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@@ -17,14 +17,6 @@ Ali, J., Ali, S., Al~Balushi, T., Nadir, Z.: Intrusion detection in industrial
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\url{https://www.mdpi.com/2078-2489/16/10/910} \url{https://www.mdpi.com/2078-2489/16/10/910}
\bibitem{austin2023structureddenoisingdiffusionmodels}
Austin, J., Johnson, D.D., Ho, J., Tarlow, D., van~den Berg, R.: Structured
denoising diffusion models in discrete state-spaces. In: Ranzato, M.,
Beygelzimer, A., Dauphin, Y., Liang, P., Vaughan, J.W. (eds.) Advances in
Neural Information Processing Systems. vol.~34, pp. 17981--17993. Curran
Associates, Inc. (2021),
\url{https://proceedings.neurips.cc/paper_files/paper/2021/file/958c530554f78bcd8e97125b70e6973d-Paper.pdf}
\bibitem{austin2021structured} \bibitem{austin2021structured}
Austin, J., Johnson, D.D., Ho, J., Tarlow, D., van~den Berg, R.: Structured Austin, J., Johnson, D.D., Ho, J., Tarlow, D., van~den Berg, R.: Structured
denoising diffusion models in discrete state-spaces. In: Ranzato, M., denoising diffusion models in discrete state-spaces. In: Ranzato, M.,

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@@ -53,7 +53,7 @@ Early generation of network data oriented towards "realism" mostly remained at t
Diffusion models exhibit good fit along this path: DDPM achieves high-quality sampling and stable optimization through efficient $\epsilon$ parameterization and weighted variational objectives \citep{NEURIPS2020_4c5bcfec}, the SDE perspective unifies score-based and diffusion, providing likelihood evaluation and prediction-correction sampling strategies based on probability flow ODEs \citep{song2021score}. For time series, TimeGrad replaces the constrained output distribution with conditional denoising, capturing high-dimensional correlations at each step \citep{rasul2021autoregressivedenoisingdiffusionmodels}; CSDI explicitly performs conditional diffusion and uses two-dimensional attention to simultaneously leverage temporal and cross-feature dependencies, suitable for conditioning and filling in missing values \citep{tashiro2021csdiconditionalscorebaseddiffusion}; in a more general spatio-temporal structure, DiffSTG generalizes diffusion to spatio-temporal graphs, combining TCN/GCN with denoising U-Net to improve CRPS and inference efficiency in a non-autoregressive manner \citep{wen2024diffstgprobabilisticspatiotemporalgraph}, and PriSTI further enhances conditional features and geographical relationships, maintaining robustness under high missing rates and sensor failures \citep{liu2023pristiconditionaldiffusionframework}; in long sequences and continuous domains, DiffWave verifies that diffusion can also match the quality of strong vocoders under non-autoregressive fast synthesis \citep{kong2021diffwaveversatilediffusionmodel}; studies on cellular communication traffic show that diffusion can recover spatio-temporal patterns and provide uncertainty characterization at the urban scale \citep{11087622}. These results overall point to a conclusion: when the research focus is on "telemetry/high-level features" rather than raw messages, diffusion models provide stable and fine-grained distribution fitting and uncertainty quantification, which is exactly in line with the requirements of ICS telemetry synthesis. Meanwhile, directly entrusting all structures to a "monolithic diffusion" is not advisable: long-range temporal skeletons and fine-grained marginal distributions often have optimization tensions, requiring explicit decoupling in modeling. Diffusion models exhibit good fit along this path: DDPM achieves high-quality sampling and stable optimization through efficient $\epsilon$ parameterization and weighted variational objectives \citep{NEURIPS2020_4c5bcfec}, the SDE perspective unifies score-based and diffusion, providing likelihood evaluation and prediction-correction sampling strategies based on probability flow ODEs \citep{song2021score}. For time series, TimeGrad replaces the constrained output distribution with conditional denoising, capturing high-dimensional correlations at each step \citep{rasul2021autoregressivedenoisingdiffusionmodels}; CSDI explicitly performs conditional diffusion and uses two-dimensional attention to simultaneously leverage temporal and cross-feature dependencies, suitable for conditioning and filling in missing values \citep{tashiro2021csdiconditionalscorebaseddiffusion}; in a more general spatio-temporal structure, DiffSTG generalizes diffusion to spatio-temporal graphs, combining TCN/GCN with denoising U-Net to improve CRPS and inference efficiency in a non-autoregressive manner \citep{wen2024diffstgprobabilisticspatiotemporalgraph}, and PriSTI further enhances conditional features and geographical relationships, maintaining robustness under high missing rates and sensor failures \citep{liu2023pristiconditionaldiffusionframework}; in long sequences and continuous domains, DiffWave verifies that diffusion can also match the quality of strong vocoders under non-autoregressive fast synthesis \citep{kong2021diffwaveversatilediffusionmodel}; studies on cellular communication traffic show that diffusion can recover spatio-temporal patterns and provide uncertainty characterization at the urban scale \citep{11087622}. These results overall point to a conclusion: when the research focus is on "telemetry/high-level features" rather than raw messages, diffusion models provide stable and fine-grained distribution fitting and uncertainty quantification, which is exactly in line with the requirements of ICS telemetry synthesis. Meanwhile, directly entrusting all structures to a "monolithic diffusion" is not advisable: long-range temporal skeletons and fine-grained marginal distributions often have optimization tensions, requiring explicit decoupling in modeling.
