Counting Parameterized Border Arrays for a Binary Alphabet

The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n, where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.

• Type: Conference
• Year: 2009
• Where: LATA
• Authors: Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
• Keywords: Automata Theory, LATA 2009, P-border Arrays, Pattern Matching, Pattern Matching Problem