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 477
Theorem 6 An NP-Complete problem exists.
Sketch of Proof We prove this by an example. One NP-complete problem is the bounded halting problem:
This problem takes as input a program X and a number K. The problem is to fi nd data D, which
when given as input to X, causes it to stop in at most K steps.
This needs some more careful defi nition: what language is X written in? What constitutes a single step?
Also for technical reasons K should be specifi ed in unary notation, so that the length of that part of the input
is K itself rather than O(log K).
To test if the data D is a correct solution, just simulate the ...
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