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On the complementation of Büchi automata
1986
Theoretical Computer Science
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Given a Biichi automaton with n states, we propose an elementary construction of a Biichi automaton with O(16 "2) states which recognizes the complement of the o,-language recognized by the first one. ...
Introduction Biichi [1] has shown that the class of ~-languages recognized by finite automata is closed under complementation. ...
The complementation of Biichi automata 97
Lemma 2 ( 2 [6] ).Let f: A +-, S be a morphism, e ~ S an idempotent, and M a subset of S for which every element m ~ M satisfies me = m. ...
doi:10.1016/0304-3975(86)90136-2
fatcat:5r33dztelrbythn2s4j7thicfi
On the complementation of asynchronous cellular Büchi automata
1996
Theoretical Computer Science
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This provides a solution to the problem of direct determinization for automata with distributed control for languages of finite traces. ...
We use the subset automaton construction and apply Klarlund's progress measure technique in order to complement non-deterministic asynchronous cellular Biichi automata for infinite traces. ...
I also thank the referees from ICALP'93 and especially from Theoretical Computer Science for the comments which led to an improved presentation of this paper. ...
doi:10.1016/s0304-3975(96)00117-x
fatcat:74ywotnkjffs3fyybgocud4dda
Büchi Store: An Open Repository of Büchi Automata
[chapter]
2011
Lecture Notes in Computer Science
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We introduce the Büchi Store, an open repository of Büchi automata for model-checking practice, research, and education. ...
Such a collection of Büchi automata is also useful as a benchmark for evaluating complementation or translation algorithms and as examples for studying Büchi automata and temporal logic. ...
The table below shows a comparison of some of the complementation algorithms for four selected Büchi automata (identified by equivalent temporal formulae). ...
doi:10.1007/978-3-642-19835-9_23
fatcat:c4iwj7becvbg3nsnztlkfqsq4a
Omega Automata and its Classes
2018
Current Science
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A variety of conditions are used to represent the set of accepting strings in ω-automata. This paper summarizes various types of ω-automata, their transition functions and accepting conditions. ...
In addition, this paper also summarizes the applicability of omega automata in various interdisciplinary fields. ...
Büchi Automata (RQ 2) Julius Richard Büchi 21 proposed in 1962 the concept of Büchi automata which works on ω-strings. ...
doi:10.18520/cs/v115/i11/2042-2051
fatcat:byu5hbxpnbaclbp2rkx3qa6uhm
GOAL for Games, Omega-Automata, and Logics
[chapter]
2013
Lecture Notes in Computer Science
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The enhancements provide more automata conversion, complementation, simplification, and testing algorithms, translation of full QPTL formulae, and better automata navigation with more layout algorithms ...
This paper introduces the second generation of GOAL, which is a graphical interactive tool for games, ω-automata, and logics. ...
We thank Jinn-Shu Chang and Yi-Wen Chang for helping with the implementations of some algorithms. ...
doi:10.1007/978-3-642-39799-8_62
fatcat:4xi3csp63fgbhn736yrrhzc3we
Reasoning About Co–Büchi Tree Automata
[chapter]
2005
Lecture Notes in Computer Science
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We consider co-Büchi tree automata along with both alternating and generalized paradigms, as a characterization of the class of languages whose complement is accepted by generalized Büchi tree automata ...
For the class of languages whose complement is accepted by deterministic generalized Büchi tree automata, we get better complexity bounds: we give a characterization of this class in terms of generalized ...
On the other hand, generalized Büchi and generalized co-Büchi tree automata are not closed under language complementation, while Rabin and Muller tree automata are [Tho90] . ...
doi:10.1007/978-3-540-31862-0_37
fatcat:xyygpeb3dvgbdawjkest4alnp4
Weak alternating automata are not that weak
2001
ACM Transactions on Computational Logic
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Beyond the independent interest of such a translation, it gives rise to a simple complementation algorithm for nondeterministic Büchi automata. ...
In this paper we describe a quadratic translation, which circumvents the need for determinization, of Büchi and co-Büchi alternating automata to weak alternating automata. ...
Acknowledgment We thank Nils Klarlund for clarifying the relation between [Kla91] and this work. ...
doi:10.1145/377978.377993
fatcat:ksuj4haclngmjgesweqlvbk7sy
Learn with SAT to Minimize Büchi Automata
2012
Electronic Proceedings in Theoretical Computer Science
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We successfully ran the minimization on over ten thousand automata with mostly up to ten states, including the complements of all possible automata with two states and alphabet size three and discuss results ...
