Higher-order logic fractional order verification method based on Grunwald-Letnikov definition

A technology of high-order logic and verification methods, applied in digital differential analyzers, calculations using non-numerical representations, etc., can solve problems such as state explosion and restricting the application of model verification methods

Inactive Publication Date: 2013-01-30
赵春娜
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Problems solved by technology

Model checking methods have achieved great success in both hardware and software design. The main advantages are complete automation and the ability to give counterexamples for verification. However, the state explosion problem has always restricted the application of model checking methods.

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  • Higher-order logic fractional order verification method based on Grunwald-Letnikov definition
  • Higher-order logic fractional order verification method based on Grunwald-Letnikov definition
  • Higher-order logic fractional order verification method based on Grunwald-Letnikov definition

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Embodiment Construction

[0068] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0069] Firstly, the unity of formal method of fractional calculus and integer order calculus is verified. Integer calculus is a special case of fractional calculus. For general functions: f(x)=x. In the higher-order logic prover, fractional-order formal methods are used:

[0070] |-a(frac_cal(\x.x)1 a b x=1)

[0071] The verifiable result is as follows: f'(x)=1. consistent with classical mathematical theory.

[0072] For fractional-order system models:

[0073] D t 1.5 0 y ( t ) + y ( t ) = u ( t )

[0074] Its corresponding fractional order transfer function:

[0075] ...

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Abstract

The invention provides a formal verification method of theorem proving. Aiming at key features of actual complex systems and based on the Grunwald-Letnikov fractional order calculus definition, correctness and validity are verified by using a higher-order logic fractional order theorem library. According to the method, the fractional order theorem library in the higher-order logic is adopted, attribute features of fractional order models of complex systems are verified in the man-machine interactive mode, and accuracy of the fractional order models is guaranteed. The fractional order models can describe the actual complex systems more accurately due to introduction of the fractional order, fractional order verification can improve completeness and accuracy of theorem proving. According to the method, verification accuracy can be improved, high reliability of systems can be guaranteed, and the method is particularly applicable to fields with high-accuracy requirements such as high-speed rails, nuclear power stations and spaceflight.

Description

technical field [0001] The invention is a formal verification method, which proposes a fractional verification method for a fractional model of a complex system, and belongs to the fields of information security and mathematics. Background technique [0002] The information infrastructure with communication, storage and computing as the core has penetrated into all aspects of politics, economy, military, culture and social life, and has become a powerful driving force for the development of contemporary productivity and the progress of human civilization. As the complexity of information system design increases exponentially, the verification method of the design is facing severe challenges. The traditional verification method uses a large number of test cases to analyze the reasoning properties of system behavior, and its inherent defect is incompleteness. For complex systems, exhaustive testing is impossible, and these methods can only prove faults but not fault-free. ...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/64
Inventor 赵春娜师丽坤骆力明王华金声震关永施智平李晓娟刘旭敏谭小慧
Owner 赵春娜
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