suffixfree

Suffixfree refers to a set of strings where no string is a suffix of another string within the same set. This is a fundamental concept in combinatorics on words and has applications in various areas of computer science, including data compression, pattern matching, and bioinformatics. A set of strings S is suffixfree if for any two distinct strings $s_1, s_2 \in S$, $s_1$ is not a suffix of $s_2$. For example, the set {"a", "b", "ab"} is suffixfree because "a" is not a suffix of "b" or "ab", "b" is not a suffix of "a" or "ab", and "ab" is not a suffix of "a" or "b". However, the set {"a", "ba", "aba"} is not suffixfree because "a" is a suffix of "ba" and "aba". Conversely, "ba" is a suffix of "aba".

The study of suffixfree sets is closely related to the concept of prefix codes, where no string is a prefix of another string. In fact, a set of strings is suffixfree if and only if its reverse is a prefix code. This duality allows for the transfer of results and techniques between these two related areas. Suffixfree sets play a role in the construction of certain types of automata and in the analysis of algorithms that deal with string manipulation. Their properties are essential for understanding the structure of formal languages and for developing efficient algorithms for string processing tasks.