Journal ArticleDOI
On the undecidability of splicing systems
TLDR
The main result is that there exist sequential splicing systems with recursively unsolvable membership problem and the technique of the proof is to embed Turing machine computations in the languages.Abstract:
The notion of splicing system has been used to abstract the process of DNA digestion by restriction enzymes and subsequent religation. A splicing system language is the formal language of all DNA strings producible by such a process. The membership problem is to devise an algorithm (if possible) to answer the question of whether or not a given DNA string belongs to a splicing system language given by initial strings and enzymes. In this paper the concept of a sequential splicing system is introduced. A sequential splicing system differs from a splicing system in that the latter allows arbitrarily many copies of any string in the initial set whereas the sequential splicing system may restrict the initial number of copies of some strings. The main result is that there exist sequential splicing systems with recursively unsolvable membership problem. The technique of the proof is to embed Turing machine computations in the languages.read more
Citations
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Journal ArticleDOI
Computing with molecules.
Mark A. Reed,James M. Tour +1 more
TL;DR: In a remarkable series of demonstrations, chemists, physicists and engineers have shown that individual molecules can conduct and switch electric current and store information, a field emerging around the premise that it is possible to build individual molecules that can perform functions identical or analogous to those of the transistors, diodes, conductors and other key components of today's microcircuits.
Journal ArticleDOI
DNA computing: Arrival of biological mathematics
TL;DR: The relationship between mathematics and biology has so far been one-way: a mathematical problem is the end toward which the tools of biology are used as discussed by the authors, which marks the first instance of the connection being reversed, and instead of categorizing the research in DNA computing as belonging to mathematical biology, we should be employing the mirror image term biological mathematics for the field born in November 1994.
Book ChapterDOI
Language theory and molecular genetics: generative mechanisms suggested by DNA recombination
TL;DR: The stimulus for the development of the theory presented in this chapter is the string behaviors exhibited by the group of molecules often referred to collectively as the informational macromolecules, and the splicing rule concept is the foundation for the present chapter.
Journal ArticleDOI
Splicing semigroups of dominoes and DNA
Karel Culik,Tero Harju +1 more
TL;DR: The main result is that in the case of alphabetic dominoes the splicing semigroup generated from an initial regular set is again regular, implying positive solution of two open problems stated by Head, namely the regularity of splicing systems and the decidability of their membership problem.
Journal ArticleDOI
On the splicing operation
TL;DR: A systematic formal study of the splicing operation introduced by Head as a model of recombinant behavior of DNA is proposed and relations between these operations and usual operations with languages are investigated, as well as the closure of Chomsky language families under these splicing operations.
References
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Book
Automata, Languages, and Machines
TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.
Journal ArticleDOI
Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors.
TL;DR: This study initiates the formal analysis of the generative power of recombinational behaviors in general by means of a new generative formalism called a splicing system and a significant subclass of these languages, which are shown to coincide with a class of regular languages which have been previously studied in other contexts: the strictly locally testable languages.
Journal ArticleDOI
Recursive Unsolvability of a Problem of Thue
TL;DR: Thue's problem is the problem of determining for arbitrarily given strings A, B on al, whether, or no, A and B are equivalent, and this problem is more readily placed if it is restated in terms of a special form of the canonical systems of [3].