Towards a Spatial Model Checker on GPU

Bussi, Laura; Ciancia, Vincenzo; Gadducci, Fabio

doi:10.1007/978-3-030-78089-0_12

Cited by 16 publications

(3 citation statements)

References 20 publications

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“…Implementation-wise, GPU computing could provide a computational boost to PolyLog-icA. See [BCG21] for a GPU implementation of the parent tool VoxLogicA. Finally, a user interface could be useful to explore large datasets, and to better visualise the interpretation of logic formulas, possibly exploiting results in [BM Ö19] for validation.…”

Section: Discussionmentioning

confidence: 99%

Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2022

Logical Methods in Computer Science

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Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.

show abstract

Section: Discussionmentioning

confidence: 99%

Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2022

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…Implementation-wise, GPU computing could provide a computational boost to PolyLogicA. See [17] for a GPU implementation of the parent tool VoxLogicA. Finally, a user interface could be useful to explore large datasets, and to better visualize the interpretation of logic formulas, possibly exploiting results in [15] for validation.…”

Section: Discussionmentioning

confidence: 99%

Geometric Model Checking of Continuous Space

Bezhanishvili¹,

Ciancia²,

Gabelaia³

et al. 2021

Preprint

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Topological Spatial Model Checking is a recent paradigm that combines Model Checking with the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. In particular, the spatial model checker VoxLogicA, that uses an extended version of SLCS, has been used successfully in the domain of medical imaging. However, SLCS is not restricted to discrete space. Following a recently developed geometric semantics of Modal Logic, we show that it is possible to assign an interpretation to SLCS in continuous space, admitting a model checking procedure, by resorting to models based on polyhedra. In medical imaging such representations of space are increasingly relevant, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We demonstrate feasibility of our approach via a new tool, PolyLogicA, aimed at efficient verification of SLCS formulas on polyhedra, while inheriting some well-established optimization techniques already adopted in VoxLogicA. Finally, we cater for a geometric definition of bisimilarity, proving that it characterises logical equivalence.

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“…In the last decade, GPUs have been successfully applied to accelerate various computations relevant for model checking, such as probability computations for probabilistic model checking (Bošnački et al, 2011;Wijs and Bošnački, 2012;Khan et al, 2021), counter-example construction (Wu et al, 2014), state space decomposition (Wijs et al, 2016a), parameter synthesis for stochastic systems ( Češka et al, 2016), and SAT solving (Youness et al, 2015(Youness et al, , 2020Osama et al, 2018Osama et al, , 2023Osama andWijs, 2019a,b, 2021;Prevot et al, 2021;Osama, 2022). VOXLOGICA-GPU applies model checking to analyse (medical) images (Bussi et al, 2021). Model checking (Baier and Katoen, 2008;Clarke et al, 2018) is a technique to exhaustively check whether a formal description of a soft-and/or hardware system adheres to a specification; the latter is typically given in the form of a number of temporal logic formulae.…”

Section: Introductionmentioning

confidence: 99%

The fast and the capacious: memory-efficient multi-GPU accelerated explicit state space exploration with GPUexplore 3.0

Wijs,

Osama

2024

Front. High Perform. Comput.

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The GPU acceleration of explicit state space exploration, for explicit-state model checking, has been the subject of previous research, but to date, the tools have been limited in their applicability and in their practical use. Considering this research, to our knowledge, we are the first to use a novel tree database for GPUs. This novel tree database allows high-performant, memory-efficient storage of states in the form of binary trees. Besides the tree compression this enables, we also propose two new hashing schemes, compact-cuckoo and compact multiple-functions. These schemes enable the use of Cleary compression to compactly store tree roots. Besides an in-depth discussion of the tree database algorithms, the input language and workflow of our tool, called GPUexplore 3.0, are presented. Finally, we explain how the algorithms can be extended to exploit multiple GPUs that reside on the same machine. Experiments show single-GPU processing speeds of up to 144 million states per second compared to 20 million states achieved by 32-core LTSmin. In the multi-GPU setting, workload and storage distributions are optimal, and, frequently, performance is even positively impacted when the number of GPUs is increased. Overall, a logarithmic acceleration up to 1.9× was achieved with four GPUs, compared to what was achieved with one and two GPUs. We believe that a linear speedup can be easily accomplished with faster P2P communications between the GPUs.

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Towards a Spatial Model Checker on GPU

Cited by 16 publications

References 20 publications

Geometric Model Checking of Continuous Space

Geometric Model Checking of Continuous Space

Geometric Model Checking of Continuous Space

The fast and the capacious: memory-efficient multi-GPU accelerated explicit state space exploration with GPUexplore 3.0

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