Two New Strategies for Developing Loop Invariants and Their Applications

The loop invariants take a very important role in the design,proof and derivation of the algorithmic program.We point out the limitations of the traditional standard strategy for developing loop invariants, and propose two new strategies for proving the existing algorithmic program and developing new ones. The strategies use recurrence as vehicle and integrate some effective methods of designing algorithms, e.g.Dynamic Programming,Greedy and Divide Conquer,into the recurrence relation of problem solving sequence.This lets us get straightforward an approach for solving a variety of complicated prob- lems,and makes the standard proof and formal derivation of their algorithmic programs possible.We show the method and advantages of applying the strategies with several typical nontrivial examples.