Levenscycle

Levenscycle is a theoretical concept in computer science and discrete mathematics that describes a closed sequence of string transformations in which each step changes the current string by a single Levenshtein edit operation (insertion, deletion, or substitution) and the sequence returns to the original string, forming a cycle in the string edit graph. The term is a portmanteau of Levenshtein distance and cycle.

In formal terms, consider the graph whose vertices are all finite strings over a fixed alphabet, with edges connecting pairs of strings at Levenshtein distance one. A Levenscycle is a simple cycle in this graph; its length equals the number of edits in the cycle, and its total cost equals the cycle length when unit costs are assumed. The minimal such cycle length is called the Levenscycle length of the starting string.

The concept is mainly used as a theoretical tool to study the structure of edit operations and to evaluate edit-script patterns in sequences of text modifications. It also appears in discussions of diff and patch generation, and in analyses of compression of edit histories where repetitive edits form small cycles.

Example: starting from the string "a", performing an insertion of "b" to yield "ab" and then a deletion of "b" returns to "a"; this 2-step sequence constitutes a simple Levenscycle.

Note: Levenscycle is not a widely established standard term in all literature; it is described here as a hypothetical or pedagogical construct to illustrate cycles in the Levenshtein edit graph.