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NFA-to-DFA Trade-Off for Regular Operations

  • Galina Jirásková
  • Ivana KrajňákováEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11612)

Abstract

We examine the operational state complexity assuming that the operands of a regular operation are represented by nondeterministic finite automata, while the language resulting from the operation is required to be represented by a deterministic finite automaton. We get tight upper bounds \(2^n\) for complementation, reversal, and star, \(2^m\) for left and right quotient, \(2^{m+n}\) for union and symmetric difference, \(2^{m+n}-2^m-2^n+2\) for intersection, \(2^{m+n}-2^n+1\) for difference, \(\frac{3}{4}2^{m+n}\) for concatenation, and \(2^{mn}\) for shuffle. We use a binary alphabet to describe witnesses for complementation, reversal, star, and left and right quotient, and a quaternary alphabet otherwise. Whenever we use a binary alphabet, it is always optimal.

Notes

Acknowledgement

We would like to kindly thank Michal Hospodár for his valuable notes and comments.

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Copyright information

© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.Mathematical Institute, Slovak Academy of SciencesKošiceSlovakia

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