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### Acyclic Automata with Easy-to-Find Short Regular Expressions [chapter]

José João Morais, Nelma Moreira, Rogério Reis
2006 Lecture Notes in Computer Science
In this work we present a class of acyclic automata for which it is easy to find a regular expression that has linear size. We call those automata UDR.  ...  Computing short regular expressions equivalent to a given finite automaton is a hard task.  ...  Conclusions In this work we have characterised a small class of acyclic automata for which it is easy to find short equivalent regular expressions.  ...

### Short Regular Expressions from Finite Automata: Empirical Results [chapter]

Hermann Gruber, Markus Holzer, Michael Tautschnig
2009 Lecture Notes in Computer Science
Morais: Approximation to the smallest regular expression for a given regular language. In Proc.  ...  regular expressions.  ...  We are indebted to Loek Cleophas, Manuel Delgado, Vincent Le Maout, and Kerri Morgan for helping us to effectively build on their previous research.  ...

### Page 752 of Mathematical Reviews Vol. , Issue 84b [page]

1984 Mathematical Reviews
Authors’ summary: “We show that it is NP complete to determine whether it is possible to edge color a regular graph of degree k with k colors for any k>3.  ...  Leven, Daniel; Galil, Zvi 84b:68045 NP completeness of finding the chromatic index of regular graphs. J. Algorithms 4 (1983), no. 1, 35-44.  ...

### Acyclic automata and small expressions using multi-tilde-bar operators

Pascal Caron, Jean-Marc Champarnaud, Ludovic Mignot
2010 Theoretical Computer Science
A regular expression with n occurrences of symbol can be converted into an equivalent automaton with (n + 1) states, the so-called Glushkov automaton of the expression.  ...  Conversely, it is possible to decide whether a given (n + 1)-state automaton is a Glushkov one and, if so, to convert it back to an equivalent regular expression of width n.  ...  Our goal is to find subclasses of the finite automata for which an efficient translation to (extended) regular expressions is possible.  ...

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

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

### Monadic logic programs and functional complexity

Armando B. Matos
1997 Theoretical Computer Science
It is also proved that the success set of a specific subclass of monadic programs ("simple" programs) corresponds exactly to regular languages with star-height not exceeding 1.  ...  It is proved that the class of monadic programs corresponds exactly to the class of regular languages. As a consequence, the "SUCCESS" problem is decidable for that class.  ...  Acknowledgements We would like to express our gratitude to a referee of the first version of this paper for calling our attention on the work of Biichi [3] .  ...

### Fly-Automata, Their Properties and Applications [chapter]

Bruno Courcelle, Irène A. Durand
2011 Lecture Notes in Computer Science
This applies to graphs of bounded tree-width because bounded tree-width implies bounded clique-width.  ...  We address the concrete problem of implementing huge bottom-up term automata.  ...  A graph has clique-width (cwd We will express graph properties using MSO formulas that formalize coloring and partitioning problems to take a few examples. for short) at most k if it is defined by some  ...

### On the complexity of decidable cases of the commutation problem of languages

Juhani Karhumäki, Wojciech Plandowski, Wojciech Rytter
2005 Theoretical Computer Science
generating a finite language, a nondeterministic finite automaton (or a regular expression), an acyclic nondeterministic finite automaton or an explicitly given finite language, respectively.  ...  For deterministic finite automata the problem remains open, due to the asymmetry of the catenation.  ...  Regular expressions and nondeterministic automata Regular languages can be represented by regular expressions or nfa's. Unfortunately, the representations are not polynomially equivalent.  ...

### Chrobak Normal Form Revisited, with Applications [chapter]

Paweł Gawrychowski
2011 Lecture Notes in Computer Science
Given an n-state NFA, we are able to find a regular expression of size O( n 2 log n ) describing the same language (which improves the previously known O(n 2 ) size bound [8] ) and a contextfree grammar  ...  Then we extend the algorithm to improve two trade-offs concerning conversions between different representations of unary regular languages.  ...  Lemma 4 . 4 A regular expression of size O(n) describing all acyclic accepting paths can be constructed in O(nm) time.Proof.  ...

### Program Boosting

Robert A. Cochran, Loris D'Antoni, Benjamin Livshits, David Molnar, Margus Veanes
2015 Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '15
easy-to-formalize specification.  ...  With the help of crowd-sourcing, we aim to capture the "wisdom of the crowds" to find good if not perfect solutions to inherently tricky programming tasks, which elude even expert developers and lack an  ...  Symbolic Finite Automata While regular expressions are succinct and relatively easy to understand, they are not easy to manipulate algebraically.  ...

### Graph Logics with Rational Relations and the Generalized Intersection Problem

Pablo Barcelo, Diego Figueira, Leonid Libkin
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science
Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by rational relations such as subword (factor) or subsequence.  ...  Evaluating formulae in such extended graph logics boils down to checking nonemptiness of the intersection of rational relations with regular or recognizable relations (or, more generally, to the generalized  ...  However, it was still short of the expressiveness needed in many applications.  ...

### From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

Hermann Gruber, Markus Holzer
2014 Electronic Proceedings in Theoretical Computer Science
algorithm that converts finite automata to regular expressions.  ...  The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956.  ...  Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper.  ...

### From Finite Automata to Regular Expressions and Back — A Summary on Descriptional Complexity

Hermann Gruber, Markus Holzer
2015 International Journal of Foundations of Computer Science
algorithm that converts finite automata to regular expressions.  ...  The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956.  ...  Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper.  ...

### Fast Learning of Restricted Regular Expressions and DTDs

Dominik D. Freydenberger, Timo Kötzing
2014 Theory of Computing Systems
Chares, and to single occurrence regular expressions, Sores).  ...  The two language classes we consider are subsets of the regular languages and have significance in the specification of XML documents (the classes corresponding to so called chain regular expressions,  ...  Acknowledgements The authors wish to thank the anonymous referees for their helpful remarks.  ...

### Fast learning of restricted regular expressions and DTDs

Dominik D. Freydenberger, Timo Kötzing
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13
Chares, and to single occurrence regular expressions, Sores).  ...  The two language classes we consider are subsets of the regular languages and have significance in the specification of XML documents (the classes corresponding to so called chain regular expressions,  ...  Acknowledgements The authors wish to thank the anonymous referees for their helpful remarks.  ...
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