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Reducing (to) the Ranks: Efficient Rank-based Büchi Automata Complementation (Technical Report) [article]

Vojtěch Havlena, Ondřej Lengál
2020 arXiv   pre-print
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

Vojtěch Havlena, Ondřej Lengál, Serge Haddad, Daniele Varacca
2021
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]

Hrishikesh Karmarkar, Supratik Chakraborty
2009 Lecture Notes in Computer Science  
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]

Filip Murlak
2008 arXiv   pre-print
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

Filip Murlak, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
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

Laurent Doyen, Jean-François Raskin, Orna Grumberg
2009 Logical Methods in Computer Science  
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]

Seth Fogarty, Moshe Y. Vardi
2010 Lecture Notes in Computer Science  
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]

Sankar Gurumurthy, Orna Kupferman, Fabio Somenzi, Moshe Y. Vardi
2003 Lecture Notes in Computer Science  
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

Sven Schewe, Marc Herbstritt
2009 Symposium on Theoretical Aspects of Computer Science  
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

Udi Boker, Karoliina Lehtinen, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
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]

Sven Schewe
2009 arXiv   pre-print
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]

Seth Fogarty, Moshe Y. Vardi
2009 Lecture Notes in Computer Science  
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]

Ming-Hsien Tsai, Seth Fogarty, Moshe Y. Vardi, Yih-Kuen Tsay
2011 Lecture Notes in Computer Science  
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]

Shoham Ben-David, Orna Kupferman
2013 Lecture Notes in Computer Science  
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

Ming-Hsien Tsai, Seth Fogarty, Moshe Vardi, Yih-Kuen Tsay, Pierre Wolper
2014 Logical Methods in Computer Science  
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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