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### The solution of two star-height problems for regular trees [chapter]

J. P. Braquelaire, B. Courcelle
1985 Lecture Notes in Computer Science
For these two types w;i-solve the star-height problem, i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal  ...  Regular trees can he detined by two types of rational exprwions.  ...  They raise a star-height problem, i.e., the problem of constructing a rational expression of minimal star-height which defines a given regular tree.  ...

### The solutions of two star-height problems for regular trees

J.P. Braquelaire, B. Courcelle
1984 Theoretical Computer Science
For these two types w;i-solve the star-height problem, i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal  ...  Regular trees can he detined by two types of rational exprwions.  ...  They raise a star-height problem, i.e., the problem of constructing a rational expression of minimal star-height which defines a given regular tree.  ...

### Page 6953 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews
Summary: “Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height  ...  We prove that an FTR language has star height one if and only if it is renewal. This gives a simple decision procedure for the star height one problem for this class of languages.  ...

### Page 478 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews
The use of larger dilation allows embeddings of trees of greater height into star graphs. For example, the difference of the heights of the trees embedded with dilation 2 and | is greater than n/2.  ...  The problem is motivated by the study of query languages for structured text databases. Simple solutions to this problem require exponential time.  ...

### Digraph Complexity Measures and Applications in Formal Language Theory [article]

Hermann Gruber
2011 arXiv   pre-print
Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem.  ...  This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages.  ...  Acknowledgment The author would like to thank Markus Holzer for carefully reading an earlier draft of this paper, and for providing some valuable suggestions.  ...

### Digraph complexity measures and applications in formal language theory

Hermann Gruber
2012 Discrete Mathematics & Theoretical Computer Science
Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem.  ...  This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages.  ...  Acknowledgements The author would like to thank Markus Holzer for carefully reading an earlier draft of this paper, and for providing some valuable suggestions.  ...

### Page 3064 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews
height hierarchy of extended regular languages of star degree at most two.  ...  This paper introduces the notion of 2-star height. The principal result is that the 2-star hierarchy is infinite when the alphabet contains at least two symbols. J.  ...

### Page 2660 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews
(F-BORD) The solution of two star-height problems for regular trees. Automata on infinite words (Le Mont-Dore, 1984), 108-117, Lecture Notes in Comput. Sci., 194, Springer, Berlin-New York, 1985.  ...  For these two types we solve the star-height problem; i.e., we show how to construct a rational expression of minimal star-height from the minimal graph of the given tree (i.e., the analogue of the minimal  ...

### Stamina: Stabilisation Monoids in Automata Theory [chapter]

Nathanaël Fijalkow, Hugo Gimbert, Edon Kelmendi, Denis Kuperberg
2017 Lecture Notes in Computer Science
First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression.  ...  Second, decide limitedness for regular cost functions.  ...  Kirsten's solution was later adapted to trees [CL08a] using the framework of regular cost functions.  ...

### The data arrangement problem on binary trees [article]

Eranda Cela, Joachim Schauer, Rostislav Stanek
2015 arXiv   pre-print
We derive a lower bound for the later problem and obtain a lower bound for the original problem by solving hG instances of the k-BPP, where hG is the height of the host graph G.  ...  The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G, called the guest graph, to the leaves of a d-regular tree T, called the host graph, such that  ...  Acknowledgements The research was funded by the Austrian Science Fund (FWF): P23829.  ...

### Page 7626 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews
An q-tree of height n is an infinite rooted tree such that any maximal chain has n +1 vertices and any vertex that is not a leaf has degree w; an w-forest of height n is the disjoint union of @ many c-trees  ...  Also by applying the properties of regular graphs, a lower bound can easily be achieved for star graphs.” 2004j:05122 05C90 92D10 Chaouiya, Claudine (F-PROV-GPB; Marseille) ; Remy, Elisabeth (F-PROV-IM  ...

### A characterization of regular expressions under bisimulation

J. C. M. Baeten, F. Corradini, C. A. Grabmayer
2007 Journal of the ACM
As an application, we consider the star height problem.  ...  We define a set of so-called well-behaved finite automata that, modulo bisimulation equivalence, corresponds exactly to the set of regular expressions, and we show how to determine whether a given finite  ...  Acknowledgements We thank Colin Stirling (University of Edinburgh), Bas Luttik (Technische Universiteit Eindhoven), Wan Fokkink (Vrije Universiteit, Amsterdam) and Luca Aceto (Reykjavik University) for  ...

### Heuristics for the data arrangement problem on regular trees

Eranda Çela, Rostislav Staněk
2013 Journal of combinatorial optimization
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of  ...  The analysis of the performance of the heuristics is based on two considerations: a) the quality of the solutions produced by the heuristics as compared to the respective lower bounds b) for a special  ...  Acknowledgements The research was funded by the Austrian Science Fund (FWF): P23829.  ...

### Heuristics for the data arrangement problem on regular trees [article]

Eranda Cela, Rostislav Stanek
2013 arXiv   pre-print
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of  ...  The analysis of the performance of the heuristics is based on two considerations: a) the quality of the solutions produced by the heuristics as compared to the respective lower bounds b) for a special  ...  Acknowledgements The research was funded by the Austrian Science Fund (FWF): P23829.  ...

### Page 1460 of Mathematical Reviews Vol. 46, Issue 5 [page]

1973 Mathematical Reviews
Just as star height is defined for regular sets, | substitution star height is defined for context-free lan- guages.  ...  In this paper the author studies formal expressions that denote solutions to such equations. Two operators, substitution and substitution star, are defined.  ...
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