Problem Detail: I have this language $ L = a^* cup left { a^mb^n|m>ngeq 0 right }^* $ I have to prove that this language is not regular but still satisfies the pumping lemma for regular languages (Since the pumping lemma Read More …
Blog
[Solved]: How to reduce from subset-sum problem?
Problem Detail: I have this problem which is described as follows: Input: You are given a multi-set $M$ (a set that can contain duplicates), and two numbers $P$ and $T$. $M = {(x_1,y_1), (x_2,y_2), …, (x_n,y_n)}$. Each $x$ and $y$ is Read More …
[Solved]: Can you reduce a precedence graph or do *all* relevant nodes need to be connected
Problem Detail: Let’s say we have the following simple transaction-schedule: T1 | T2 | T3 —–+——+—– w(x)| | | w(x) | | | w(x) T1 comes before T2, so in the precedence graph, we draw an arrow from T1 to T2. Read More …
[Solved]: How to obtain a trilateration ordering in a graph?
Problem Detail: In a sensor network graph $G = (V,E)$ $V = {1,2,…,n}$ is the set of sensors and the edge $(i,j)$ denotes that sensor $i$ and sensor $j$ are inside each other’s sensing range. The weight of that edge denotes Read More …
[Solved]: baz_num_elts exercise from Software Foundations
Problem Detail: I’m at the following exercise in Software Foundations: (** **** Exercise: 2 stars (baz_num_elts) *) (** Consider the following inductive definition: *) Inductive baz : Type := | x : baz -> baz | y : baz -> bool Read More …
[Solved]: Not understand exchanging argument proof for optimal prefix code
Problem Detail: I am currently reading the Algorithm Design textbook by Kleinberg and Tardos and I am having difficulty understanding a proof using an exchange argument Statement: A binary tree corresponding to the optimal prefix code is full Proof: This is Read More …
[Solved]: Building static hash table with particular collisions
Problem Detail: Is there efficient algorithm to encode keys in hash function with provided collisions? By efficient I mean with low-ish runtime of lookup operation (taking constants into account) and realistic time of finding such function. Keys are floating point Read More …
[Solved]: Integer Knapsack Problem – No duplicates Allowed
Problem Detail: In the bounded Integer Knapsack problem, we are given N items of sizes S1 through SN, having values V1 through VN. The problem requires us to find the maximum value that can be attained for a given capacity C, Read More …
[Solved]: Number of Final States Subset Construction for NFA to DFA
Problem Detail: “Suppose we use the subset construction to convert a $7$-state NFA $M = (Q,Sigma, delta, q_0, F)$ into a DFA $M’ = (Q’, Sigma, delta’, q_0, F’)$ for the same language. Then $M’$ will have $|Q’| = 128$ states. Read More …
[Solved]: Is it $mathsf{NP}$-hard to decide whether $mathsf{P}=mathsf{NP}$?
Problem Detail: Is it $mathsf{NP}$-hard to decide whether $mathsf{P}=mathsf{NP}$ ? If so, what are the implications ? Is there result suggesting that it is the case ? Asked By : eig Answered By : Mike B. A similar question is this: Is Read More …
