CS3231 Theory of Computation 归档 计算理论 (Theory of Computation) 当之无愧是计算机科学王冠上的明珠;考虑到我贫瘠的智商,以后估计不会朝 TCS 方向来走;但对这些优雅的理论有一个最基本的了解应当是 CS 学生的素养。 讽刺的是,你坑近二十年前就没有开设这门课了 [1],只得留待交换来上。老师是印度人,口...
input : Players' bids bi = (xi, πi) output: An outcome o∗ and first-price payments pi. 1 Let bi(o) = max(0, xi(o) − πi); // bi(o) is i's effective bid for outcome o. 2 Compute o∗ = argmaxo i∈[n] bi(o); // Choose the outcome with the highest total...
The use of function symbols in our notation for predicate logic allows us to create a simple representation of binary trees. Namely, let the constant symbol represent the root node of the tree, and the unary functions and represent the left and right children of a node. The idea is that (...
Let Parties P1, ..., Pn have datasets DS1, ..., DSn where DSi = (x(i), y(i)) contains a set of in- stances x(i) = (x(1i), x(2i), ..., x(mi)), where m is the number of features, and their corresponding labels y(i), for i in 1 to n. Every party Pi makes...
a SAT solver so that it generates refinements that are close to minimal, thus greatly reducing the time required for their minimization. 1. Introduction Model checking [6] decides whether a model satisfies a property by exploring its state space. This approach leads to a high degree of...
For any alphabet A of size Q there exists error correction codes of length n, dimension k, and minimum distance ( n k) (Notation ( n, k; n k codes)) under the following conditions: Let K be a finite field containing p r elements. If I = p r Q > 0 then n can be up to ...
Similar to the real plane, the standard form of a complex number may be turned into polar form. How To Write Complex Numbers in Polar Form To write a complex number in polar form given its standard form, there are a few easy steps. Let z = a + bi be a complex number....
focus&improveon.Recallthatmost(andperhapsevenall)ofthemidtermandfinalexamquestionsinthiscoursewillcomefromtheseproblemsets,soyourbeststrategyofstudyingfortheexamsinthiscourseistosolve(instudygroups)asmanyoftheseproblemsaspossible,andthesoonerthebetter!Advice:Pleasetrytosolvetheeasierproblemsfirst(wherethemeta-...
For exam- ple, for c = 2 and p = 3, the parameter vector will be: Ψ = (π , β ) = (π1, β11, β21, β31, β12, β22, β32). In the application presented above, these parameters would correspond to the proportion of 'republicans', the log- 34 D.W. Gudicha, F.B...
Let I be the integral before step id. The rule adds coeff · I to the current expression, then divide by coeff + 1 and simplify. For example, in the evaluation of π/2 0 e2x cos x dx, after some steps we get −2 + eπ − 4 π/2 0 e2x cos x dx. Then, applying ...