The computational power of Watson-Crick grammars: Revisited

A Watson-Crick finite automaton is one of DNA computational models using the Watson-Crick complementarity feature of deoxyribonucleic acid (DNA). We are interested in investigating a grammar counterpart of Watson-Crick automata. In this paper, we present results concerning the generative power of Watson-Crick (regular, linear, context-free) grammars. We show that the family of Watson-Crick context-free languages is included in the family of matrix languages

Watson–Crick context-free grammars: Grammar simplifications and a parsing algorithm

A Watson–Crick (WK) context-free grammar, a context-free grammar with productions whose right-hand sides contain nonterminals and double-stranded terminal strings, generates complete double-stranded strings under Watson–Crick complementarity. In this paper, we investigate the simplification processes of Watson–Crick context-free grammars, which lead to defining Chomsky like normal form for Watson–Crick context-free grammars. The main result of the paper is a modified CYK (Cocke–Younger–Kasami) algorithm for Watson–Crick context-free grammars in WK-Chomsky normal form, allowing to parse double-stranded strings in O(n^6) time

On the Languages Accepted by Watson-Crick Finite Automata with Delays

[EN] In this work, we analyze the computational power of Watson-Crick finite automata (WKFA) if some restrictions over the transition function in the model are imposed. We consider that the restrictions imposed refer to the maximum length difference between the two input strands which is called the delay. We prove that the language class accepted by WKFA with such restrictions is a proper subclass of the languages accepted by arbitrary WKFA in general. In addition, we initiate the study of the language classes characterized by WKFAs with bounded delays. We prove some of the results by means of various relationships between WKFA and sticker systems.This work has been developed with the financial support of the European Union's Horizon 2020 research and innovation programme under grant agreement No. 952215 corresponding to the TAILOR project.Sempere Luna, JM. (2021). On the Languages Accepted by Watson-Crick Finite Automata with Delays. Mathematics. 9(8):1-12. https://doi.org/10.3390/math9080813S1129

On language classes accepted by stateless 5′ → 3′ Watson-Crick finite automata

Watson-Crick automata are belonging to the natural computing paradigm as these finite automata are working on strings representing DNA molecules. Watson-Crick automata have two reading heads, and in the 5 ′ → 3 ′ models these two heads start from the two extremes of the input. This is well motivated by the fact that DNA strands have 5 ′ and 3 ′ ends based on the fact which carbon atoms of the sugar group is used in the covalent bonds to continue the strand. However, in the two stranded DNA, the directions of the strands are opposite, so that, if an enzyme would read the strand it may read each strand in its 5 ′ to 3 ′ direction, which means physically opposite directions starting from the two extremes of the molecule. On the other hand, enzymes may not have inner states, thus those Watson-Crick automata which are stateless (i.e. have exactly one state) are more realistic from this point of view. In this paper these stateless 5 ′ → 3 ′ Watson-Crick automata are studied and some properties of the language classes accepted by their variants are proven. We show hierarchy results, and also a “pumping”, i.e., iteration result for these languages that can be used to prove that some languages may not be in the class accepted by the class of stateless 5 ′ → 3 ′ Watson-Crick automata