Weaknesses Analysis Of C Language Based On Topological Space

C and C++ language are very effective and widely-used computer programming language,but they still have many weaknesses while programming.If C language is not properly used,it will produce weaknesses.The main reason for the weaknesses is the lack of syntax security,especially the lack of boundary checking in data.Point-set topology is a mathematical discipline that studies the properties of figures that can be kept as constant properties under continuous changes.In this paper,we give a method which can determine the buffer overflow weaknesses of some string function in C language by using the continuous property of point-set topology.How to determine the existence of weaknesses is very important and difficult in computer science,there are several methods mainly used in computer science currently.In this paper,we combine C language weaknesses detection and point-set topology and get a new static method for determining weaknesses.We construct a topological space of string function which is called character sequential topological space and give the derivation set and condensation point of this space.We define the mapping of string function with the same name and prove that the mapping is continuous when there is not any weaknesses in the code.According to this theory,we can get a conclusion that there is a weakness in the code if the mapping is discontinuous.Using this method we can determine the weaknesses in string function based on the continuous of the topology space.This method is a reasonable and innovative static detection method,which can be helpful for programmers to improve the codes,increase the precision of weaknesses finding,and develop better and safer C language software.