On the Shuffle Automaton Size for Words

  title={On the Shuffle Automaton Size for Words},
  author={Franziska Biegler and Mark Daley and Ian McQuillan},
  journal={J. Autom. Lang. Comb.},
We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential. 

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