Ildikó Sain TOTAL CORRECTNESS IN NONSTANDARD DYNAMIC

In this paper we investigate total correctness (termination and correctness simultaneously) in Nonstandard Dynamic Logic (NDL). Here we show that despite of the celebrated Kfoury-Park [5] result, termination is a first order notion if approached properly (e.g. via NDL). In Definition 1 below we recall the famous Manna-Cooper Q-method for proving total correctness. Then we do the same things to Manna-Cooper total correctness method ` that were done in [1] to Floyd’s partial correctness method ` . Among others, we shall give an explicit characterization of the information content of ` as well as prove that NDL is strictly stronger than ` w.r.t. proving total correctness (that is, more programs can be proved totally correct by NDL than by `). The same results apply if we replace ` by Burstall’s method for total correctness (this is because Burstall’s method is very close to our version of `) as it will be demonstrated in the other paper. Since these methods (Burstall’s and Manna-Cooper’s) are widely used and accepted to be strong enough for practical purposes we show indirectly that NDL is strong for practical purposes. Since by [1], NDL is also stronger than ` we have evidence at our hand to disagree with those opinions who maintain that nonstandard time in NDL makes it too weak. Just as is was the case with Floyd’s method in [1] , we have to define ` more precisely than in the original publications. The first careful reformulation of the Manna-Cooper ` method was given in Sec. 3.2 of [4] pp. 34-38. The Chang-Lee book [6] on programverification introduced `