Looking further into the mechanism complexity of ICS: its channel types are inherently mixed, containing both continuous process trajectories and discrete supervision/status variables, and discrete channels must be "legal" under operational constraints. The aforementioned progress in time series diffusion has mainly occurred in continuous spaces, but discrete diffusion has also developed systematic methods: D3PM improves sampling quality and likelihood through absorption/masking and structured transitions in discrete state spaces \citep{austin2023structureddenoisingdiffusionmodels}, subsequent masked diffusion provides stable reconstruction on categorical data in a more simplified form \citep{Lin_2020}, multinomial diffusion directly defines diffusion on a finite vocabulary through mechanisms such as argmax flows \citep{hoogeboom2021argmaxflowsmultinomialdiffusion}, and Diffusion-LM demonstrates an effective path for controllable text generation by imposing gradient constraints in continuous latent spaces \citep{li2022diffusionlmimprovescontrollabletext}. From the perspectives of protocols and finite-state machines, coverage-guided fuzz testing emphasizes the criticality of "sequence legality and state coverage" \citep{meng2025aflnetyearslatercoverageguided,godefroid2017learnfuzzmachinelearninginput,she2019neuzzefficientfuzzingneural}, echoing the concept of "legality by construction" in discrete diffusion: preferentially adopting absorption/masking diffusion on discrete channels, supplemented by type-aware conditioning and sampling constraints, to avoid semantic invalidity and marginal distortion caused by post hoc thresholding. Looking further into the mechanism complexity of ICS: its channel types are inherently mixed, containing both continuous process trajectories and discrete supervision/status variables, and discrete channels must be "legal" under operational constraints. The aforementioned progress in time series diffusion has mainly occurred in continuous spaces, but discrete diffusion has also developed systematic methods: D3PM improves sampling quality and likelihood through absorption/masking and structured transitions in discrete state spaces \citep{austin2021structured}, subsequent masked diffusion provides stable reconstruction on categorical data in a more simplified form \citep{Lin_2020}, multinomial diffusion directly defines diffusion on a finite vocabulary through mechanisms such as argmax flows \citep{hoogeboom2021argmaxflowsmultinomialdiffusion}, and Diffusion-LM demonstrates an effective path for controllable text generation by imposing gradient constraints in continuous latent spaces \citep{li2022diffusionlmimprovescontrollabletext}. From the perspectives of protocols and finite-state machines, coverage-guided fuzz testing emphasizes the criticality of "sequence legality and state coverage" \citep{meng2025aflnetyearslatercoverageguided,godefroid2017learnfuzzmachinelearninginput,she2019neuzzefficientfuzzingneural}, echoing the concept of "legality by construction" in discrete diffusion: preferentially adopting absorption/masking diffusion on discrete channels, supplemented by type-aware conditioning and sampling constraints, to avoid semantic invalidity and marginal distortion caused by post hoc thresholding.
