Complementing Büchi Automata with Ranker

Havlena, Vojtěch; Lengál, Ondřej; Šmahlíková, Barbora

doi:10.1007/978-3-031-13188-2_10

Cited by 5 publications

(10 citation statements)

References 40 publications

(54 reference statements)

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“…Sec. 4.1), while for partition blocks with only DACs, one can use an algorithm with the state complexity O (4 𝑛 ) based on an adaptation of the NCSB construction [5,6,11,25] for SDBAs (cf. Sec.…”

Section: A Modular Complementation Algorithmmentioning

confidence: 99%

“…Let 𝑃 be a partition block of A such that A 𝑃 |= 𝜑 CSB . Our approach is based on the NCSB family of algorithms [5,6,11,25] for complementing SDBAs, in particular the NCSB-MaxRank construction [25]. The algorithm utilizes the fact that runs in DACs are deterministic, i.e., they do not branch into new runs.…”

Section: Complementation Of Deterministic Accepting Componentsmentioning

confidence: 99%

“…It is worth noting that when the given partition block 𝑃 contains all DACs of A, we can still use the construction above, while the construction in [25] only works on SDBAs. Example 1.…”

Section: Lemma 2 the Partial Algorithm Csb Is Correctmentioning

confidence: 99%

“…Complementation of SDBAs using one from the family of the so-called NCSB algorithms [5,6,11,25] has the worst-case complexity O (4 𝑛 ) (and usually also works much better in practice than general BA complementation procedures). Similarly, there are efficient complementation procedures for other subclasses of BAs, e.g., (i) deterministic BAs (DBAs) can be complemented into BAs with 2𝑛 states [32] (or into co-Büchi automata with 𝑛 + 1 states) or (ii) inherently weak BAs (BAs where in each strongly connected component (SCC), either all cycles are accepting or all cycles are rejecting) can be complemented into DBAs with O (3 𝑛 ) states using the Miyano-Hayashi algorithm [39].…”

Section: Introductionmentioning

confidence: 99%

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Modular Mix-and-Match Complementation of Büchi Automata (Technical Report)

Havlena¹,

Lengál²,

Li³

et al. 2023

Preprint

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Complementation of nondeterministic Büchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of some logics. We build on ideas from a recent work on BA determinization by Li et al. and propose a new modular algorithm for BA complementation. Our algorithm allows to combine several BA complementation procedures together, with one procedure for a subset of the BA's strongly connected components (SCCs). In this way, one can exploit the structure of particular SCCs (such as when they are inherently weak or deterministic) and use more efficient specialized algorithms, regardless of the structure of the whole BA. We give a general framework into which partial complementation procedures can be plugged in, and its instantiation with several algorithms. The framework can, in general, produce a complement with an Emerson-Lei acceptance condition, which can often be more compact. Using the algorithm, we were able to establish an exponentially better new upper bound of O (4 𝑛 ) for complementation of the recently introduced class of elevator automata. We implemented the algorithm in a prototype and performed a comprehensive set of experiments on a large set of benchmarks, showing that our framework complements well the state of the art and that it can serve as a basis for future efficient BA complementation and inclusion checking algorithms.Here, we consider model checking w.r.t. a specification given in some more expressive logic, such as S1S [8], QPTL [47], or HyperLTL [12], rather than LTL [41], where negation is simple.

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Section: A Modular Complementation Algorithmmentioning

confidence: 99%

Section: Complementation Of Deterministic Accepting Componentsmentioning

confidence: 99%

“…It is worth noting that when the given partition block 𝑃 contains all DACs of A, we can still use the construction above, while the construction in [25] only works on SDBAs. Example 1.…”

Section: Lemma 2 the Partial Algorithm Csb Is Correctmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modular Mix-and-Match Complementation of Büchi Automata (Technical Report)

Havlena¹,

Lengál²,

Li³

et al. 2023

Preprint

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show abstract

“…Zielonka Trees and Alternating Cycle Decomposition [15,16] Spot this way), or to use it as a research/development toolbox, since it provides helper tools for generation of random formulas/automata, verification of LTLto-automata translation, simplifications, syntax conversions, etc. Nowadays, the algorithms for ω-automata implemented in Spot are often used as baseline for studying better algorithms [e.g., 18,25,32,33], but we also see some new applications built on top of ω-automata algorithms from Spot [e.g., 12,13].…”

Section: 9mentioning

confidence: 99%

From Spot 2.0 to Spot 2.10: What’s New?

Duret-Lutz

Renault

Colange

et al. 2022

Lecture Notes in Computer Science

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Spot is a C++17 library for LTL and $$\omega $$ ω -automata manipulation, with command-line utilities, and Python bindings. This paper summarizes its evolution over the past six years, since the release of Spot 2.0, which was the first version to support $$\omega $$ ω -automata with arbitrary acceptance conditions, and the last version presented at a conference. Since then, Spot has been extended with several features such as acceptance transformations, alternating automata, games, LTL synthesis, and more. We also shed some lights on the data-structure used to store automata.Artifact:https://zenodo.org/record/6521395.

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