Prefixvrij

Prefixvrij is a Dutch term that translates to "prefix-free" in English. It is primarily used in the context of formal languages and computer science to describe a set of strings where no string is a prefix of another string in the same set. This property is crucial for efficient decoding and parsing of data.

In a prefix-free code, when a sequence of symbols is received, the decoder can immediately identify the complete symbols without ambiguity. For example, if you have a set of codes where "01" and "010" are both present, it's impossible to know whether "01" represents a single symbol or the beginning of a longer symbol "010". However, in a prefix-free set, such ambiguity is eliminated.

Common examples of prefix-free codes include Huffman codes, which are used for data compression, and some forms of error-correcting codes. The prefix-free property ensures that a code word can be uniquely and unambiguously identified as soon as its last symbol is received. This makes it simpler and faster for systems to interpret the encoded information. The mathematical concept behind prefix-free sets is related to trees, where each string in the set corresponds to a leaf node, and no leaf node is an ancestor of another leaf node.