Communication complexity and parallel computing
Communication complexity and parallel computing
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 Computation
Introduction To Automata Theory, Languages, And Computation
A lower bound on the size of ɛ-free NFA corresponding to a regular expression
Information Processing Letters
Journal of Computer and System Sciences
Ambiguity in Graphs and Expressions
IEEE Transactions on Computers
Finite automata and their decision problems
IBM Journal of Research and Development
Regular expressions and NFAs without Ε-transitions
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The Tractability Frontier for NFA Minimization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Nondeterministic Finite Automata--Recent Results on the Descriptional and Computational Complexity
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
On the Hardness of Determining Small NFA's and of Proving Lower Bounds on Their Sizes
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Lower bounds for the transition complexity of NFAs
Journal of Computer and System Sciences
The tractability frontier for NFA minimization
Journal of Computer and System Sciences
State-based model slicing: A survey
ACM Computing Surveys (CSUR)
Algorithms for path-constrained sequence alignment
Journal of Discrete Algorithms
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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 @W(n^2@?|@S|) transitions for an NFA with n states and alphabet @S. 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 L"n that can be recognized by NFAs with O(nlog"2n) transitions, but @e-free NFAs need @W(n^2) transitions to accept L"n. Hence the standard conversion cannot be improved drastically. However, L"n requires an alphabet of size n, but we also construct regular languages K"n over {0,1} with NFAs of size O(nlog"2n), whereas @e-free NFAs require size n@?2^c^@?^l^o^g^"^2^n for every c