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Reducing (to) the Ranks: Efficient Rank-based Büchi Automata Complementation (Technical Report)
[article]
2020
arXiv
pre-print
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This paper provides several optimizations of the rank-based approach for complementing Büchi automata. ...
Our evaluation on a large benchmark shows that the optimizations indeed significantly help the rank-based approach and that, in a large number of cases, the obtained complement is the smallest from those ...
Complementing Büchi Automata In this section we describe the basic rank-based complementation algorithm presented by Schewe in [13] and some results related to runs with the minimal ranking. ...
arXiv:2010.07834v2
fatcat:w2xsa7sqmncafhwpfxxyqyfa5y
Reducing (To) the Ranks: Efficient Rank-Based Büchi Automata Complementation
2021
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This paper provides several optimizations of the rank-based approach for complementing Büchi automata. ...
produced by state-of-the-art tools for Büchi complementation. ...
Complementing Büchi Automata In this section we first describe the basic rank-based complementation algorithm proposed by Kupferman and Vardi in [22] and then its optimization presented by Schewe in ...
doi:10.4230/lipics.concur.2021.2
fatcat:6uvgm4xqjzdc5bzdmg2lmqd56u
On Minimal Odd Rankings for Büchi Complementation
[chapter]
2009
Lecture Notes in Computer Science
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We exploit this to reduce the size of the complement Büchi automaton by eliminating all redundant slices. ...
This allows us to determine minimally inessential ranks and redundant slices in ranking-based complementation constructions. ...
(ii) We show how to reduce the size of the complement automaton by efficiently identifying and removing redundant slices without language containment checks. ...
doi:10.1007/978-3-642-04761-9_18
fatcat:jnlispbtsbhvjivknlr2fnycjm
Weak index versus Borel rank
[article]
2008
arXiv
pre-print
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The algorithm works within the time of solving the emptiness problem. ...
We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. ...
Acknowledgments The author thanks Damian Niwiński for reading carefully a preliminary version of this paper and the anonymous referees for their helpful comments. ...
arXiv:0802.2842v1
fatcat:apnjrdnxnferfntaa46qpeuwhe
Weak index versus Borel rank
2008
Symposium on Theoretical Aspects of Computer Science
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The algorithm works within the time of solving the emptiness problem. ...
We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. ...
Acknowledgments The author thanks Damian Niwiński for reading carefully a preliminary version of this paper and the anonymous referees for their helpful comments. ...
doi:10.4230/lipics.stacs.2008.1318
dblp:conf/stacs/Murlak08
fatcat:ylqhcwb37vfmll4ekfbm7mdeqi
Antichains for the Automata-Based Approach to Model-Checking
2009
Logical Methods in Computer Science
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To obtain those algorithms, we establish the existence of simulation pre-orders that can be exploited to efficiently evaluate fixed points on the automata defined during the complementation step (that ...
We propose and evaluate antichain algorithms to solve the universality and language inclusion problems for nondeterministic Buechi automata, and the emptiness problem for alternating Buechi automata. ...
Our approach is based on fixed points computation and the existence of simulation relations for the (exponential) constructions used in complementation of Büchi automata. ...
doi:10.2168/lmcs-5(1:5)2009
fatcat:pcmazfmsqraczl4zlcohxrohwm
Efficient Büchi Universality Checking
[chapter]
2010
Lecture Notes in Computer Science
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The complementation of Büchi automata, required for checking automata universality, remains one of the outstanding automata-theoretic challenges in formal verification. ...
We then empirically compare the Ramsey-based tool to the rank-based tool of Doyen and Raskin over a terrain of random Büchi universality problems. ...
The Lee, Jones, and Ben-Amram (LJB) algorithm was provided as a practical alternative to reducing the SCT problems to Büchi containment, but bears a striking resemblance to the 1987 Ramsey-based complementation ...
doi:10.1007/978-3-642-12002-2_17
fatcat:7ntaqt3byfgo3exa65u5l2zy6i
On Complementing Nondeterministic Büchi Automata
[chapter]
2003
Lecture Notes in Computer Science
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Several optimal algorithms have been proposed for the complementation of nondeterministic Büchi word automata. ...
