141 research outputs found
Reversible Two-Party Computations
Deterministic synchronous systems consisting of two finite automata running
in opposite directions on a shared read-only input are studied with respect to
their ability to perform reversible computations, which means that the automata
are also backward deterministic and, thus, are able to uniquely step the
computation back and forth. We study the computational capacity of such devices
and obtain on the one hand that there are regular languages that cannot be
accepted by such systems. On the other hand, such systems can accept even
non-semilinear languages. Since the systems communicate by sending messages, we
consider also systems where the number of messages sent during a computation is
restricted. We obtain a finite hierarchy with respect to the allowed amount of
communication inside the reversible classes and separations to general, not
necessarily reversible, classes. Finally, we study closure properties and
decidability questions and obtain that the questions of emptiness, finiteness,
inclusion, and equivalence are not semidecidable if a superlogarithmic amount
of communication is allowed.Comment: In Proceedings AFL 2023, arXiv:2309.0112
State-deterministic Finite Automata with Translucent Letters and Finite Automata with Nondeterministically Translucent Letters
Deterministic and nondeterministic finite automata with translucent letters
were introduced by Nagy and Otto more than a decade ago as Cooperative
Distributed systems of a kind of stateless restarting automata with window size
one. These finite state machines have a surprisingly large expressive power:
all commutative semi-linear languages and all rational trace languages can be
accepted by them including various not context-free languages. While the
nondeterministic variant defines a language class with nice closure properties,
the deterministic variant is weaker, however it contains all regular languages,
some non-regular context-free languages, as the Dyck language, and also some
languages that are not even context-free. In all those models for each state,
the letters of the alphabet could be in one of the following categories: the
automaton cannot see the letter (it is translucent), there is a transition
defined on the letter (maybe more than one transitions in nondeterministic
case) or none of the above categories (the automaton gets stuck by seeing this
letter at the given state and this computation is not accepting).
State-deterministic automata are recent models, where the next state of the
computation determined by the structure of the automata and it is independent
of the processed letters. In this paper our aim is twofold, on the one hand, we
investigate state-deterministic finite automata with translucent letters. These
automata are specially restricted deterministic finite automata with
translucent letters.
In the other novel model we present, it is allowed that for a state the set
of translucent letters and the set of letters for which transition is defined
are not disjoint. One can interpret this fact that the automaton has a
nondeterministic choice for each occurrence of such letters to see them (and
then erase and make the transition) or not to see that occurrence at that time.
Based on these semi-translucent letters, the expressive power of the automata
increases, i.e., in this way a proper generalization of the previous models is
obtained.Comment: In Proceedings AFL 2023, arXiv:2309.0112
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
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
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