Communication complexity
Programming Techniques: Regular expression search algorithm
Communications of the ACM
Translating regular expressions into small εe-free nondeterministic finite automata
Journal of Computer and System Sciences
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
A lower bound on the size of ɛ-free NFA corresponding to a regular expression
Information Processing Letters
Transition complexity of language operations
Theoretical Computer Science
On the average state and transition complexity of finite languages
Theoretical Computer Science
On transition minimality of bideterministic automata
DLT'07 Proceedings of the 11th international conference on Developments in language theory
On a maximal NFA without mergible states
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Regular expressions and NFAs without Ε-transitions
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Lower bounds for the transition complexity of NFAs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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The construction of an ε-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 increase the number of transitions quadratically and its optimality with respect to the number of transitions is a long standing open problem. We show that there exist regular languages Ln that can be recognized by NFAs with O(n log2n) transitions, but ε-free NFAs need Ω(n2) transitions to accept Ln. Hence the standard conversion cannot be improved significantly. However Ln requires an alphabet of size n, but we also construct regular languages Kn over {0,1} with NFAs of size O(n log2n), whereas ε-free NFAs require size $n \cdot 2^{c \cdot\sqrt{{\rm log}_{2}n}}$ for every c