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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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Proceedings ArticleDOI
06 Jul 2015
TL;DR: The finite version of the problem is solved, and the hardness of the infinite version is shown, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set.
Abstract: The target discounted-sum problem is the following: Given a rational discount factor 0 < a#x03BB; < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence a#x03C9; a#x2208;(a, b)* or a#x03C9; a#x2208;(a, b)a#x03C9;, such that a#x3A3;|a#x03C9;| i=0 a#x03C9;(i)a#x03BB;i equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: a#x03B2;-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that a#x03BB; a#x03BB; 1/2 or a#x03BB; = 1/n, for every n a#x2208; N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata.

25 citations

Book ChapterDOI
08 Sep 2003
TL;DR: In this article, it was shown that the construction of team automata according to certain natural types of synchronization guarantees compositionality, and the conditions under which such automata satisfy compositionality were investigated.
Abstract: A team automaton is said to satisfy compositionality if its behaviour can be described in terms of the behaviour of its constituting component automata. As an initial investigation of the conditions under which team automata satisfy compositionality, we study their computations and behaviour in relation to those of their constituting component automata. We show that the construction of team automata according to certain natural types of synchronization guarantees compositionality.

25 citations

Journal ArticleDOI
TL;DR: It is proved that there is an infinite sequence of distinct integers n, languages L"n, and quantum finite automata with mixed states with 5n states recognizing language L"N with probability 34, while any deterministic finite automaton recognizing L" n needs at least e^O^(^n^l^n ^n^n*) states.

25 citations

Journal ArticleDOI
TL;DR: This work introduces session automata, an automata model to process data words, i.e., words over an infinite alphabet, which are well suited for modeling protocols in which sessions using fresh values are of major interest, like in security protocols or ad-hoc networks.
Abstract: We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using fresh values are of major interest, like in security protocols or ad-hoc networks. Session automata have an expressiveness partly extending, partly reducing that of classical register automata. We show that, unlike register automata and their various extensions, session automata are robust: They (i) are closed under intersection, union, and (resource-sensitive) complementation, (ii) admit a symbolic regular representation, (iii) have a decidable inclusion problem (unlike register automata), and (iv) enjoy logical characterizations. Using these results, we establish a learning algorithm to infer session automata through membership and equivalence queries.

25 citations

27 Oct 2006
TL;DR: The emptiness of generalized nondeterministic automata is shown to be testable without giving up generalized transition-based acceptance by using a new variant of the well-known nested depth-first search algorithm with improved worst-case resource requirements.
Abstract: Automata theory provides powerful tools for designing and implementing decision procedures for temporal logics and their applications to the automatic verification of systems against their logical specifications. Implementing these decision procedures by making use of automata built from the systems and their specifications with translation procedures is challenging in practice due to the tendency of the automata to grow easily unmanageably large as the size of the systems or the logical specifications increases. This thesis develops the theory of translating propositional linear time temporal logic (LTL) into nondeterministic automata via self-loop alternating automata. Unlike nondeterministic automata, self-loop alternating automata are expressively equivalent to LTL and allow a conceptually simple translation of LTL specifications into automata using a set of rules for building automata incrementally from smaller components. The use of generalized transition-based acceptance for automata throughout all constructions gives rise to new optimized translation rules and facilitates designing heuristics for the minimization of automata by making use of language containment tests combined with structural analysis of automata. The generalized definition also supports the translation of self-loop alternating automata into nondeterministic automata by essentially applying the standard subset construction; this construction can be further simplified and optimized when working with automata built from LTL formulas. The translation rules can also be used to identify a syntactic subclass of LTL for which the exponential increase caused by the subset construction in the number of states of the automaton can always be avoided; consequently, the satisfiability problem for this subclass, which is shown to extend related subclasses known from the literature, is NP-complete. Additionally, the emptiness of generalized nondeterministic automata is shown to be testable without giving up generalized transition-based acceptance by using a new variant of the well-known nested depth-first search algorithmwith improved worst-case resource requirements.

25 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202219
20201
20191
20185
201748