We could try the same with NP, and define $L$ to contain pairs $(\langle T\rangle,x)$ such that $T$ is a non-deterministic Turing machine that has no accepting path of length $\leq |\langle T\rangle,x|^3$ on input $(\langle T\rangle,x)$. It's easy to see that $L$ is in P, and it is also easy to see that if a machine $M$ could decide this problem in time $\leq n^3$ on all sufficiently large inputs, then the behavior of $M$ on input $\langle M\rangle,x$, for every $x$ long enough, leads to a contradiction. We define the language $L$ that contains all pairs $(\langle T\rangle,x)$ where: (i) $T$ is a Turing machine, (ii) $x$ is a binary string, (iii) $T$ rejects the input $(\langle T\rangle,x)$ within $|(\langle T\rangle,x)|^3$ steps, where $|z|$ denotes the length of a string $z$. In the deterministic case, where we want to find a language in P not solvable in time $o(n^3)$, it's very simple. (If one does not want to talk about non-deterministic Turing machines, the same proof will apply to other quantitative restrictions on NP, such as bounding the length of the witness and the running time of the verification.) Though the full result is more general, say we want to prove that there is a language in NP that cannot be solved by non-deterministic Turing machines in time $o(n^3)$. To get started, I proved Cook's non-deterministic hierarchy theorem, a 1970s result with a beautifully clever proof, which I first learned from Sanjeev Arora. (If the author could get some mileage out of being an undergrad at Harvard, just imagine what it can do for you to be a grad student at Berkeley!)Īfter a hiatus of almost four year, the graduate computational complexity course returns to Berkeley. Living the life of the mind is very rewarding, and, apparently, the chances of dating male models are not bad either. Women in their sophomore or junior year of college who are thinking about doing research and going to graduate school should read this article (via Andrew Sullivan). Especially avocado: when I eat it, my throat gets all scratchy. Young Homeless Guy: is there garlic or avocado in it? Guy With Bags: would you like something to eat? Another guy walks by, holding what look like large leftover bags from a restaurant. Young Homeless Guy is sitting on the floor with a cardboard sign. This will be taken care of in the "near" future. While all old posts and comments are there, the move has broken the latex hacks, the videos, and the cross-links between posts. Please update your bookmarks, your RSS readers, and your blogrolls, to We ring in the year of the rat with a move to wordpress, and to its superior handling of latex. If, for some reason, this is not enough, click on to view the actual page in a new windows. If you click on the blog title, it will expand out the page in the table. (Sometimes you may also get blogs that are not in English: you should mark these as such.)įor each blog, you should select "NotEng" if it is not English, "NotCS" if it is not a CS/math/stats blog, and "CS" if it is a CS/math/stats blog. Your goal is to determine whether a blog in question is related to computer science, mathematics or statistics and is a research blog or not. Muy parecido a pulp fiction lo del desorden.pero me ha encantado el finalĪ lo tonto, puede haber nacido (y muerto) un personaje carismático con ese cerdito.You are presented with a set of blogs. Muchas risas xD, me he descojonado malamente con el detalle de la pajarita torcida xDDD, muy grande Luego me pasa un poco como el hijo de Tarantino, que me pierdo, aunque imagino que ahí está la gracia, claro. Me mola el diálogo flash-back en blanco y negro. Lo más terrorífico de todo, para el niño, es, sin duda, el cuadro.
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