Concept of Complete Testing | Exhaustive testing is impossible

It is not unusual to find people making claims such as “I have exhaustively tested the program.” Complete, or exhaustive, testing means there are no undiscovered faults at the end of the test phase. All problems must be known at the end of complete testing. For most of the systems, complete testing is near impossible because of the following reasons:

• The domain of possible inputs of a program is too large to be completely used in testing a system. There are both valid inputs and invalid inputs.
  The program may have a large number of states. There may be timing constraints on the inputs, that is, an input may be valid at a certain time and invalid at other times. An input value which is valid but is not properly timed is called an inopportune input. The input domain of a system can be very large to be completely used in testing a program.
• The design issues may be too complex to completely test. The design may have included implicit design decisions and assumptions. For example, a programmer may use a global variable or a static variable to control program execution.
• It may not be possible to create all possible execution environments of the system. This becomes more significant when the behaviour of the software system depends on the real, outside world, such as weather, temperature, altitude, pressure, and so on.

[From book – Software testing and quality assurance: theory and practice By Kshirasagar Naik, Priyadarshi Tripathy]

Must Read: Testing Limitations
The Impossibility of Complete Testing by Dr. Cem Kaner