Graph connectivity, partial words, and a theorem of Fine and Wilf

The problem of computing periods in words, or finite sequences of symbols from a finite alphabet, has important applications in several areas including data compression, string searching and pattern matching algorithms. The notion of period of a word is central in combinatorics on words. There are many fundamental results on periods of words. Among them is the well known and basic periodicity result of Fine and Wilf which intuitively determines how far two periodic events have to match in order to guarantee a common period. More precisely, any word with length at least p + q - gcd(p, q) having periods p and q has also period the greatest common divisor of p and q, gcd(p, q). Moreover, the bound p + q - gcd(p, q) is optimal since counterexamples can be provided for words of smaller length. Partial words, or finite sequences that may contain a number of "do not know" symbols or holes, appear in natural ways in several areas of current interest such as molecular biology, data c...

• Type: Journal
• Year: 2008
• Where: IANDC
• Authors: Francine Blanchet-Sadri, Deepak Bal, Gautam Sisodia
• Keywords: Finite Alphabet, Greatest Common Divisor, IANDC 2008, Partial Word