Abstrakt
Combinatorics on Words is a rather young domain encompassing the study of words and formal languages. An archetypal example of a task in Combinatorics on Words is to solve the equation x . y = y . x, i.e., to describe words that commute.
This contribution contains formalization of three important classical results in Isabelle/HOL. Namely i) the Periodicity Lemma (a.k.a. the theorem of Fine and Wilf), including a construction of a word proving its optimality; ii) the solution of the equation xa . yb = zc with 2 <= a, b, c, known as the Lyndon-Schützenberger Equation; and iii) the Graph Lemma, which yields a generic upper bound on the rank of a solution of a system of equations.
The formalization of those results is based on an evolving toolkit of several hundred auxiliary results which provide for smooth reasoning within more complex tasks.