The halting problem for linear turing assemblers

Authors:
Robert M. Baer;Jan van Leeuwen
Affiliations:
Department of Computer Science, University of California, Berkeley, California, USA and Department of Biochemistry and Biophysics, University of California, San Francisco, California, USA;Department of Computer Science, University of California, Berkeley, USA and Department of Mathematics, University of Utrecht, Utrecht, The Netherlands
Venue:
Journal of Computer and System Sciences
Year:
1976

Citing 3
Cited 0

Formal languages and their relation to automata

Formal languages and their relation to automata
Crossing sequences and off-line turing machine computations

FOCS '65 Proceedings of the 6th Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1965)
Computation by assembly

Journal of Computer and System Sciences

Quantified Score

Hi-index	0.02

Visualization

Abstract

Turing assemblers are Turing machines which operate on n-dimensional tapes under restrictions which characterize a procedure of assembly rather than computation, and which are intended as an abstraction of certain algorithmic processes of molecular biology. It has been previously shown that Turing assemblers with n-dimensional tapes can simulate arbitrary Turing machines for all n1. Here it is shown that for n=1 even nondeterministic Turing assemblers have a sharply restricted computational capability, being able to successfully assemble only regular sets. The halting problem for linear Turing assemblers is therefore algorithmically solvable, and a characterization of the set of achievable final assemblies will be given as a subclass of the context-free languages.