Partial Derivative Automaton for Regular Expressions with Shuffle

TL;DR

This paper extends the partial derivative automaton concept to regular expressions with shuffle, analyzing its size and efficiency in worst-case and average scenarios, showing significant state size reductions.

Contribution

It introduces a generalized automaton for shuffle-regular expressions and provides size bounds, improving understanding of automaton complexity for these expressions.

Findings

Worst-case automaton size is at most 2^m states.

Average automaton size is no more than (4/3)^m states.

Provides theoretical bounds on automaton size for shuffle-regular expressions.

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 (4/3)^m.