Practical Applications of the Alternating Cycle Decomposition

Casares, Antonio; Duret-Lutz, Alexandre; Meyer, Philipp J.; Renkin, Florian; Sickert, Salomon

doi:10.1007/978-3-030-99527-0_6

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…Translation to Deterministic Parity Automata (DPAs). We note that there is an optimal translation from a DRA to a DPA described in [7], implemented in Spot via the function acd transform [8].…”

Section: Corollary 1 (1) Given a Weak Büchi Automatonmentioning

confidence: 99%

“…To make the comparison fair, we let all tools generate DPAs, so we used the command autfilt --deterministic --parity=min\ even -F file.hoa to call Spot and owl nbadet -i file.hoa to call Owl. Recall that we use the function acd transform [8] from Spot for obtaining DPAs from our DRAs. The tools above also implement optimizations for reducing the size of the output DPA, like simulation and state merging [29], or stutter invariance [22] (except for Owl); we use the default settings for all tools.…”

Section: Empirical Evaluationmentioning

confidence: 99%

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Divide-and-Conquer Determinization of Büchi Automata Based on SCC Decomposition

Turrini

Feng

et al. 2022

Computer Aided Verification

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The determinization of a nondeterministic Büchi automaton (NBA) is a fundamental construction of automata theory, with applications to probabilistic verification and reactive synthesis. The standard determinization constructions, such as the ones based on the Safra-Piterman’s approach, work on the whole NBA. In this work we propose a divide-and-conquer determinization approach. To this end, we first classify the strongly connected components (SCCs) of the given NBA as inherently weak, deterministic accepting, and nondeterministic accepting. We then present how to determinize each type of SCC independently from the others; this results in an easier handling of the determinization algorithm that takes advantage of the structure of that SCC. Once all SCCs have been determinized, we show how to compose them so to obtain the final equivalent deterministic Emerson-Lei automaton, which can be converted into a deterministic Rabin automaton without blow-up of states and transitions. We implement our algorithm in our tool COLA and empirically evaluate COLA with the state-of-the-art tools Spot and Owl on a large set of benchmarks from the literature. The experimental results show that our prototype COLA outperforms Spot and Owl regarding the number of states and transitions.

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Section: Corollary 1 (1) Given a Weak Büchi Automatonmentioning

confidence: 99%

Section: Empirical Evaluationmentioning

confidence: 99%

Divide-and-Conquer Determinization of Büchi Automata Based on SCC Decomposition

Turrini

Feng

et al. 2022

Computer Aided Verification

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“…This was ultimately fixed by developing a generic emptiness check [6]. Additionally the support for arbitrary acceptance conditions has allowed us to implement many useful algorithms; the most recent being the Alternating Cycle Decomposition [15,16] a powerful data structure with many applications (conversion to parity acceptance, degeneralization, typeness checks...) 3 .…”

Section: Büchimentioning

confidence: 99%

“…Support for transition-based Büchi. Zielonka Trees and Alternating Cycle Decomposition [15,16] studying better algorithms [e.g., 33,32,25,18], but we also see some new applications built on top of ω-automata algorithms from Spot [e.g., 12,13].…”

Section: 8mentioning

confidence: 99%

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

Duret-Lutz¹,

Renault²,

Colange³

et al. 2022

Preprint

Self Cite

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Spot is a C ++ 17 library for LTL and 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 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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“…The third result shows that, on top of the central role it plays in the work of Manna and Pnueli, normalization leads to novel algorithms for questions in the theory of LTL that continue to be investigated today (see e.g. [3,4,9,10,15,16]). In particular, our determinization algorithm based on normalization has already become part of the O library for -atomata [17] and in the S synthesis tool [27].…”

Section: Introductionmentioning

confidence: 99%

A Unified Translation of Linear Temporal Logic to ω-Automata

Esparza

Křetínský

Sickert

2020

J. ACM

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We present a unified translation of linear temporal logic (LTL) formulas into deterministic Rabin automata (DRA), limit-deterministic Büchi automata (LDBA), and nondeterministic Büchi automata (NBA). The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive Boolean combination of languages that can be translated into ω-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed. We further give evidence that this theoretical clean and compositional approach does not lead to large automata per se and in fact in the case of DRAs yields significantly smaller automata compared to the previously known approach using determinisation of NBAs. CCS Concepts: • Theory of computation → Automata over infinite objects; Modal and temporal logics;

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Practical Applications of the Alternating Cycle Decomposition

Cited by 9 publications

References 26 publications

Divide-and-Conquer Determinization of Büchi Automata Based on SCC Decomposition

Divide-and-Conquer Determinization of Büchi Automata Based on SCC Decomposition

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

A Unified Translation of Linear Temporal Logic to ω-Automata

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