Date: Thu, 5 Feb 2004 12:08:02 -0500
From: Amittai Aviram <amittai@amittai.com>
To: Marco Valtorta <mgv@cse.sc.edu>
Subject: Rules for testing algorithm correctness

<...>

Here is how I would summarize the rules we have learned about testing
algorithm correctness.  

<...>

I.  Test to make sure that algorithm will terminate.
II.  Define a precondition (allowable input and state) and a postcondition
(correct output).
III.  Test that, given precondition, algorithm will fulfill postcondition.
In many cases, the algorithm is either recursive or iterative.  Determine
which one applies.
A.  Recursive algorithms.
Use induction to show correct fulfillment of postcondition in
(1) basis case(s)
(2) case where input is of size n+1, assuming that postcondition is
fulfilled when input is of size n.

B.  Iterative algorithms.
(1)  Determine an appropriate invariant.
(2)
    (a)  Show that invariant is true for basis case.
    (b)  Show that, if invariant is always true, postcondition is fulfilled.
    (c)  Show, by induction, that, if invariant is true for input of size n,
it is also true for input of size n+1.

Thank you!

Best wishes,
Amittai