Sticker systems over monoids

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study

Arithmetically Controlled H Systems

We consider two classes of restricted H systems, both dealing with numbers associated to the terms of splicing operations. In one of them, these numbers indicate the age of the strings (the generation when the strings are produced), in the second one the numbers can be interpreted as valences of the strings. Restricting the splicing to strings of "a similar age", or accepting as complete splicing processes only those processes which produce strings with a null valence increase the generative power of H systems (with finite sets of rules)

Arithmetically Controlled H Systems

We consider two classes of restricted H systems, both dealing with numbers associated to the terms of splicing operations. In one of them, these numbers indicate the age of the strings (the generation when the strings are produced), in the second one the numbers can be interpreted as valences of the strings. Restricting the splicing to strings of "a similar age", or accepting as complete splicing processes only those processes which produce strings with a null valence increase the generative power of H systems (with finite sets of rules)