Sets of integers in different number systems and the Chomsky hierarchy

The classes of the Chomsky hierarchy are characterized in respect of converting between canonical number systems. We show that the relations of the bases of the original and converted number systems fall into four distinct categories, and we examine the four Chomsky classes in each of the four cases. We also prove that all of the Chomsky classes are closed under constant addition and multiplication. The classes RE and CS are closed under every examined operation. The regular languages axe closed under addition, but not under multiplication

On implementing relational databases on DNA strands

This work describes the theoretical bases of the implementation of relational databases in test tubes, using an abstract model of molecular computing. It specifies the representation of relations and the execution program of the relational algebra (RA) operations. We investigate the possibilities of practical usage of the proposed model as well as the bounds of it

A Note on Restricted Insertion-Deletion Systems

In the past few years several papers showed, that various generative mechanisms in formal language theory that use insertion and deletion operations are capable of generating any recursively enumerable languages [1, 2, 3, 4, 5, 6, 7, 8, 9]. Since such systems are also models of molecular computing, for practical reasons it is important to examine these systems in a restricted case, in which the number of symbols in the model of the alphabet is limited. In [4] it is showed that we can define the generated language of an insertion-deletion system in such a way, that a two-letter alphabet is enough to generate any recursively enumerable language. In this note we complete this result by showing that the same generative capacity can be obtained even if we define the generated language the traditional way.

Restricted Insertion-Deletion Systems

In the past few years several paper showed, that various generative mechanisms in formal language theory that used context-dependent insertions and deletions are capable of generating any recursively enumerable languages [1, 2, 3, 4, 5, 6, 7, 8, 9]. Since such systems are also models of molecular computing, for practical reasons it is important to examine these systems in a restricted case, in which the number of symbols in the model of the alphabet is limited. In [4] it is showed that we can define the generated language of an insertion-deletion system in such a way, that a two-letter alphabet is enough to generate any recursively enumerable language. In this paper we complete this result by showing that the same generative capacity can be obtained even if we define the generated language the traditional way