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Synthesis of ranking functions via DNN

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Abstract

We propose a new approach to synthesis of non-polynomial ranking functions for loops via deep neural network(DNN). Firstly, we construct a ranking function template by DNN structure. And then the coefficients of the template can be learned by the train-set we construct to get a candidate ranking function, which is transcendental and non-polynomial because of the existence of sigmoid activation function in the neural network. Finally, the candidate ranking function will be verified to show if it is a real ranking function. Most of the existing methods focus on linear or polynomial ranking functions, and are limited to verification tools, while in this paper we make progress regarding the synthesis of non-polynomial ranking functions and new verification method for candidate ranking functions. The experimental results show us that for some of loops from other work, we can find their ranking functions efficiently. Moreover, for some loops having multi-phase ranking functions obtained by existing methods, our method can directly detect their global ranking functions. Especially, our method can also detect the global ranking functions for some loops with transcendental terms, which cannot be dealt with by existing methods.

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Acknowledgements

This research is partially supported by the National Natural Science Foundation of China NNSFC(61572024, 11771421,61103110), the Natural Science Foundation of Chongqing (cstc2019jcyj-msxmX0638), Chinese Academy of Sciences “Light of West China” program, Chongqing science and Technology Innovation Guidance Special project(cstc2018jcyj-yszxX0002, cstc2019yszx-jcyjX003), National Key Research and Development Project(2020YFA07123000).

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Authors and Affiliations

  1. Chongqing Key Laboratory of Automated Reasoning and Cognition, Automated Reasoning and Cognition Center, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, 400714, China

    Wang Tan & Yi Li

  2. University of Chinese Academy of Sciences, Beijing, 101408, China

    Wang Tan

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  1. Wang Tan
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  2. Yi Li
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Correspondence to Yi Li.

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The authors declare that no support, financial or otherwise, has been received from any organization that may have an interest in the submitted work and there are no other relationships or activities that could appear to have influenced the submitted work.

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Tan, W., Li, Y. Synthesis of ranking functions via DNN. Neural Comput & Applic 33, 9939–9959 (2021). https://doi.org/10.1007/s00521-021-05763-8

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