Some Remarks on the Formal Operations Inspired by the Gene Assembly in Ciliates

We continue here the theoretical study initiated approximately twenty years ago on the possibility of using living cells for computing. In this paper, we reconsider the formal operations inspired by the intramolecular DNA rearrangements in the evolution of the macronucleus from the micronucleus in a group of ciliates. After introducing the concept of a valid string, we propose an efficient algorithm for checking this property for a given string. Then we investigate which of the considered operations preserve the property of a string to be valid. We also show that just one of the operations can be simulated by a finite transducer. The important problem regarding the order of applying the operations is then investigated showing that one operation can commute with the other two. Finally, we introduce the iterated variants and investigate a few properties. A sort of a "normal form" for the gene assembly in ciliates is obtained. The paper ends by a short discussion about open problems and further directions of research.