Abstract
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 L n that can be recognized by NFAs with O(n log2 n) transitions, but ε-free NFAs need Ω(n 2) transitions to accept L n . Hence the standard conversion cannot be improved significantly. 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(n log2 n), whereas ε-free NFAs require size \(n \cdot 2^{c \cdot\sqrt{{\rm log}_{2}n}}\) for every c < 1/2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
