. However, in this particular case, a slightly di erent approach makes it possible to carry out a generation in O(n) arithmetic operations with a prepropcessing stage in O(n) too [12]. We consider a regular grammar of the language, in which any rule has the shape T T 1 j : j Tm , where either T i = xT j or T i = x (x 2 X) or T i = The T ( s are computed using the following recurrences: T T 1 j : j Tm ) T (n) T 1 (n) Tm (n) 5) T i = xT j ) T i ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM J. Comput., 12(4):645-655, 1983.

....distribution, then recursively generate the root subtrees. Several of the basic principles of this recursive top down approach have been formalized by Nijenhuis and Wilf in their reference book on combinatorial algorithms [28] by Hickey and Cohen in the case of context free languages [16], and under a fairly general setting by Greene within the framework of labelled grammars [14] The present work is in many ways a systematization and a continuation of the pioneering research of these authors. The class H of all hierarchies can be viewed as a recursively defined type, H = Z ....

....time complexity O(n ) when applied to objects of size n; the boustrophedonic algorithms are based on a special search technique that proceeds in a bidirectional fashion and they exhibit O(n log n) worst case time complexity. The sequential method relies on existing technologies set forth by [14, 16, 28]; the boustrophedonic search extends to the realm of random generation an idea of Knuth for finding cycle leaders in permutations [19] Both methods appeal to precomputed numerical tables of size O(n) produced by a preprocessing phase of cost O(n to be effected once only. In the process of ....

[Article contains additional citation context not shown here]

Hickey, T., and Cohen, J. Uniform random generation of strings in a context--free language. SIAM Journal on Computing 12, 4 (1983), 645--655.

....as constants. There are two obvious applications of ranking and unranking algorithms for left Szilard languages: random generation of words over a given context free language and compression of program files. Random generation of words over a context free language is used in testing parsers [5], or in more theoretically oriented applications such as studying formulas in the propositional calculus or the degree of ambiguity of a context free grammar [5] For recent results concerning random generation of words in an ambiguous context free grammar, see [9] Applications of random ....

....language and compression of program files. Random generation of words over a context free language is used in testing parsers [5] or in more theoretically oriented applications such as studying formulas in the propositional calculus or the degree of ambiguity of a context free grammar [5]. For recent results concerning random generation of words in an ambiguous context free grammar, see [9] Applications of random generation of words in computational biology are mentioned in [3] For compression of program files, see e.g. 1,7] Parallel algorithms for ranking context free ....

Timothy Hickey and Jacques Cohen, Uniform random generation of strings in a context-free grammar. SIAM J. Comput. 12 (1983), 645-655.

....of languages including regular, context free (c.f. for short) and more generally languages accepted by one way nondeterministic auxiliary push down automata (1 NAuxPDA) Several sequential algorithms have been proposed for the random generation of strings in regular and context free languages [12, 10, 9, 11]. The problem is particularly interesting in the c.f. case because these languages can codify a wide variety of combinatorial structures; moreover, sampling words from c.f. languages is naturally motivated by other applications such as testing parsers of programming languages [12] or evaluating ....

....[12, 10, 9, 11] The problem is particularly interesting in the c.f. case because these languages can codify a wide variety of combinatorial structures; moreover, sampling words from c.f. languages is naturally motivated by other applications such as testing parsers of programming languages [12] or evaluating the performance of algorithms which process DNA sequences [20, 19] In the case of unambiguous c.f. languages the best known algorithm for random generation works in O(n log n) arithmetic time [10] this is a special case of more general procedures for the random generation of so ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM Journal on Computing, 12(4):645--655, November 1983.

....as constants. 2 There are two obvious applications of ranking and unranking algorithms for left Szilard languages: random generation of words over a given context free language and compression of program files. Random generation of words over a context free language is used in testing parsers [5], or in more theoretically oriented applications such as studying formulas in the propositional calculus or the degree of ambiguity of a context free grammar [5] For recent results concerning random generation of words in an ambiguous context free grammar, see [9] Applications of random ....

....language and compression of program files. Random generation of words over a context free language is used in testing parsers [5] or in more theoretically oriented applications such as studying formulas in the propositional calculus or the degree of ambiguity of a context free grammar [5]. For recent results concerning random generation of words in an ambiguous context free grammar, see [9] Applications of random generation of words in computational biology are mentioned in [3] For compression of program files, see e.g. 1,7] Parallel algorithms for ranking context free ....

Timothy Hickey and Jacques Cohen, Uniform random generation of strings in a context-free grammar. SIAM J. Comput. 12 (1983), 645-655.

.... descriptions, the uniform random generation and counting problems have been widely studied in the literature (see, for instance, 14, 8] In particular, due to their well known applications, the uniform random generation of unambiguous context free languages has been considered in several papers [18, 25, 14, 15]. This problem is implicitely treated in [14] as a special case of a more general analysis of algorithms for uniform random generation of combinatorial structures speci ed by (unambiguous) formal grammars that involve operations of union, product, construction of sets, sequences and cycles. Many ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM Journal on Computing, 12(4):645655, nov 1983.

.... automata (1 NAuxPDA) Recall that the random generation is a classical problem widely studied in the literature of the last decades [22, 27, 19, 18, 14, 12] In particular several (sequential) algorithms have been proposed for the random generation of strings in regular and context free languages [16, 24, 14, 11, 15]. The problem is particularly interesting in the c.f. case because these languages can codify a wide variety of combinatorial structures; moreover, sampling words from c.f. languages is naturally motivated by other applications such as testing parsers of programming This work has been partially ....

