BLAST isn't a dynamic programming algorithm. It's not guaranteed to find an optimal solution, unlike a DP algorithm. It has some elements of DP, but that's it.
"The heart of many well-known programs is a dynamic programming algorithm, or a fast approximation of one, including sequence database search programs like BLAST..."
All DP algorithms guarantee an optimal result. It's a defining characteristic of DP. BLAST doesn't. I'm really surprised that you're attempting to debate this.
I'm clearly not going to understand your motivation so I think I'll stop here.
(edit: There is absolutely nothing stopping heuristics and DP being combined; in fact they have to be in eg. database optimisation. A pure DP solution to query optimisation will be optimal, but will take unbounded (lthough finite) time, which is unacceptable. DP and heuristics are combined to both guide the DP search and bound it after a strict time (usually a couple of seconds CPU) by when it is hopefully 'good enough').
You're wrong, and I don't know why you're being stubborn about this. HDP is a different class of algorithms that uses DP, but it is not DP. A basic read of wikipedia of dynamic programming reveals the key pieces of DP:
There are two key attributes that a problem must have in order for dynamic programming to be applicable: optimal substructure and overlapping sub-problems. ... Optimal substructure means that the solution to a given optimization problem can be obtained by the combination of optimal solutions to its sub-problems.
Well, perhaps you use different definitions than I do, but it should be obvious that it is possible to design an algorithm using dynamic programming that does not solve the problem optimally. By optimally here, I mean always output the optimal solution.
If you, by optimization mean that there's a function value you are maximizing or minimizing, than that's not true either, since Subset Sum and Hamiltonian path are canonical decision problems for which DP is used.
Heck, you can even take the standard TSP DP algorithm and, instead of looking at all possible "exit vertices" in linear time, look at a randomly chosen constant number of candidates, thereby reducing the running time by a factor n and getting a randomized heuristic function not guaranteed to give the optimal value.
Technically if you car is recent, it is a cell phone with wheels but I digress.
This reminds me of biologists bickering about what is or is not a gene,
and endless snorefests of ontologists bickering about the semantics of a label on an edge in a graph.
