Abstract
We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial derivative automata is in the worst case at most \(2^m\), where \(m\) is the number of letters in the expression, while asymptotically and on average it is no more than \((\frac{4}{3})^m\).
Authors partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under projects UID/MAT/00144/2013 and FCOMP-01-0124-FEDER-020486.
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Notes
- 1.
This upper bound corresponds to the case where all unions in \(\pi (\alpha )\) are disjoint.
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Broda, S., Machiavelo, A., Moreira, N., Reis, R. (2015). Partial Derivative Automaton for Regular Expressions with Shuffle. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_2
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