# On the Shuffle Automaton Size for Words

@article{Biegler2009OnTS, title={On the Shuffle Automaton Size for Words}, author={Franziska Biegler and Mark Daley and Ian McQuillan}, journal={J. Autom. Lang. Comb.}, year={2009}, volume={15}, pages={53-70} }

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.

## 9 Citations

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