The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal de...The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.展开更多
The program construction process is based on rigorous mathematical reasoning,which leads to a fully correct algorithmic program via step-by-step refinement of the program specifications.The existing program constructi...The program construction process is based on rigorous mathematical reasoning,which leads to a fully correct algorithmic program via step-by-step refinement of the program specifications.The existing program construction methods'refinement process is partly based on individual subjective speculation and analysis,which lacks a precise guidance method.Meanwhile,efficiency factors have usually been ignored in the construction process,and most of the constructed abstract programs cannot be run directly by machines.In order to solve these problems,a novel program construction method for the sequence statistical class algorithms based on bidirectional scan induction is proposed in this paper.The method takes into account the efficiency factor and thus improves the Morgan's refinement calculus.Furthermore,this paper validates the method's feasibility using an efficiency-sensitive sequential statistics class algorithm as a program construction example.The method proposed in this paper realizes the correctness construction process from program specifications to efficient executable programs.展开更多
基金Supported by the National Natural Science Foundation of China (61862033, 61762049, 61902162)Jiangxi Provincial Natural Science Foundation (20202BABL202026, 20202BABL202025, 20202BAB202015)。
文摘The development of algebraic and numerical algorithms is a kind of complicated creative work and it is difficult to guarantee the correctness of the algorithms. This paper introduces a systematic and unified formal development method of algebraic and numerical algorithms. The method implements the complete refinement process from abstract specifications to a concrete executable program. It uses the core idea of partition and recursion for formal derivation and combines the mathematical induction based on strict mathematical logic with Hoare axiom for correctness verification. This development method converts creative work into non-creative work as much as possible while ensuring the correctness of the algorithm, which can not only verify the correctness of the existing algebraic and numerical algorithms but also guide the development of efficient unknown algorithms for such problems. This paper takes the non-recursive implementation of the Extended Euclidean Algorithm and Horner's method as examples. Therefore, the effectiveness and feasibility of this method are further verified.
基金Supported by the National Natural Science Foundation of China(62262031)the Jiangxi Provincial Natural Science Foundation(20232BAB202010)+1 种基金the Science and Technology Project of Education Department of Jiangxi Province(GJJ210307,GJJ2200302)the Cultivation Project for Academic and Technical Leader in Major Disciplines in Jiangxi Province(20232BCJ22013)。
文摘The program construction process is based on rigorous mathematical reasoning,which leads to a fully correct algorithmic program via step-by-step refinement of the program specifications.The existing program construction methods'refinement process is partly based on individual subjective speculation and analysis,which lacks a precise guidance method.Meanwhile,efficiency factors have usually been ignored in the construction process,and most of the constructed abstract programs cannot be run directly by machines.In order to solve these problems,a novel program construction method for the sequence statistical class algorithms based on bidirectional scan induction is proposed in this paper.The method takes into account the efficiency factor and thus improves the Morgan's refinement calculus.Furthermore,this paper validates the method's feasibility using an efficiency-sensitive sequential statistics class algorithm as a program construction example.The method proposed in this paper realizes the correctness construction process from program specifications to efficient executable programs.
