What are the characteristics of testing and a good test?

Testing goal is to find errors. It should exhibit a set of characteristics that achieve the goal of finding the errors with minimum effort. The characteristics of software testing includes:
- How easily a software can be tested? i.e. test-ability
- How efficiently it can be tested? i.e. oper-ability
- What you see is what you test? i.e. observability
- How much we control the software so that testing can be automated and optimized? i.e. controllability
- Isolating problems and perform smarter retesting by controlling scope of testing i.e. decomposability.
- The program should be simple so that it can become easy to test i.e. simplicity.
- The fewer the changes, the fewer the disruptions to testing i.e. stability.
- The more information we have, the smarter we will test i.e. understandability.

A good test has the following characteristics:
- A good test has a high probability of finding an error.
- A good test is not redundant.
- A good test has the highest likelihood of uncovering a whole class of errors.
- A good test should be neither too simple nor too complex.

There are two ways to test an engineered product:
- Knowing the internal workings of product and tests can be conducted that can ensure that internal workings are performed according to specifications and all internal components are exercised properly.
- Knowing the output or the function for which the product is designed, tests are conducted to demonstrate each function is fully operational and checking the errors at the same time.