# $k$-Position, Follow, Equation and $k$-C-Continuation Tree Automata Constructions

@inproceedings{Mignot2014kPositionFE, title={\$k\$-Position, Follow, Equation and \$k\$-C-Continuation Tree Automata Constructions}, author={Ludovic Mignot and Nadia Ouali Sebti and Djelloul Ziadi}, booktitle={AFL}, year={2014} }

There exist several methods of computing an automaton recognizing the language denoted by a given regular expression: In the case of words, the position automaton P due to Glushkov, the c-continuation automaton C due to Champarnaud and Ziadi, the follow automaton F due to Ilie and Yu and the equation automaton E due to Antimirov. It has been shown that P and C are isomorphic and that E (resp. F) is a quotient of C (resp. of P). In this paper, we define from a given regular tree expression the k…

## 3 Citations

### Algorithm for the k-Position Tree Automaton Construction

- Computer ScienceArXiv
- 2015

An efficient algorithm is given that computes the \Follow sets, which are used in different algorithms of conversion of a regular expression into tree automata, and it is proved that for aregular expression \E of a size |\E| and alphabetic width ||\E||, the\Follow sets can be computed in O(||\E ||\cdot |\ E|) time complexity.

### Bottom Up Quotients and Residuals for Tree Languages

- Computer ScienceArXiv
- 2015

This paper shows how to compute a set of k-ary trees, where k is an arbitrary integer, and defines the quotient formula for different combinations of tree languages: union, symbol products, compositions, iterated symbol products and iterated composition.

### Construction of rational expression from tree automata using a generalization of Arden's Lemma

- Computer ScienceArXiv
- 2015

This paper proposes a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton and generalizes Arden's Lemma to the rational tree languages.

## References

SHOWING 1-10 OF 14 REFERENCES

### Canonical derivatives, partial derivatives and finite automaton constructions

- MathematicsTheor. Comput. Sci.
- 2002

### From C-Continuations to New Quadratic Algorithms for Automaton Synthesis

- Computer ScienceInt. J. Algebra Comput.
- 2001

An O(|E|2) space and time algorithm to compute the equation automaton is presented, based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives.

### An Efficient Algorithm for the Equation Tree Automaton via the k-C-Continuations

- Computer ScienceCiE
- 2014

A full description of the algorithm based on the acyclic minimization of Revuz is given, which is performed in an Open image in new window time and space complexity, is more efficient than the one obtained by Kuske and Meinecke.

### Tree automata techniques and applications

- Computer Science
- 1997

The goal of this book is to provide a textbook which presents the basics ofTree automata and several variants of tree automata which have been devised for applications in the aforementioned domains.

### Construction of tree automata from regular expressions

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2008

This work transfers Antimirov's partial derivatives from regular word expressions to regular tree expressions for an analysis of the size of the resulting automaton and the methods of Champarnaud and Ziadi from words to trees.

### From Regular Tree Expression to Position Tree Automaton

- Computer ScienceLATA
- 2013

It is shown that the conversion of a regular tree expression of size |E| and alphabetic width ||E|| into its reduced tree automaton can be done in O(|E|·||E||) time.

### Derivatives of Regular Expressions

- MathematicsJACM
- 1964

In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators.