Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

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

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