On the Shuffle Automaton Size for Words

Franziska Biegler
Mark Daley
Ian McQuillan

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.

In Jürgen Dassow, Giovanni Pighizzini and Bianca Truthe: Proceedings Eleventh International Workshop on Descriptional Complexity of Formal Systems (DCFS 2009), Magdeburg, Germany, July 6-9, 2009, Electronic Proceedings in Theoretical Computer Science 3, pp. 79–89.
Published: 30th July 2009.

ArXived at: http://dx.doi.org/10.4204/EPTCS.3.7 bibtex PDF

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