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Formal verification of cP systems using Coq

Abstract

P systems are widely used to solve computationally hard problems. In this study, we formally verify cP systems (P systems with complex objects) in the Coq proof assistant, and provide a corresponding open source library. To help transform cP notation into Gallina, we propose two sets of modelling guidelines. Comparing to existing P system formal verification studies, our approach shows many advantages and has great potential. To the best of our knowledge, this is the first study to formally verify membrane computing models using an interactive theorem prover.

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Notes

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    cP-Coq and verification examples can be found in https://github.com/YezhouLiu/cP-Coq

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Correspondence to Yezhou Liu.

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Appendices

Appendix 1.A: A simulation of the minimum finding cP system, input = {3, 7, 6, 8}

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Appendix 1.B: The subset sum cP system in Gallina

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The Coq representation of R1, R2, and R3

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The Coq representation of R4 and R5

Appendix 1.C: A simulation of the subset sum cP system, S = {1, 2, 3, 4}, T = 10

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A simulation of the subset sum cP system, S = {1, 2, 3, 4}, T = 10.

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Liu, Y., Nicolescu, R. & Sun, J. Formal verification of cP systems using Coq. J Membr Comput 3, 205–220 (2021). https://doi.org/10.1007/s41965-021-00080-4

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Keywords

  • Membrane computing
  • P systems
  • cP systems
  • Formal verification
  • Theorem prover
  • Coq