Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
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01 Jan 2009TL;DR: This paper defines a class of Constrained Probabilistic Automata with a new accepting condition on runs and proves that the emptiness problem for the language of a constrained probabilistic Buchi automaton with the probable semantics is decidable.
Abstract: In a context of $\omega$-regular specifications for infinite execution
sequences, the classical B\"uchi condition, or repeated liveness
condition, asks that an accepting state is visited infinitely often. In
this paper, we show that in a probabilistic context it is relevant to
strengthen this infinitely often condition. An execution path is now
accepting if the \emph{proportion} of time spent on an accepting state
does not go to zero as the length of the path goes to infinity. We
introduce associated notions of recurrence and transience for
non-homogeneous finite Markov chains and study the computational
complexity of the associated problems. As Probabilistic B\"uchi Automata
(PBA) have been an attempt to generalize B\"uchi automata to a
probabilistic context, we define a class of Constrained Probabilistic
Automata with our new accepting condition on runs. The accepted language
is defined by the requirement that the measure of the set of accepting
runs is positive (probable semantics) or equals 1 (almost-sure
semantics). In contrast to the PBA case, we prove that
the emptiness problem for the language of a constrained probabilistic
B\"uchi automaton with the probable semantics is decidable.
17 citations
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16 Sep 2008TL;DR: Two formalisms for representing regular languages are considered: constant height pushdown automata and straight line programs for regular expressions, and it is constructively proved that their sizes are polynomially related.
Abstract: We consider two formalisms for representing regular languages: constant height pushdown automata and straight line programs for regular expressions. We constructively prove that their sizes are polynomially related. Comparing them with the sizes of finite state automata and regular expressions, we obtain optimal exponential and double exponential gaps, i.e., a more concise representation of regular languages.
17 citations
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22 Aug 1995TL;DR: It is shown that emptiness is decidable for three-way two-dimensional nondeterministic finite automata as well as the universe problem for the corresponding class of deterministic automata.
Abstract: We show that emptiness is decidable for three-way two-dimensional nondeterministic finite automata as well as the universe problem for the corresponding class of deterministic automata. Emptiness is undecidable for three-way (and even two-way) two-dimensional alternating finite automata over a single-letter alphabet. Consequently inclusion, equivalence, and disjointness for these automata are undecidable properties.
17 citations
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01 Aug 1977
TL;DR: The consequences of adding a new teacher to an existing n-teacher set as it affects the choice of a switching strategy for a specific automaton structure are concentrated on.
Abstract: The concept of an automaton operating in a multi-teacher environment is introduced, and several interesting questions that arise in this context are examined. In particular, we concentrate on the consequences of adding a new teacher to an existing n-teacher set as it affects the choice of a switching strategy. The effect of this choice on expediency and speed of convergence is presented for a specific automaton structure.
17 citations
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TL;DR: This work considers several subclasses of automata: aperiodic, D- trivial, monotonic, partially Monotonic automata and automata with a zero state, which study the computational complexity of the following problems: Does there exist a reset word for a given automaton?
Abstract: A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, D- trivial, monotonic, partially monotonic automata and automata with a zero state. For these subclasses we study the computational complexity of the following problems. Does there exist a reset word for a given automaton? Does there exist a reset word of given length for a given automaton? What is the length of the shortest reset word for a given automaton? Moreover, we consider complexity of the same problems for compressing words.
17 citations