Is it possible to find all error in the application?

Software testing is an integral phase of software testing, testers are the people who always question the reliability and stability of the software application, considering the role of software testing, it is also claimed that it is not possible to find all errors in the application. Let’s use basic testing types in order to start discussion about this statement.

Black Box Testing
Lets explore Black testing type, this testing type is also called Data Driven testing, Input/Output testing. As it quite known in this type of testing, testers are only concerned with the functionality of testing, and treat system as a black box, they derive their test cases from the functional behavior and least bothered about the internal structure of the application. So if we want to find all errors in the application using black box testing , then we have to use to technique of exhaustive input. That is we have to cater each possible input to the application.
Testing software with each possible input, sounds impossible because it is impossible to measure all possible valid or invalid input condition for example consider a program, which takes any two numbers for addition, now if we analyze the input to that program, it can be from 0 to infinity, in the same way negatives infinity to zero. All of us is agreed that it is the most simple computer program, but still in order to test program with each possible input condition is not possible. Consider a program like Compilers, operation system, or flight control system in which you have to derive test case for each possible input, what do you think it is possible?
So testing software with all exhaustive input is not possible, so we can test the program with every input to the program, thus claiming that software is error free for all possible input can not be feasible and practically impossible task to do,
But yes we can use different techniques to build our confidence about the stability of the program by using test case design technique that is (Equivalence partition, boundary value analysis etc and the objective should be to maximize the yield on software testing investment by finding maximum number of errors in definite number of test cases.

White Box testing
Another testing technique, white box testing also know as logic driven testing, in this type of testing test cases are derived from the internal code logic of the program, that by considering all logical paths, testers design test cases, in this type of testing all logical path are tested to find maximum errors, so as we discussed in black box testing we test program with exhaustive input, in this scenario we will say it as exhaustive logic path testing.
Testing software by designing test cases that cover all logic paths to ensure that software is error free, is quite impossible because we have to go through all possible paths of control flow in order to test software 100 % accurately, when we talk about testing each logical control path, consider a program which runs almost 50 line of code within loop, and for every iteration of loop, it passes through different branching conditions, so writing test case for every nested statement, seems impractical, if not impossible.
Considering if we are somehow able to test each control flow path of the program, but still it is not sure that software will be error free, due to following reasons:
1-If we test all logical code paths, it will not ensure that code has been written according to specification provided. For example if programmer writes ascending order routine instead of descending order, by testing all logical paths, we can not guarantee that there will be no error in the application.
2-There can be error due to missing input paths, because exhaustive input can not determine important logical paths.
3-Exhaustive input testing does not cover data sensitivity errors.
Looking for your feedback :)

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