Watson-Crick D0L Systems Research Articles

Networks of Watson-Crick D0L systems with communication by substrings

Watson-Crick D0L systems (WD0L systems) are augmented variants of D0L systems defined over a DNA-like alphabet, where each letter has a complementary letter and this relation is symmetric. WD0L systems operate under a control that is inspired by the well-known phenomenon of Watson-Crick complementarity of the double helix of DNA. Depending on a trigger, the standard D0L rewriting step is applied either to the string or to its complementary string. In this paper, we examine extended networks of standard Watson-Crick D0L systems (ENSWD0L systems) with a variant of incomplete communication. An NWD0L system is a finite set of WD0L systems defined over a common DNA-like alphabet and operating in a synchronized manner. After rewriting their own strings in the WD0L manner, they communicate copies of certain generated strings (the so-called good strings) to the other nodes. In some previous papers, it was shown that ENSWD0L systems are computationally complete, and their computational power does not change if the communicated string is a non-empty prefix (non-empty suffix) of the generated string. We strengthen the previous results, namely we show that ENSWD0L systems are computationally complete even if the communicated string is an arbitrary substring of the generated string.

Watson-crick (D)0 L systems: a survey

AbstractWatson-Crick L systems are string generating formal models obtained by augmenting Lindenmayer systems with the Watson-Crick morphism inspired by the Watson-Crick complementarity principle. The Watson-Crick morphism is controlled by a trigger—a boolean condition eventually met by the generated word. Despite their simplicity, Watson-Crick (D)0 L systems have interesting mathematical properties, a strong generative power, and they can also characterize some open decision problems. Furthermore, networks of Watson-Crick D0L systems are capable of trading space for time, and thus of characterizing linear time solutions to intractable problems. We provide a survey of results in this field since its origin in 1997 to the present, and we conclude with a series of open research problems and ideas.

Discrete Watson–Crick dynamical systems

We generalize previous ideas by Mihalache and Salomaa to define discrete Watson–Crick dynamical systems. We study decision problems for these systems and apply our results to Watson–Crick D0L systems.

Watson–Crick D0L systems: generative power and undecidable problems

The properties of Watson–Crick D0L system, a language–theoretical formalism inspired by natural DNA processing, are studied. The model incorporates the iterated D0L-like morphism and the DNA complementarity principle represented by a letter-to-letter morphism. These two morphisms are connected by a natural condition called the trigger.We show first that this very simple model has rather unexpected power; it can closely and simply simulate any Minsky register machine. As a consequence, any recursively enumerable language can be obtained as a projection of the language of some standard Watson–Crick D0L system. Finally, we show that the graph reachability problem, equivalence problems and some other problems of standard Watson–Crick D0L systems are undecidable.

Decidability results for Watson–Crick D0L systems with nonregular triggers

We show that sequence equivalence, language equivalence, growth equivalence and road equivalence are decidable for standard Watson–Crick D0L systems having bounded balance.

Watson–Crick D0L systems: the power of one transition

We investigate the class of functions computable by uni-transitional Watson–Crick D0L systems: only one complementarity transition is possible during each derivation. The class is characterized in terms of a certain min-operation applied to Z-rational functions. We also exhibit functions outside the class, and show that the basic decision problems are equivalent or harder than a celebrated open problem. For instance, the latter alternative applies to the growth-bound problem for functions in the class.

Universal computation with Watson-Crick D0L systems

Watson-Crick D0L systems, introduced in 1997 by Mihalache and Salomaa, arise from two major principles: the Lindenmayer rewriting and the Watson-Crick complementarity principle. Complementarity can be viewed as a purely language-theoretic operation. Majority of a certain type of symbols in a string (purines vs. pyrimidines) triggers a transition to the complementary string. The paper deals with an expressive power of deterministic interactionless Watson-Crick Lindenmayer systems. A rather surprising result is obtained: these systems, consisting of iterated morphism and a basic DNA operation, are able to compute any Turing computable function.

Uni-transitional Watson–Crick D0L systems

The phenomenon known as Watson–Crick complementarity is basic both in the experiments and theory of DNA computing. While the massive parallelism of DNA strands makes exhaustive searches possible, complementarity constitutes a powerful computational tool. It is also very fruitful to view complementarity as a language-theoretic operation: “bad” words obtained through a generative process are replaced by their complementary ones. This idea seems particularly suitable for Lindenmayer systems. D0L systems augmented with a specific complementarity transition, Watson–Crick D0L systems, have turned out to be a most interesting model and have already been extensively studied. A language is generated by a Watson–Crick D0L system as a sequence of words. Consequently, the systems can be applied also to compute functions in a natural way. In the present paper, attention is focused on uni-transitional systems, where at most one complementarity transition takes place in the generated sequence. In spite of their seeming simplicity, uni-transitional systems represent a vast extension of ordinary D0L systems. This becomes apparent in their capacity of defining functions. Quite remarkably, all basic decision problems for uni-transitional systems are algorithmically equivalent among themselves, as well as equivalent to a celebrated open problem. We investigate also a simpler case of systems with regular triggers, as well as pose some open problems.

Watson–Crick D0L systems with regular triggers

Watson–Crick complementarity has been used as a basis for massive parallelism in DNA computing. Also its use in an operational sense has turned out to be very promising in the study of Watson–Crick D0L systems. The latter generalize D0L systems in a way not investigated so far in the theory of Lindenmayer systems. The complexity of the “trigger” is crucial for decidability properties concerning Watson–Crick D0L systems. The purpose of this paper is to settle the basic decision problems in the case of regular triggers.