onestring

Onestring is a term used in formal language theory and computer science to denote a string that consists of only a single repeated symbol from an alphabet. Formally, for an alphabet Σ and a symbol a ∈ Σ, a onestring of length n is a^n with n ≥ 1. The set of all onestrings is {a^n | a ∈ Σ, n ≥ 1}. The empty string is typically excluded from this definition, though some sources allow n = 0 as a degenerate case.

Examples include "aaa" over the alphabet {a}, "1111" over {1}, and in binary, "0" and "1" of any positive length. For each fixed length n, there are |Σ| different onestrings; equivalently, the language of all onestrings is a^+ if you fix a in the alphabet.

Properties: onestrings form a simple, regular language. They serve as basic test cases in automata, parsing, and pattern-matching tasks. In data compression and Kolmogorov complexity, a onestring a^n is straightforward to describe: choosing the symbol a and the length n.

Generation and recognition: given a string s, you can recognize a onestring by checking whether all characters equal the first character; generating a onestring is accomplished by repeating a chosen symbol n times.

Variants: some discussions use the terms uniform string or constant string for the same concept. See also: string, alphabet, regular language, repetition.