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Problem Detail: I have to generate a grammar for the language $L = { w in { a, b}^* mid |w| in 2mathbb{N}, w neq w^R}$ and give the type of the language. I’ve generated the grammar $qquad begin{align} S &to Read More …

Problem Detail: Dynamic programming algorithm for Knapsack is stated to have complexity $mathcal O (nW)$. However, I’ve also seen the complexity stated as $mathcal O (n^2V)$, where $V=max v_i$. (Here $n$ is the number of items and $W$ the weight limit). Read More …

Problem Detail: I have been told than $n^{1000001} = O(1.000001^n)$. If that’s the case, there must be some value $n$ at which $1.000001^n$ exceeds $n^{1000001}$. However, when I consult Wolfram Alpha, I get a negative value for when that occurs. http://www.wolframalpha.com/input/?i=1.000001%5Ex+%3D+x%5E1000001 Read More …

Problem Detail: I have the following grammar for a context-free language: $G = ({S,A,B}, {x,y,z}, P, S)$ with $P = {S rightarrow A, A rightarrow xAz, A rightarrow xBz, B rightarrow y}$ My question is: How to construct a pushdown automaton Read More …

Problem Detail: In resolution theorem proving, it is normally assumed variables in different clauses are distinct. This is not something that happens automatically; it requires significant extra code and computation to implement. Given that, I’m looking for a test case for Read More …

Problem Detail: Are there programming languages(or logic) that can implement(or express) a function $f:mathbb{N}to mathbb{N}$ if and only if $f$ is a computable bijective functions? Asked By : Chao Xu Answered By : Andrej Bauer There is no such language. However, have a Read More …

Problem Detail: I’m trying to count the number of divisors an integer $n$ has. The simple way to do this is to just enumerate all integers from 1 to $sqrt{n}$, and count how many integers evenly divide $n$. For example, 28 Read More …

Problem Detail: An undirected graph is a near clique if adding an additional edge would make it a clique. Formally, a graph $G = (V,E)$ contains a near clique of size $k$ where $k$ is a positive integer in $G$ if Read More …

Problem Detail:  Let $$f(x)=begin{cases} x quad text{if Goldbach’s conjecture is true } 0 quad text{otherwise}end{cases}$$ Show that f(x) is primitive recursive. I know a primitive recursive function is obtained by composition or recursion, but I don’t know what should I Read More …