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- 1$\begingroup$ This statement When we say that a problem takes exponentially long time, what we mean is that as we tweak the input parameters a little then the problem takes more time by a 'constant factor' sounds very inaccurate or meaningless. Can you rephrase what you mean? $\endgroup$JimN– JimN2023-05-08 22:27:50 +00:00Commented May 8, 2023 at 22:27
- $\begingroup$ I'm having a hard time understanding what your question is. Perhaps one of the challenges is that I don't understand what you are imagining as the alternative. I suspect that the questions marked as 'duplicate' might answer your question; or might give you a bunch of additional information might help you formulate more clearly what you are asking. I suggest reviewing the material there, and then if that doesn't answer your question, use that background to help you more clearly state your question (either by editing this question, or posting a new question). $\endgroup$D.W.– D.W. ♦2023-05-09 00:02:15 +00:00Commented May 9, 2023 at 0:02
- $\begingroup$ If you do ask a new question or edit this one, I suggest trying to specify more precisely and in more detail what you are imagining as an alternative definition of 'easiness'. You might also review what are the good properties of "polynomial time" listed in the linked questions, and then analyze whether your alternative definition has those good properties or not, and update your question to summarize what your conclusions on that are. $\endgroup$D.W.– D.W. ♦2023-05-09 00:03:12 +00:00Commented May 9, 2023 at 0:03
- $\begingroup$ When the time is polynomial, doubling the size of the input multiplies the time by a power of 2. When it is exponential, the new time is raised to a power. E.g. n³ makes 100000 turn to 800000, while 3^n makes 100000 turn to 10000000000. Tripling the size, 100000 becomes 2700000 vs. 1000000000000000. $\endgroup$user16034– user160342023-05-09 07:57:06 +00:00Commented May 9, 2023 at 7:57
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