39,686 research outputs found
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
Hyper-Minimization for Deterministic Weighted Tree Automata
Hyper-minimization is a state reduction technique that allows a finite change
in the semantics. The theory for hyper-minimization of deterministic weighted
tree automata is provided. The presence of weights slightly complicates the
situation in comparison to the unweighted case. In addition, the first
hyper-minimization algorithm for deterministic weighted tree automata, weighted
over commutative semifields, is provided together with some implementation
remarks that enable an efficient implementation. In fact, the same run-time O(m
log n) as in the unweighted case is obtained, where m is the size of the
deterministic weighted tree automaton and n is its number of states.Comment: In Proceedings AFL 2014, arXiv:1405.527
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
Entry times in automata with simple defect dynamics
In this paper, we consider a simple cellular automaton with two particles of
different speeds that annihilate on contact. Following a previous work by K\r
urka et al., we study the asymptotic distribution, starting from a random
configuration, of the waiting time before a particle crosses the central column
after time n. Drawing a parallel between the behaviour of this automata on a
random initial configuration and a certain random walk, we approximate this
walk using a Brownian motion, and we obtain explicit results for a wide class
of initial measures and other automata with similar dynamics.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
JohnnyVon: Self-Replicating Automata in Continuous Two-Dimensional Space
JohnnyVon is an implementation of self-replicating automata in continuous two-dimensional space. Two types of particles drift about in a virtual liquid. The particles are automata with discrete internal states but continuous external relationships. Their internal states are governed by finite state machines but their external relationships are governed by a simulated physics that includes brownian motion, viscosity, and spring-like attractive and repulsive forces. The particles can be assembled into patterns that can encode arbitrary strings of bits. We demonstrate that, if an arbitrary “seed” pattern is put in a “soup” of separate individual particles, the pattern will replicate by assembling the individual particles into copies of itself. We also show that, given sufficient time, a soup of separate individual particles will eventually spontaneously form self-replicating patterns. We discuss the implications of JohnnyVon for research in nanotechnology, theoretical biology, and artificial life
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