Program Construction Method for Sequential Statistics Class Algorithm Based on Bidirectional Scanning Induction

Abstract

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.