Failure of equivalence yields new positive or negative examples. Our method proved successful on complete samplings of small automata and of quite some examples of bigger automata. ...
We present here the first procedure that computes for a given Büchi automaton an equivalent one of minimal size among all Büchi automata equivalent to the given one. ...
doi:10.4204/eptcs.96.6
fatcat:zz4a6den4rhlfpcon4mzio2frm
Büchi Complementation Made Tight
2009
Symposium on Theoretical Aspects of Computer Science
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The precise complexity of complementing Büchi automata is an intriguing and long standing problem. ...
Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. ...
The first complementation algorithm dates back to the introduction of Büchi automata in 1962. ...
doi:10.4230/lipics.stacs.2009.1854
dblp:conf/stacs/Schewe09
fatcat:3f254ssspfbthh3z6ty6siawrm
Büchi complementation made tight
[article]
2009
arXiv
pre-print
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Also, the upper bound on the size of the complement automaton is not linear in the bound of its state space. ...
The precise complexity of complementing B\"uchi automata is an intriguing and long standing problem. ...
The first complementation algorithm dates back to the introduction of Büchi automata in 1962. ...
arXiv:0902.2152v1
fatcat:tpruggcw6jaxtdp66vptyt6ybm
Partially Ordered Two-Way Büchi Automata
[chapter]
2011
Lecture Notes in Computer Science
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A small model property yields coNP-completeness of the emptiness problem and the inclusion problem for deterministic partially ordered two-way B\"uchi automata. ...
We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. ...
Theorem 2 2 The class of languages recognized by deterministic po2-Büchi automata is effectively closed under complementation, union, and intersection.Proof: Effective closure under complementation of ...
doi:10.1007/978-3-642-18098-9_20
fatcat:zcncfcrr4fezxaazpoamaae6ue
PARTIALLY ORDERED TWO-WAY BÜCHI AUTOMATA
2011
International Journal of Foundations of Computer Science
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As a byproduct of our results, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations. ...
In addition, we have coNP-completeness results for the emptiness problem and the inclusion problem over deterministic partially ordered two-way Büchi automata. ...
Theorem 2 2 The class of languages recognized by deterministic po2-Büchi automata is effectively closed under complementation, union, and intersection.Proof: Effective closure under complementation of ...
doi:10.1142/s0129054111009082
fatcat:7sndiflwirafjd7me7tz4ieqvm
Seminator 2 Can Complement Generalized Büchi Automata via Improved Semi-determinization
[chapter]
2020
Lecture Notes in Computer Science
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We present the second generation of the tool Seminator that transforms transition-based generalized Büchi automata (TGBAs) into equivalent semi-deterministic automata. ...
In connection with the state-of-the-art LTL to TGBAs translator Spot, Seminator 2 produces smaller (on average) semi-deterministic automata than the direct LTL to semi-deterministic automata translator ...
Comparison of tools complementing Büchi automata, using the same conventions as In the (semi-)deterministic category, the automaton produced by ltl2tgba and passed to both versions of Seminator is already ...
doi:10.1007/978-3-030-53291-8_2
fatcat:5cdx2umrffhrrpgvx7ysvhj5d4
How Deterministic are Good-For-Games Automata?
[article]
2017
arXiv
pre-print
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Specifically, considering automata complementation, we show that GFG automata lean toward nondeterministic ones, admitting an exponential state blow-up in the complementation of a Streett automaton into ...
In particular, when Rabin or Streett GFG automata have equivalent Buchi or co-Buchi GFG automata, respectively, then such equivalent automata can be defined on a substructure of the original automata. ...
with deterministic automata, while the complementation of a co-Büchi automaton into a Büchi automaton as well as the complementation of a Streett automaton into a Rabin automaton is exponential, as opposed ...
arXiv:1710.04115v1
fatcat:y4ycowj7lvf7fjrmnxyz5zsnau
Can Nondeterminism Help Complementation?
2012
Electronic Proceedings in Theoretical Computer Science
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In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Theta(2^n) where n is the state size. ...
The same similarity between determinization and complementation was found for Buchi automata, where both operations were shown to have 2^\Theta(n lg n) state complexity. ...
Büchi automata on conventional alphabets of fixed size. ...
doi:10.4204/eptcs.96.5
fatcat:lhuw2lyr45ae5ih52wx4nni77u
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