From the perspective of high-level synthesis, the temporal structure is equally indispensable: ICS control often involves delay effects, phased operating conditions, and cross-channel coupling, requiring models to be able to characterize low-frequency, long-range dependencies while also overlaying multi-facated fine-grained fluctuations on them. The Transformer series has provided sufficient evidence in long-sequence time series tasks: Transformer-XL breaks through the fixed-length context limitation through a reusable memory mechanism and significantly enhances long-range dependency expression \citep{dai2019transformerxlattentivelanguagemodels}; Informer uses ProbSparse attention and efficient decoding to balance span and efficiency in long-sequence prediction \citep{zhou2021informerefficienttransformerlong}; Autoformer robustly models long-term seasonality and trends through autocorrelation and decomposition mechanisms \citep{wu2022autoformerdecompositiontransformersautocorrelation}; FEDformer further improves long-period prediction performance in frequency domain enhancement and decomposition \citep{zhou2022fedformerfrequencyenhanceddecomposed}; PatchTST enhances the stability and generalization of long-sequence multivariate prediction through local patch-based representation and channel-independent modeling \citep{nie2023patchtst}. Combining our previous positioning of diffusion, this chain of evidence points to a natural division of labor: using attention-based sequence models to first extract stable low-frequency trends/conditions (long-range skeletons), and then allowing diffusion to focus on margins and details in the residual space; meanwhile, discrete masking/absorbing diffusion is applied to supervised/pattern variables to ensure vocabulary legality by construction. This design not only inherits the advantages of time series diffusion in distribution fitting and uncertainty characterization \citep{rasul2021autoregressivedenoisingdiffusionmodels,tashiro2021csdiconditionalscorebaseddiffusion,wen2024diffstgprobabilisticspatiotemporalgraph,liu2023pristiconditionaldiffusionframework,kong2021diffwaveversatilediffusionmodel,11087622}, but also stabilizes the macroscopic temporal support through the long-range attention of Transformer, enabling the formation of an operational integrated generation pipeline under the mixed types and multi-scale dynamics of ICS. From the perspective of high-level synthesis, the temporal structure is equally indispensable: ICS control often involves delay effects, phased operating conditions, and cross-channel coupling, requiring models to be able to characterize low-frequency, long-range dependencies while also overlaying multi-facated fine-grained fluctuations on them. The Transformer series has provided sufficient evidence in long-sequence time series tasks: Transformer-XL breaks through the fixed-length context limitation through a reusable memory mechanism and significantly enhances long-range dependency expression \citep{dai2019transformerxlattentivelanguagemodels}; Informer uses ProbSparse attention and efficient decoding to balance span and efficiency in long-sequence prediction \citep{zhou2021informerefficienttransformerlong}; Autoformer robustly models long-term seasonality and trends through autocorrelation and decomposition mechanisms \citep{wu2022autoformerdecompositiontransformersautocorrelation}; FEDformer further improves long-period prediction performance in frequency domain enhancement and decomposition \citep{zhou2022fedformerfrequencyenhanceddecomposed}; PatchTST enhances the stability and generalization of long-sequence multivariate prediction through local patch-based representation and channel-independent modeling \citep{nie2023patchtst}. Combining our previous positioning of diffusion, this chain of evidence points to a natural division of labor: using attention-based sequence models to first extract stable low-frequency trends/conditions (long-range skeletons), and then allowing diffusion to focus on margins and details in the residual space; meanwhile, discrete masking/absorbing diffusion is applied to supervised/pattern variables to ensure vocabulary legality by construction. This design not only inherits the advantages of time series diffusion in distribution fitting and uncertainty characterization \citep{rasul2021autoregressivedenoisingdiffusionmodels,tashiro2021csdiconditionalscorebaseddiffusion,wen2024diffstgprobabilisticspatiotemporalgraph,liu2023pristiconditionaldiffusionframework,kong2021diffwaveversatilediffusionmodel,11087622}, but also stabilizes the macroscopic temporal support through the long-range attention of Transformer, enabling the formation of an operational integrated generation pipeline under the mixed types and multi-scale dynamics of ICS.

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@@ -604,18 +604,6 @@ keywords = {Safety interlock system, Symbolic model checking, Safety verificatio
abstract = {The safety interlock system (SIS) is one of the most important protective measurements in industrial processes that provide automatic actions to correct an abnormal plant event. This paper considers the use of formal techniques based on symbolic model checking and computation tree logic (CTL) in the specification to automatically verify the SIS for industrial processes. It addresses the problem of modelling industrial processes and presenting the SIS in CTL. It shows how symbolic model checking can be used efficiently in the verification of a SIS. A transferring system for a penicillin process is used as a case study.} abstract = {The safety interlock system (SIS) is one of the most important protective measurements in industrial processes that provide automatic actions to correct an abnormal plant event. This paper considers the use of formal techniques based on symbolic model checking and computation tree logic (CTL) in the specification to automatically verify the SIS for industrial processes. It addresses the problem of modelling industrial processes and presenting the SIS in CTL. It shows how symbolic model checking can be used efficiently in the verification of a SIS. A transferring system for a penicillin process is used as a case study.}
} }
@inproceedings{austin2023structureddenoisingdiffusionmodels,
author = {Austin, Jacob and Johnson, Daniel D. and Ho, Jonathan and Tarlow, Daniel and van den Berg, Rianne},
booktitle = {Advances in Neural Information Processing Systems},
editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
pages = {17981--17993},
publisher = {Curran Associates, Inc.},
title = {Structured Denoising Diffusion Models in Discrete State-Spaces},
url = {https://proceedings.neurips.cc/paper_files/paper/2021/file/958c530554f78bcd8e97125b70e6973d-Paper.pdf},
volume = {34},
year = {2021}
}
@article{10.1145/1151659.1159928, @article{10.1145/1151659.1159928,
author = {Vishwanath, Kashi Venkatesh and Vahdat, Amin}, author = {Vishwanath, Kashi Venkatesh and Vahdat, Amin},
title = {Realistic and responsive network traffic generation}, title = {Realistic and responsive network traffic generation},