1. Show that the following language is undecidable: {M | M is a TM that has polynomial worst-case running time} Rice's thereom doesn't apply here! Be careful, because the worst-case running time of a TM is a global property of the TM, that involves its behavior on all inputs.

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1. Show that the following language is undecidable:
{M | M is a TM that has polynomial worst-case running time}
Rice's thereom doesn't apply here! Be careful, because the worst-case running time of a TM is a global
property of the TM, that involves its behavior on all inputs.
Also, this problem is not asking about {M | L(M) e P}. That language is undecidable as an immedi-
ate corrolary of Rice's theorem. Remember that a TM M might decide a problem in P but do it with an
exponential-time algorithm. The language in this homework is asking about the running time of M, not
about L(M).
Transcribed Image Text:1. Show that the following language is undecidable: {M | M is a TM that has polynomial worst-case running time} Rice's thereom doesn't apply here! Be careful, because the worst-case running time of a TM is a global property of the TM, that involves its behavior on all inputs. Also, this problem is not asking about {M | L(M) e P}. That language is undecidable as an immedi- ate corrolary of Rice's theorem. Remember that a TM M might decide a problem in P but do it with an exponential-time algorithm. The language in this homework is asking about the running time of M, not about L(M).
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