Simplifying Regular Expressions. A Quantitative Perspective

Abstract. We consider the efficient simplification of regular expressions and suggest a quantitative comparison of heuristics for simplifying regular expressions. To this end, we propose a new normal form for regular expressions, which outperforms previous heuristics while still being computable in linear time. We apply this normal form to determine an exact bound for the relation between the two prevalent measures for regular expression - size, namely alphabetic width and reverse polish notation length. In addition, we show that every regular expression of alphabetic with n can be converted into a nondeterministic finite automaton with ε-transitions of size at most 42 5 n + 1, and prove this bound to be optimal. This answers a question posed by Ilie and Yu, who had obtained lower and upper bounds of 4n − 1 and 9n − 1 2 , respectively [16]. For reverse polish notation length as input size measure, an optimal bound was recently determined by Gulan and Fernau [14]. We prove that,...

• Type: Conference
• Year: 2010
• Where: LATA
• Authors: Hermann Gruber and Stefan Gulan
• Keywords: LATA 2010, Polish Notation Length, Regular Expression, Reverse Polish Notation