Characterization of the structure-generating functions of regular sets and the DOL growth functions

Katayama, Takuya; Okamoto, Masayuki; Enomoto, Hajime

doi:10.1016/s0019-9958(78)90247-4

Cited by 24 publications

(9 citation statements)

References 2 publications

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“…The techniques for constructing R -invariant polytopes developed here are the basis of our progress beyond Heller's work. The characterization of discrete phase-type distributions (Theorem 1.2) is essentially equivalent to the characterization of the structure generating functions of regular languages proved by Katayama, Okamoto, and Enomoto [6]. (The author thanks Robert S. Maier of the Department of Mathematics, University of Arizona, for bringing this paper to his attention).…”

Section: Introductionmentioning

confidence: 93%

“…Our proof of Theorem 1.2 given in Section 6 maintains the probabilistic intuition throughout. It appears at this time that the techniques of [6] do not extend to the more difficult continuous case.…”

Section: Introductionmentioning

confidence: 94%

“…R -invariance of ri (Span ( p ) n P M ) and ri (W n P M ) is a consequence of the fact that if the density f, of v satisfies (5. 6) Let us write k for the dimension of Span ( p ) , so that k-1 is the algebraic degree of p by Theorem 2.1. Then the dimension of W is k-d+l, since Span@) is the direct sum of the vector spaces W and span((z2, T~, .…”

Section: (B) Let V E Span (P) Then V E Ri (Span ( P ) N P M ) If Andmentioning

confidence: 99%

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Characterization of phase-type distributions

O’Cinneide

1990

Communications in Statistics. Stochastic Models

190

128

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A distribution with rational Laplace-Stieltjes transform is of phase type if and only if it is either the point mass at zero, or it has a continuous positive density on the positive reals and its Laplace-Stieltjes transform has a unique pole of maximal real part (which is therefore real). This result is proved, and the corresponding characterization of discrete phase-type distributions is stated and proved. Our methods are based on a geometric property of the set of phase-type distributions associated with a Markov chain.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 94%

Section: (B) Let V E Span (P) Then V E Ri (Span ( P ) N P M ) If Andmentioning

confidence: 99%

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Characterization of phase-type distributions

O’Cinneide

1990

Communications in Statistics. Stochastic Models

190

128

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“…It is known that a nonnegative Z-rational sequence that has a dominating pole is regular [Soittola 1976, Katayama et al 1978Berstel and Reutenauer [1988, p. 83]; or also Salomaa and Soittola [1978]). From this result and the results of Section 4 follows that any Z-representation of a nonnegative sequence that has a dominating pole is equivalent over Z to a regular representation.…”

Section: From a Z-representation To An N-representationmentioning

confidence: 99%

On the generating sequences of regular languages on k symbols

Béal

Perrin

2003

J. ACM

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The main result is a characterization of the generating sequences of the length of words in a regular language on k symbols. We say that a sequence s of integers is regular if there is a finite graph G with two vertices i, t such that s n is the number of paths of length n from i to t in G. Thus the generating sequence of a regular language is regular. We prove that a sequence s is the generating sequence of a regular language on k symbols if and only if both sequences s = (s n ) n≥0 and t = (k n − s n ) n≥0 are regular.

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“…There is a theorem bases, forming a loop or a bulge, is taken to have a phase-type of the author's on such distributions [8], which grew out of distribution: that of the hitting time in a finite-state Markov resuts on such distribution s whic grew It chain. Without loss of generality, each such Markov chain can results on positively weighted regular sequences [4], [15]. It be taken to have a bounded complexity.…”

mentioning

confidence: 99%

Parametrized Stochastic Grammars for RNA Secondary Structure Prediction

Maier

2007

2007 Information Theory and Applications Workshop

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We propose a two-level stochastic context-free grammar (SCFG) architecture for parametrized stochastic modeling of a family of RNA sequences, including their secondary structure. A stochastic model of this type can be used for maximum a posteriori estimation of the secondary structure of any new sequence in the family. The proposed SCFG architecture models RNA subsequences comprising paired bases as stochastically weighted Dyck-language words, i.e., as weighted balanced-parenthesis expressions. The length of each run of unpaired bases, forming a loop or a bulge, is taken to have a phase-type distribution: that of the hitting time in a finite-state Markov chain. Without loss of generality, each such Markov chain can be taken to have a bounded complexity. The scheme yields an overall family SCFG with a manageable number of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications Workshop (ITA 2007

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Characterization of the structure-generating functions of regular sets and the DOL growth functions

Cited by 24 publications

References 2 publications

Characterization of phase-type distributions

Characterization of phase-type distributions

On the generating sequences of regular languages on k symbols

Parametrized Stochastic Grammars for RNA Secondary Structure Prediction

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