Problem Detail: I was reading about Turing machines and realized I’m not sure about the difference between the following scenario. Given the alphabet $Sigma = {a, b }$, we have the following assertions: $a in R $ ${a} in R$ I Read More …
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[Solved]: Do you know of a brute-force algorithm for optimizing polynomial expressions?
Problem Detail: For instance, given the polynomial expression $xy + x + y + 1$ it will output $(x+1)(y+1)$. Thanks! Asked By : Fruitful Approach Answered By : user2566092 “Brute-force” in the context of factoring polynomials may involve factoring of integers, which is Read More …
[Solved]: Basic action for every data structure O(1)
Problem Detail: My lecturer for Algorithms said that most of the data structures I will encounter in the algorithms course I am taking have a basic action which is of O(1). Ex: Binary heap. Basic action is: Compare 2 childen. Compare Read More …
[Solved]: Find subsequence of maximal length simultaneously satisfying two ordering constraints
Problem Detail: We are given a set $F={f_1, f_2, f_3, …, f_N}$ of $N$ Fruits. Each Fruit has price $P_i$ and vitamin content $V_i$; we associated fruit $f_i$ with the ordered pair $(P_i, V_i)$. Now we have to arrange these fruits Read More …
[Solved]: Context free language and the complement of it
Problem Detail: Given the language $L_1 = {a^i b^j c^k mid i neq j vee i neq k}$, I need to determine whether it is context-free by using the pumping lemma. I must do the same for the complement of this Read More …
[Solved]: Peer grading design – choosing a graph, to get accurate rankings/ratings
Problem Detail: Background. I am writing some code for semi-automated grading, using peer grading as part of the grading process. Students are given pairs of essays at a time, and the students have a slider to choose which is better and Read More …
[Solved]: Would adding recursive named functions to Simply typed lambda calculus make it Turing complete?
Problem Detail: Say I have Simply typed lambda calculus, and add an assignment rule: <identifier> : <type> = <abstraction> Where <identifier> is the name of the function, <type> is the function type and <abstraction> is the abstraction to be assigned to Read More …
[Solved]: What kind of reductions are usually used in order to prove PP-completeness?
Problem Detail: I’ve read that MAJSAT is PP-complete. Under what type of reduction is this true? What kind of reductions are usually used in order to prove PP-completeness? Asked By : Fayez Abdlrazaq Deab Answered By : D.W. Here “PP-complete” means “complete for Read More …
[Solved]: Partition problem with distinct integers
Problem Detail: Partition problem is a well known NP-complete problem. In the definitions I have seen, the input is assumed to be a multiset of integers and we want to decide the existance of a partition into two sets that have Read More …
[Solved]: What’s a fast algorithm to decide whether there is an $A_G$ corresponding to a given $chi_G(lambda)$?
Problem Detail: Given an adjacency matrix $A_G$ of an undirected graph $G$, it is easy and straightforward to compute the characteristic polynomial $chi_G(lambda)$. What about the other way around? The problem can be formulated as follows. Problem Given a polynomial $P$, Read More …
