Result: Comparing the size of NFAs with and without ε -transitions

Title:
Comparing the size of NFAs with and without ε -transitions
Authors:
HROMKOVIC, Juraj, SCHNITGER, Georg
Source:
Automata, languages and programming (ICALP 2005)Theoretical computer science. 380(1-2):100-114
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 12 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Théorie des langages et analyse syntaxique, Language theory and syntactical analysis, Divers, Miscellaneous, Logiciel, Software, Langages de programmation, Programming languages, Systèmes informatiques et systèmes répartis. Interface utilisateur, Computer systems and distributed systems. User interface, Alphabet, Alfabeto, Automate fini, Finite automaton, Autómata estado finito, Borne inférieure, Lower bound, Cota inferior, Compilateur, Compiler, Compilador, Complexité, Complexity, Complejidad, Construction, Construcción, Conversion, Conversión, Informatique théorique, Computer theory, Informática teórica, Langage rationnel, Regular language, Lenguaje racional, Ordinateur, Computer, Computadora, Système informatique, Computer system, Sistema informático, Transition, Transición, 68Mxx, 68N20, 68Q45, Langage régulier, Descriptional complexity, Finite automata, Lower bounds on complexity
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, Swiss Federal Institute of Technology, ETH Zürich, ETH Zentrum, CAB F16, 8092 Zürich, Switzerland
Institut für Informatik, Johann Wolfgang Goethe-Universität, Robert Mayer Strafe 11-15, 60054 Frankfurt am Main, Germany
ISSN:
0304-3975
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18821616
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Accession Number:
edscal.18821616
Database:
PASCAL Archive

Further Information

The construction of an e-free nondeterministic finite automaton (NFA) from a given NFA is a basic step in the development of compilers and computer systems. The standard conversion may produce an e-free NFA with up to Ω(n2·|Σ|) transitions for an NFA with n states and alphabet Z. To determine the largest asymptotic gap between the minimal number of transitions of NFAs and their equivalent e-free NFAs has been a longstanding open problem. We show that there exist regular languages Ln that can be recognized by NFAs with 0(n log2 n) transitions, but e-free NFAs need Ω(n2) transitions to accept Ln. Hence the standard conversion cannot be improved drastically. However, Ln requires an alphabet of size n, but we also construct regular languages Kn over (0, 1} with NFAs of size 0(n log2 n), whereas e-free NFAs require size n ·2c·√log2nfor every c < 1/2.