  In 2003, Leonid A. Levin presented the idea of a combinatorial complete
one-way function and a sketch of the proof that Tiling represents such a
function. In this paper, we present two new one-way functions based on
semi-Thue string rewriting systems and a version of the Post Correspondence
Problem and prove their completeness. Besides, we present an alternative proof
of Levin's result. We also discuss the properties a combinatorial problem
should have in order to hold a complete one-way function.
