April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Tractable and Non-tractable Problems 497
of the problems discussed till now have such fi nite certifi cates. For example, for the HP, to demonstrate that
a checking program indeed halts with algorithm A with input W, we may give a complete trace of all the
variables and sequence of statements executed by A on input W. We can check this certifi cate by simulating
the action of A and checking each step against the certifi cate. Note that such a certifi cate for an undecidable
problem is by necessity “one-way” certifi cate, that is, for either Yes or No answer.
If both kinds of certifi cates are available for all the inputs, then it is easy to see that ...
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