On the Shuffle Automaton Size for Words
Formal Languages and Automata Theory
2009-07-30 v1 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.0907.5111,
title = {On the Shuffle Automaton Size for Words},
author = {Franziska Biegler and Mark Daley and Ian McQuillan},
journal= {arXiv preprint arXiv:0907.5111},
year = {2009}
}