Congruences, Infix and Cohesive Prefix Codes

Abstract A language L ⊆ X * is called cohesive prefix code if xLy ∩ L ≠ ∅ implies that y = 1 and xL ⊆ L for any x , y ϵ X *. An example of cohesive prefix codes is an infix code. We determine first the structure of cohesive prefix codes and then we study several relationships between maximal infix codes and maximal cohesive prefix codes. Finally, we determine the structure of a cohesive prefix code that is a right semaphore code.