Sampling different kinds of acyclic automata using Markov chains

Carnino, Vincent; Felice, Sven De

doi:10.1016/j.tcs.2012.04.025

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…Second, the R 1 -like class being in bijection to R 2, cannot be empty, and the initial sequence on level 0 has to be appended. Thus, the substitution (11) has to be used where R 2,1 (z) is replaced by R 2, (z), and R 2,0 (z) by R 2, −1 (z). This gives for ≥ 1…”

Section: Relaxed Trees Of Right Height At Most Kmentioning

confidence: 99%

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Asymptotic enumeration of compacted binary trees of bounded right height

Genitrini

Gittenberger

Kauers

et al. 2020

Journal of Combinatorial Theory, Series A

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A compacted tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special class of directed acyclic graphs. We are interested in the asymptotic number of compacted trees of given size, where the size of a compacted tree is given by the number of its internal nodes. Due to its superexponential growth this problem poses many difficulties. Therefore we restrict our investigations to compacted trees of bounded right height, which is the maximal number of edges going to the right on any path from the root to a leaf.We solve the asymptotic counting problem for this class as well as a closely related, further simplified class.For this purpose, we develop a calculus on exponential generating functions for compacted trees of bounded right height and for relaxed trees of bounded right height, which differ from compacted trees by dropping the above described uniqueness condition. This enables us to derive a recursively defined sequence of differential equations for the exponential generating functions. The coefficients can then be determined by performing a singularity analysis of the solutions of these differential equations.Our main results are the computation of the asymptotic numbers of relaxed as well as compacted trees of bounded right height and given size, when the size tends to infinity. Proposition 4.3. From any binary tree of size n, we can build a compacted tree of size n, with the following operations:1. Add a leaf as left child of the leftmost node of the binary tree.2. Add pointers to every node such that every node except the leaf has out-degree 2.

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Section: Relaxed Trees Of Right Height At Most Kmentioning

confidence: 99%

“…The first investigation of shape parameters seems to go back to McKay [22]. Recently, enumeration results for many particular classes of DAGs can be found in the literature, see for instance [7-9, 16, 20, 21, 32-34], as well as investigations on the (random) generation of particular DAGs, see [3,11,23,24].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic enumeration of compacted binary trees of bounded right height

Genitrini

Gittenberger

Kauers

et al. 2020

Journal of Combinatorial Theory, Series A

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“…Combined with the correlation theory of MC [3], we get the transfer rate matrix Q. Assume the probability set X= (x 0 ,x 1 ,x 2 ,…,x 18 ) and put it into:…”

Section: Single Channel Gspn Model Establishmentmentioning

confidence: 99%

Bottlenecks Identification - Airport Security Checkpoint Process Optimization based on the GSPN theory

Hu¹

2017

Proceedings of the 2017 5th International Conference on Machinery, Materials and Computing Technology (ICMMCT 2017)

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Customers satisfaction degree is critical to airlines. Therefore, it is significant for airlines to provide a positive flying experience for passengers by minimizing the time they spend waiting in line at an airport security checkpoint. The key of this problem is to identify the bottlenecks of the airport security process. Based on the Generalized Stochastic Petri Net (GSPN) theory, this article build the bottlenecks identification model to achieve this goal.

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“…In [8,9] NFAs are obtained by the random generation of a regular expression and by transforming it into an equivalent automaton using Glushkov Algorithm. The use of Markov chains based techniques to randomly generate finite automata was introduced in [10,11] for acyclic automata.…”

Section: Introductionmentioning

confidence: 99%

On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

Héam

Joly²

2015

Implementation and Application of Automata

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International audienceIn this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution

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Sampling different kinds of acyclic automata using Markov chains

Cited by 4 publications

References 12 publications

Asymptotic enumeration of compacted binary trees of bounded right height

Asymptotic enumeration of compacted binary trees of bounded right height

Bottlenecks Identification - Airport Security Checkpoint Process Optimization based on the GSPN theory

On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

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