LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

On Some Classes of Splicing Languages ⋆
Rodica Ceterchi 1 , Carlos Martín-Vide 2 , and K.G. Subramanian 3
1 Faculty of Mathematics, University of Bucharest
14, Academiei st., 70109 Bucharest, Romania
rc@funinf.math.unibuc.ro, rc@fll.urv.es
2 Research Group in Mathematical Linguistics
Rovira i Virgili University
Pl. Imperial Tàrraco 1, 43005 Tarragona, Spain
cmv@astor.urv.es
3 Department of Mathematics
Madras Christian College
Tambaram, Chennai 600059, India
kgsmani@vsnl.net
Abstract. We introduce some classes of splicing languages generated
with simple and semi-simple splicing rules, in both, the linear and circular
cases. We investigate some of their properties.
1 Introduction
The operation of splicing was introduced as a generative mechanism in formal
language theory by Tom Head in [9], and lays at the foundation of the field of
DNA based computing (see [11] and [14].)
We are concerned in this paper with some classes of languages which arise
when considering very simple types of splicing rules. Our main inspiration is the
study of [12], where the notion of simple H system and the associated notion of
simple splicing languages have been introduced.
A simple splicing rule is a rule of the form (a, 1; a, 1) with a ∈ A asymbol
called marker. More precisely, we will call such a rule a (1, 3)-simple splicing
rule, since the marker a appears on the 1 and 3 positions of the splicing rule,
and since one can conceive of (i, j)-simple splicing rules for all pairs (i, j) with
i =1, 2, j =3, 4. We denote by SH(i, j) the class of languages generated by
simple splicing rules of type (i, j). The paper [12] focuses basically on the study
of the SH(1, 3) class (which is equal to the SH(2, 4) class and is denoted by SH).
Only towards the end of the paper the authors of [12] show that there are three
such distinct and incomparable classes, SH = SH(1, 3) = SH(2, 4), SH(2, 3)
and SH(1, 4), of (linear) simple splicing languages. They infer that most of the
results proven for the SH class will hold also for the other classes, and point out
towards studying one-sided splicing rules of radius at most k: rules(u1, 1; u3, 1)
⋆ This work was possible thanks to the grants SAB2000-0145, and SAB2001-0007,
from the Secretaría de Estado de Educación y Universidades, Spanish Ministry for
Education, Culture and Sport.
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 84–105, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004