Due to the intricacy of the problem and the exponential blow-up that complementation involves, these algorithms have never been used in practice, even though an effective complementation construction would ...
Doron Bustan called our attention to the improved bound on the rank of a UCW. ...
doi:10.1007/978-3-540-39724-3_10
fatcat:3ybtjlyehndelkybkjgn4y6mny
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. ...
lower bound to a simple exponent (of (6e) n for Büchi automata with n states) took four decades. ...
The improved cut-point construction is inspired by the efficient translation from generalized to ordinary Büchi automata. ...
doi:10.4230/lipics.stacs.2009.1854
dblp:conf/stacs/Schewe09
fatcat:3f254ssspfbthh3z6ty6siawrm
On the Way to Alternating Weak Automata
2018
Foundations of Software Technology and Theoretical Computer Science
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Along the way, we present a family of game languages, strict for the levels of the weak hierarchy of tree automata, which corresponds to a weak version of the canonical game languages known to be strict ...
Universal co-Büchi tree automata, a special case of alternating parity tree automata, can be exponentially more concise than alternating weak automata. ...
Weak definability is decidable for tree languages recognised by alternating Büchi automata, as was first shown for ranked trees by Colcombet et al [6] via reduction to cost automata. ...
doi:10.4230/lipics.fsttcs.2018.21
dblp:conf/fsttcs/BokerL18
fatcat:v2bviizkqfcbtj7chq5j6ey7de
Büchi complementation made tight
[article]
2009
arXiv
pre-print
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While optimal complementation techniques for finite automata are simple - it suffices to determinize them using a simple subset construction and to dualize the acceptance condition of the resulting automaton ...
The precise complexity of complementing B\"uchi automata is an intriguing and long standing problem. ...
The improved cut-point construction is inspired by the efficient translation from generalized to ordinary Büchi automata. ...
arXiv:0902.2152v1
fatcat:tpruggcw6jaxtdp66vptyt6ybm
Büchi Complementation and Size-Change Termination
[chapter]
2009
Lecture Notes in Computer Science
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In 2001 Lee et al. presented the size-change termination (SCT) problem, along with both a reduction to Büchi automata and a Ramsey-based algorithm. ...
This algorithm strongly resembles the initial complementation constructions for Büchi automata. ...
In 2001, Kupferman and Vardi employed a rank-based analysis of Büchi automata to simplify complementation [9] . ...
doi:10.1007/978-3-642-00768-2_2
fatcat:2w2tsepxwzdetef3rug2loxen4
State of Büchi Complementation
[chapter]
2011
Lecture Notes in Computer Science
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Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and slice-based approaches. ...
Büchi complementation has been studied for five decades since the formalism was introduced in 1960. ...
In the improved construction, referred to as Ramsey in this paper, the complement is obtained by composing certain automata among a set of Büchi automata which form a partition of Σ ω , based on Ramsey's ...
doi:10.1007/978-3-642-18098-9_28
fatcat:kdkafdjv2faz7gli26g63el47u
A Framework for Ranking Vacuity Results
[chapter]
2013
Lecture Notes in Computer Science
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From a practical point of view, we propose an efficient algorithm for estimating the probability of LTL formulas, and argue that ranking vacuity results according to our probability-based criteria corresponds ...
We suggest and study such a framework, based on the probability of the mutated specification to hold in a random computation. ...
The language of A, denoted L(A), is the set of words that A accepts. We use NBW and DBW to abbreviate nondeterministic and deterministic Büchi automata, respectively. ...
doi:10.1007/978-3-319-02444-8_12
fatcat:rgdnpuukhjd3rfmhufzkcv5diy
State of Büchi Complementation
2014
Logical Methods in Computer Science
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Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and slice-based approaches. ...
Complementation of B\"uchi automata has been studied for over five decades since the formalism was introduced in 1960. ...
Approaches to Complementation We review the four approaches to the complementation of Büchi automata in this section. ...
doi:10.2168/lmcs-10(4:13)2014
fatcat:4scx4mmybnflrmerfpg5opowoq
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