prover;theproofsourcefilesareavailable.Thecontributionsalsoincludesuggestionsforinvariantinference andformodel-basedspecification. CategoriesandSubjectDescriptors:D.2.4[Software/ProgramVerification]:CorrectnessProofs;F.3.1 [SpecifyingandVerifyingandReasoningaboutPrograms]:Invariants ...
solving sequence.This lets us get straightforward an approach for solving a variety of complicated problems,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 nontivial examples.薛锦云...
Another presentation of the problem is that of Pickrell (1987), where he obtains a family of quasi-invariant measures on Grassmannians. Given a family of measures (μt)t≥0 on the path space of a Riemannian manifold, one defines a heat operator as a family Ltt≥0 of operators depending...
Fig. 1 Two running examples with unsolvable recurrence operators. Nevertheless, P admits a closed-form for combinations of variables and PSC admits a polynomial invariant. Herein we use (rather than a loop guard or true) as loop termination is not our focus. For the avoidance of doubt, in ...
(5.68) However, since Kronnecker forms are invariant under shifts by integers, arguments of the form zj ´ 1 are ruled out. This particularly simple set of arguments is special to the sunrise example. For more complicated examples (e.g., see [80]), one should expect to find additional...
A closed-loop system identification method is developed to estimate the parameters of a single input single output (SISO) linear time invariant system (LTI) operating within a feedback loop. The method uses the reference command in addition to the input–output data and establishes a correlation ...
It means that under the transformation (30) the β functions should transform in an analogous way while all the observables including critical exponents should be invariant with respect to above replacement (see [10], [29], [43] for details and extra examples). The expansions (12) and (13...
whichallowstoexpressanysu(N)invarianttensorintermsofbasiconesi.e.forests(products oftrees).Insection3weproveseverallemmasandeventuallythemainresult.Insection4we presentafewexamplestogivetheinsightintothemethod. Wewillusethefollowingconventions λ i λ j = 2 N δ ij 1+d ijk λ k +if ijk λ k ...
2Of course, the exact location of the branch cut is of no invariant meaning. What is important here is that the function P iω does not return to its initial value when the argument P goes a full circle around P = 0. –2– Figure 1. The function P iω with ω = 4 on the ...
example, in ##EQU9## a decision to vectorize loop-i results in vector accesses which are strider but are conditional. A decision to vectorize loop-j avoids the condition problem (c(i) is invariant with respect to loop-j) but the access to b(i,indx(j)) requires an additional vector ...