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Theory of Program Testing, Program Erros, Fundamental Concepts, Theory of…

- - - - Theory of Gourlay
        
        Adequacy of testing
        
        Limitations of Testing
        
        Due to the impractical nature of proving even small programs to be correct , customers and software developers rely on the efficacy of testing,two main limitations of testing:
        
        Testing means executing a program with a generally small , proper subset of the input domain of the program
        
        A small , proper subset of the input domain is chosen because cost may not allow a much larger subset to be chosen , let alone the full input set . Testing with the full input set is known as exhaustive testing
        
        Once we have selected a subset of the input domain , we are faced with the problem of verifying the correctness of the program outputs for individual test input . That is , a program output is examined to determine if the program performed correctly on the test input
        
        Testing gives designers and programmers much confidence in a software component or a complete product if it passes their test cases
        
        Intuitively . the idea behind specifying a criterion for evaluating test adequacy is to know whether or not sufficient testing has been done . In the absence of test adequacy , developers will be forced to use ad hoc measures to decide when to stop testing . Some examples of ad hoc measures for stopping testing are as follows
        
        Stop when the allocated time for testing expires
        
        Stop when it is time to release the product
        
        Stop when all the test cases execute without revealing faults
        
        Is important to design test cases independent of an adequacy criterion because the primary goal of testing is to locate errors , and , thus , test design should not be constrained by an adequacy criterion
        
        Intuitively , a test set T is said to be adequate if it covers all aspects of the actual computation performed by a program and all computations intended by its specifi cation . Two practical methods for evaluating test adequacy are as follows
        
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        To motivate a theoretical discussion of testing , we begin with an ideal process for software development , which consists of the following steps
        
        A customer and a development team specify the needs
        
        The development team takes the specification and attempts to write a pro gram to meet the specification
        
        A test engineer takes both the specification and the program and selects a set of test cases . The test cases are based on the specification and the program
        
        The program is executed with the selected test data , and the test outcome is compared with the expected outcome
        
        The program is said to have faults if some tests fail
        
        One can say the program to be ready for use if it passes all the test cases
        
        The program is said to be correct if and only if it satisfies the specification . Gourlay's testing theory establishes a relationship between three sets of entities , namely , specifications , programs , and tests , and provides a basis for comparing different methods for selecting tests
        
        A test consists of a number of trials of some sort , and success of the test as a whole depends on success of all the trials . In fact , this is the rule in testing practice , where a test engineer must run a program again and again on a variety of test data . Failure of any one run is enough to invalidate the program
        
        That is , in the general case , a test method takes the specification S and an imple mentation program P and produces test cases . In practice , test methods are pre dominantly program dependent , specification dependent , or totally dependent on the expectations of customers
        
        Program Dependent
        
        Specification Dependent
        
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      - He reliability and validity of a criterion depend upon the presence of faults in a program and their types
        
        Weyuker and Ostrand provide a modified theory in which the validity and reliability of test selection criteria are dependent only on the program specifi cation , rather than a program . They propose the concept of a uniformly ideal test selection criterion for a given output specification
        
        However , the concept of uniformly ideal test selection also has several flaws
        
        Theorem . A criterion C is uniformly valid if and only if C is trivially valid .
        
        Theorem . A criterion C is uniformly reliable if and only if C selects a single test set
        
        Corollary: A criterion C is uniformly vaLID nad uniformly reliable if and only if C selects only the single test set T=D
        
        Reliability and validity of test selection criterion are ideal goals , and ideal goals are rarely achieved . It is useful to seek less ideal but usable goals . By set tling for less ideal goals , we essentially accept the reality that correctness of large programs is not something that we strive to achieve
        
        Weyuker and Ostrand have introduced the concept of a revealing crite rion with respect to a subdomain
        
        An important task in applying the idea of a revealing criterion is to partition the input domain into smaller subdomains , which is akin to partitioning a problem into a set of subproblems . However , partitioning a problem into subproblems has been recognized to be a difficult task
  - - - A theoretical foundation of testing gives testers and developers valuable insight into software systems and the development processes . As a consequence , testers design more effective test cases at a lower cost
- - - - This class of faults leads to a failure of the program to produce expected results within specified or desired resource limitations