7 research outputs found
A Note on Limited Pushdown Alphabets in Stateless Deterministic Pushdown Automata
Recently, an infinite hierarchy of languages accepted by stateless
deterministic pushdown automata has been established based on the number of
pushdown symbols. However, the witness language for the n-th level of the
hierarchy is over an input alphabet with 2(n-1) elements. In this paper, we
improve this result by showing that a binary alphabet is sufficient to
establish this hierarchy. As a consequence of our construction, we solve the
open problem formulated by Meduna et al. Then we extend these results to
m-state realtime deterministic pushdown automata, for all m at least 1. The
existence of such a hierarchy for m-state deterministic pushdown automata is
left open
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