16 research outputs found
Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata
This papers presents a general framework for the uniform random generation of
deterministic real-time accessible pushdown automata. A polynomial time
algorithm to randomly generate a pushdown automaton having a fixed stack
operations total size is proposed. The influence of the accepting condition
(empty stack, final state) on the reachability of the generated automata is
investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
Synchronizing Random Almost-Group Automata
In this paper we address the question of synchronizing random automata in the
critical settings of almost-group automata. Group automata are automata where
all letters act as permutations on the set of states, and they are not
synchronizing (unless they have one state). In almost-group automata, one of
the letters acts as a permutation on states, and the others as
permutations. We prove that this small change is enough for automata to become
synchronizing with high probability. More precisely, we establish that the
probability that a strongly connected almost-group automaton is not
synchronizing is , for a -letter
alphabet.Comment: full version prepared for CIAA 201
On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism
In this paper we address the problem of the uniform random generation of non
deterministic automata (NFA) up to isomorphism. First, we show how to use a
Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use
the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism.
Using labeling techniques, we show that in practice it is possible to move into
the modified Markov Chain efficiently, allowing the random generation of NFAs
up to isomorphism with dozens of states. This general approach is also applied
to several interesting subclasses of NFAs (up to isomorphism), such as NFAs
having a unique initial states and a bounded output degree. Finally, we prove
that for these interesting subclasses of NFAs, moving into the Metropolis
Markov chain can be done in polynomial time. Promising experimental results
constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
One Drop of Non-Determinism in a Random Deterministic Automaton
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from n states to 2? states. In this article, we investigate this classical result in a probabilistic setting where we take a deterministic automaton with n states uniformly at random and add just one random transition. These automata are almost deterministic in the sense that only one state has a non-deterministic choice when reading an input letter. In our model each state has a fixed probability to be final. We prove that for any d ? 1, with non-negligible probability the minimal (deterministic) automaton of the language recognized by such an automaton has more than n^d states; as a byproduct, the expected size of its minimal automaton grows faster than any polynomial. Our result also holds when each state is final with some probability that depends on n, as long as it is not too close to 0 and 1, at distance at least ?(1/?n) to be precise, therefore allowing models with a sublinear number of final states in expectation
On the Uniform Random Generation of Determinisitic Partially Ordered Automata using Monte Carlo Techniques
Partially ordered automata are finite automata admitting no simple loops of length greater than or equal to 2. In this paper we show how to randomly and uniformly generate deterministic accessible partially ordered automata using Monte-Carlo techniques
Active Learning Over Large Alphabets
El siguiente proyecto es una extensión y reestructura del framework de algoritmos de aprendizaje de autómatas basados en MAT, desarrollado por la Cátedra de Inteligencia Artificial de la Universidad ORT Uruguay. El objetivo del trabajo es doble, primero re-arquitecturar el framework para que sea más fácilmente extensible, y segundo, agregar un algoritmo de aprendizaje de autómatas simbólicos. La primera etapa del trabajo consistió en la revisión, rediseño y reimplementación de gran parte de la plataforma de aprendizaje activo desarrollada por la Cátedra de Inteligencia Artificial. En la segunda etapa, se llevó adelante una investigación teórica que se centró en la inferencia gramatical y en el estudio de dos algoritmos de aprendizaje de autómatas simbólicos, concretamente los propuestos por Maler-Mens y Argyros-D'Antoni. Luego de un análisis de estos, se decidió por el uso de autómatas simbólicos por la facilidad que pueden tener para la representación de alfabetos grandes, potencialmente infinitos. Una vez implementado, se comparará el algoritmo contra el algoritmo desarrollado por Angluin.Agencia Nacional de Investigación e Innovació
Random Wheeler Automata
Wheeler automata were introduced in 2017 as a tool to generalize existing
indexing and compression techniques based on the Burrows-Wheeler transform.
Intuitively, an automaton is said to be Wheeler if there exists a total order
on its states reflecting the co-lexicographic order of the strings labeling the
automaton's paths; this property makes it possible to represent the automaton's
topology in a constant number of bits per transition, as well as efficiently
solving pattern matching queries on its accepted regular language. After their
introduction, Wheeler automata have been the subject of a prolific line of
research, both from the algorithmic and language-theoretic points of view. A
recurring issue faced in these studies is the lack of large datasets of Wheeler
automata on which the developed algorithms and theories could be tested. One
possible way to overcome this issue is to generate random Wheeler automata.
Motivated by this observation, in this paper we initiate the theoretical study
of random Wheeler automata, focusing on the deterministic case (Wheeler DFAs --
WDFAs). We start by extending the Erd\H{o}s-R\'enyi random graph model to
WDFAs, and proceed by providing an algorithm generating uniform WDFAs according
to this model. Our algorithm generates a uniform WDFA with states,
transitions, and alphabet's cardinality in expected time
( worst-case time w.h.p.) and constant working space for all
alphabets of size . As a by-product, we also give formulas
for the number of distinct WDFAs and obtain that bits are necessary and sufficient to encode a WDFA with states and
alphabet of size , up to an additive term. We present an
implementation of our algorithm and show that it is extremely fast in practice,
with a throughput of over 8 million transitions per second.Comment: 19 pages, 3 figure
A quadratic algorithm for road coloring
The Road Coloring Theorem states that every aperiodic directed graph with
constant out-degree has a synchronized coloring. This theorem had been
conjectured during many years as the Road Coloring Problem before being settled
by A. Trahtman. Trahtman's proof leads to an algorithm that finds a
synchronized labeling with a cubic worst-case time complexity. We show a
variant of his construction with a worst-case complexity which is quadratic in
time and linear in space. We also extend the Road Coloring Theorem to the
periodic case