Dominator Tree Certification and Divergent Spanning Trees

Author:

Georgiadis Loukas1,Tarjan Robert E.2

Affiliation:

1. University of Ioannina, Greece

2. Princeton University and Intertrust Technologies, Princeton, NJ

Abstract

How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively, one can check that the output produced for a particular input satisfies the desired input--output relation by running a checker on the input--output pair. Then one only needs to prove the correctness of the checker. For some problems, however, even such a checker may be too complicated to formally verify. There is a third alternative: augment the original program to produce not only an output but also a correctness certificate , with the property that a very simple program (whose correctness is easy to prove) can use the certificate to verify that the input--output pair satisfies the desired input--output relation. We consider the following important instance of this general question: How does one verify that the dominator tree of a flow graph is correct? Existing fast algorithms for finding dominators are complicated, and even verifying the correctness of a dominator tree in the absence of additional information seems complicated. We define a correctness certificate for a dominator tree, show how to use it to easily verify the correctness of the tree, and show how to augment fast dominator-finding algorithms so that they produce a correctness certificate. We also relate the dominator certificate problem to the problem of finding divergent spanning trees in a flow graph, and we develop algorithms to find such trees. All our algorithms run in linear time. Previous algorithms apply just to the special case of only trivial dominators, and they take at least quadratic time.

Funder

NSF

AFOSR MURI

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3