....structures; moreover, sampling words from c.f. languages is naturally motivated by other applications such as testing parsers of programming This work has been partially supported by MURST Research Program Unconventional computational models: syntactic and combinatorial methods . languages [2, 16] or evaluating the performance of algorithms which process DNA sequences [29, 28] In the case of unambiguous c.f. languages the best known algorithm for random generation works in O(n log n) arithmetic time [14] this is a special case of more general procedures for the random generation of so ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM Journal on Computing, 12(4):645655, November 1983.

....time and space. Previously known algorithms were either limited to small classes of structures: balanced parenthesis strings in [3] regular languages in [12] some kinds of trees in [2] or they did not have a quasi linear time or space complexity: the algorithms proposed by Hickey and Cohen [10] (resp. Mairson [14] for context free languages with r nonterminals either have O(n r 1 ) resp. O(n 2 ) space complexity, or O(n 2 log 2 n) resp. O(n 2 ) time complexity. Goldwurm s algorithm [9] works in linear space, but does not improve the time complexity of the recursive ....

Hickey, T., and Cohen, J. Uniform random generation of strings in a context-free language. SIAM J. Comput. 12, 4 (Nov. 1983), 645--655.

....have a general approach. They base the recursive procedure on an acyclic directed rooted graph with a terminal vertex and numbered edges, graph which depends on the family of objects. The recursive method has been also formalized by Hickey and Cohen in the special case of context free languages [10], and by Greene within the framework of the labelled formal languages [9] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method with specifications of structures by grammars involving set, sequence and cycle constructions [8] The methods that they have ....

Hickey, T. and Cohen, J. (1983). Uniform Random Generation of Strings in a Context-Free Language. SIAM. J. Comput. 12(4): 645--655

....a terminal vertex and numbered edges, graph which depends on the family of objects. The recursive method has been also formalized by Hickey and Cohen in the special case of e mail : dutour labri.u bordeaux.fr y e mail : fedou unice.fr 1 Figure 1: Complete binary trees. context free languages [10] and by Greene within the framework of the labelled formal languages [9] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method with specications of structures by grammars involving set, sequence and cycle constructions [8] The methods that they have ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput., 12(4):645655, 1983.

....the case of unambiguous formal descriptions, the uniform random generation and counting problems have been widely studied in the literature. In particular, due to their well known applications, the uniform random generation of unambiguous context free languages has been considered in several paper [29, 35, 24, 25]. This problem is implicitely treated in [24] as a special case of a more general analysis of algorithms for uniform random generation of combinatorial structures specified by (unambiguous) formal grammars that involve operations of union, product, construction of sets, sequences and cycles. Many ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM Journal on Computing, 12(4):645--655, nov 1983.

....distribution, then recursively generate the root subtrees. Several of the basic principles of this recursive top down approach have been formalized by Nijenhuis and Wilf in their reference book on combinatorial algorithms [28] by Hickey and Cohen in the case of context free languages [16], and under a fairly general setting by Greene 1 within the framework of labelled grammars [14] The present work is in many ways a systematization and a continuation of the pioneering research of these authors. The class H of all hierarchies can be viewed as a recursively defined type, H = Z ....

....time complexity O(n 2 ) when applied to objects of size n; the boustrophedonic algorithms are based on a special search technique that proceeds in a bidirectional fashion and they exhibit O(n log n) worst case time complexity. The sequential method relies on existing technologies set forth by [14, 16, 28]; the boustrophedonic search extends to the realm of random generation an idea of Knuth for finding cycle leaders in permutations [19] Both methods appeal to precomputed numerical tables of size O(n) produced by a preprocessing phase of cost O(n 2 ) to be effected once only. In the process of ....

[Article contains additional citation context not shown here]

Hickey, T., and Cohen, J. Uniform random generation of strings in a context--free language. SIAM Journal on Computing 12, 4 (1983), 645--655.

....Related research includes: Alonso and Schott [1] who consider fast random generation techniques, Bergeron et al. 3] who give an extensive algebraic treatment of species, and Jerrum, Vazirani, and Valiant [8] who give an abstract analysis of the complexity of generation. Hickey and Cohen [7] and Mairson [11] give algorithms for constructing words from unambiguous context free grammars. The concerns here are for giving an efficient, constructive, bijective method (ranking unranking) for a general class of species. The plan of the paper is as follows. First, we will show the algebraic ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM J. Comput., 12(4):645--655, 1983.

....shows that exact counting results can be obtained with low computational complexity. Accordingly, this has consequences in the automatic generation of random structures in the class, since the top down generation of structures of size n relies on these splitting probabilities. Hickey and Cohen [19] use similar techniques in order to generate words in context free languages uniformly. Greene has given an interesting discussion of more general issues, as well as an implementation for structures definable by his labelled grammars [40, Chap. 4] 3.4 Programme Constructions We now introduce ....

Cohen, J., and Hickey, T. Uniform random generation of strings in a context-free language. SIAM Journal of Computing 12, 4 (November 1983), 645--655.

....by interpreting the enumeration recurrence relations. This generation e mail : dutour labri.u bordeaux.fr y e mail : fedou unice.fr Figure 1: Complete binary trees. process have been formalized by Nijenhuis and Wilf [16] then by Hickey and Cohen in the case of context free languages [13] and by Greene within the framework of the labelled formal languages [12] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method concerning their speci cations of structures [11] The methods that they have examined enable to start from any hight level ....

T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput., 12(4):645655, 1983.

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T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput, 12(4):645--655, 1983.

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T. Hickey and J. Cohen. Uniform random generation of strings in a context-free language. SIAM. J. Comput, 12(4):645655, 1983.

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