https://ocw.cs.pub.ro/ppcarte/ 2026-05-13T23:32:53+03:00 https://ocw.cs.pub.ro/ppcarte/ https://ocw.cs.pub.ro/ppcarte/lib/tpl/bootstrap3/images/favicon.ico text/html 2016-08-01T16:33:34+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=aa:intro:bibliography&rev=1470058414&do=diff [1] A. J. Hildebrand. Asymptotic methods in analysis - <http://www.math.uiuc.edu/hildebr/595ama/> . Math595AMA,2009 . [2] Christos M. Papadimitriou. Computational complexity. Addison-Wesley, Reading, Massachusetts, 1994. text/html 2016-08-03T11:34:15+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=aa:intro:complexity_theory&rev=1470213255&do=diff 1. Complexity Theory 1.1. Measuring time and space In Computability Theory, we have classified problems (e.g. in classes $ R$ and $ RE$ ) based on Turing Machine's ability to decide/accept them. In order to classify problems based on hardness, we need to account for the $ M$$ \mathcal{T}_M, \mathcal{S}_M : \Sigma^* \rightarrow \mathbb{N}$$ \mathcal{T}_M(w)$$ \mathcal{S}_M(w)$$ M$$ w$$ \mathbf{while} \mbox{ } n \lt 100$$ \quad n=n+1$$ \mathbf{return} \mbox{ } 1$$ Alg$$ n=0$$ n \geq 100$$ \sta… text/html 2016-08-01T16:36:42+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=aa:intro:computability_theory&rev=1470058602&do=diff 1. Computability Theory 1.1. Motivation Goldbach conjecture [Matei: <https://en.wikipedia.org/wiki/Wang_tile#Applications]> 1.2. Problems and problem instances In the previous section, we have illustrated the problem SAT, as well as a pseudocode which describes a solution in exponential time. We have seen that such a solution is infeasible in practice, and also that no (predictible) technological advance can help. The main question we asked (and also answered) is whether there exists a faste… text/html 2016-07-27T16:49:40+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=aa:intro:introduction&rev=1469627380&do=diff Introduction About the lecture Post's Correspondence Problem Statement Let $\alpha_1, \ldots, \alpha_n$ and $\beta_1, \ldots, \beta_n$ be sequences of words over a fixed alphabet. There exists a finite sequence $ a_1a_2 \ldots a_k$ , with $ a_i = 1, \ldots, n$ such that: $\alpha_{a_1}\alpha_{a_2}\ldots \alpha_{a_k} = \beta_{a_1}\beta_{a_2}\ldots \beta_{a_k}$ Example * Motivation: * Simplifications: * Limit the length of text/html 2025-11-07T13:15:24+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=aa:intro:rules&rev=1762514124&do=diff Regulament 2025-2026 Punctaj * Parcurs: 50p * Examen: 50p Punctajul pe parcurs constă în: * o temă: 15p * examen parțial: 20p * implicare laboratoare: 5p * teste curs: 10p Pentru a putea susține examenul, este necesară obținerea a minim 25 puncte pe parcurs.$ \frac{\text{punctaj} \times 50}{60}$