794 research outputs found
Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages
Circular splicing systems are a formal model of a generative mechanism of
circular words, inspired by a recombinant behaviour of circular DNA. Some
unanswered questions are related to the computational power of such systems,
and finding a characterization of the class of circular languages generated by
circular splicing systems is still an open problem. In this paper we solve this
problem for complete systems, which are special finite circular splicing
systems. We show that a circular language L is generated by a complete system
if and only if the set Lin(L) of all words corresponding to L is a pure unitary
language generated by a set closed under the conjugacy relation. The class of
pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G.
Rozenberg in 1983, as a subclass of the class of context-free languages,
together with a characterization of regular pure unitary languages by means of
a decidable property. As a direct consequence, we characterize (regular)
circular languages generated by complete systems. We can also decide whether
the language generated by a complete system is regular. Finally, we point out
that complete systems have the same computational power as finite simple
systems, an easy type of circular splicing system defined in the literature
from the very beginning, when only one rule is allowed. From our results on
complete systems, it follows that finite simple systems generate a class of
context-free languages containing non-regular languages, showing the
incorrectness of a longstanding result on simple systems
Flat Splicing Array Grammar Systems Generating Picture Arrays
While studying the recombinant behaviour of DNA molecules, Head (1987) introduced a new operation, called splicing on words or strings, which are finite sequences of symbols. There has been intensive research using the concept of splicing on strings in the context of DNA computing, establishing important theoretical results on computational universality. A particular class of splicing, known as flat splicing on strings was recently considered and this operation was extended to provide picture array generating two-dimensional models. Making use of the operation of flat splicing on arrays, we propose here a grammar system, called flat splicing regular array grammar system (FSRAGS), as a new model of picture generation. The components of a FSRAGS generate picture arrays working in parallel using the rules of a two-phase grammar called 2RLG and with two different components of the FSRAGS communicating using the array flat splicing operations on columns and rows of the arrays. We establish some comparison results bringing out the generative power of FSRAGS and also exhibit the power of FSRAGS in generating certain “floor designs”
Splicing systems and the Chomsky hierarchy
In this paper, we prove decidability properties and new results on the
position of the family of languages generated by (circular) splicing systems
within the Chomsky hierarchy. The two main results of the paper are the
following. First, we show that it is decidable, given a circular splicing
language and a regular language, whether they are equal. Second, we prove the
language generated by an alphabetic splicing system is context-free. Alphabetic
splicing systems are a generalization of simple and semi-simple splicin systems
already considered in the literature
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
Splicing Systems from Past to Future: Old and New Challenges
A splicing system is a formal model of a recombinant behaviour of sets of
double stranded DNA molecules when acted on by restriction enzymes and ligase.
In this survey we will concentrate on a specific behaviour of a type of
splicing systems, introduced by P\u{a}un and subsequently developed by many
researchers in both linear and circular case of splicing definition. In
particular, we will present recent results on this topic and how they stimulate
new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in
Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian
Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other
author
Computing with Membranes and Picture Arrays
Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and
parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages
A note on the strong and weak generative powers of formal systems
AbstractThis paper is a note on some relationships between the strong and weak generative powers of formal systems, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We will comment on some old and new results from this perspective. Our main goal of this note is to comment on the strong generative power of context-free grammars, lexicalized tree-adjoining grammars (and some of their variants) and Lambek grammars, especially in the context of crossing dependencies, in view of the recent work of Tiede (Ph.D. Dissertation, Indiana University, Bloomington, 1999)
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