Problem Detail: Let $L = { <M> | M$ halts on every input $x$ in at most $200 * |x|$ steps $}$. Is $L$ decidable? Recognizable? Given that membership in $L$ asserts something about $M$’s behavior on an infinite set of Read More …
Category: Uncategorized
[Solved]: lexicographic depth-first search complexity class
Problem Detail: It seems to me to be incorrect to say that lexicographic DFS is P-complete, since it isn’t a decision problem. There is a corresponding decision problem, first DFS ordering, which is known to be P-complete. However, I want to Read More …
[Solved]: Genetic Algorithm Minimum Population Size
Problem Detail: Is there a minimum limit to a pool (population) size when using the genetic algorithm to solve an optimization problem? For example a population of size 2. Asked By : Declan Murphy Answered By : Philippe Olivier I had a similar Read More …
[Solved]: What happens to multi-qubit quantum state after one of qubits is measured?
Problem Detail: If we have a quantum state consisting of (let’s say) 3 entangled qubits and we read the value of one of them, what happens to the probabilities of the remaining possible states? For example, if we have three entangled Read More …
[Solved]: 2 cases for P = NP
Problem Detail: As we all know the million dollar question in Computer Science P=NP or not. I was trying to understand it and got some doubts please tell me whether I’m right or wrong N=NP in two cases Case 1: We Read More …
[Solved]: Sorting numbers in $O(1)$
Problem Detail: Here is an experiment I came up with (I don’t have sufficient material to make it): Say that, you have a list of $n$ numbers $L = {l_1, l_2, …, l_n}$. And you have bars representing those numbers like Read More …
[Solved]: Proof of big theta using induction
Problem Detail: Here is a recursive definition for the runtime of some unspecified function. $a$ and $c$ are positive constants. $T(n) = a$, if $n = 2$ $T(n) = 2T(n/2) + cn$ if $n > 2$ Use induction to prove that Read More …
[Solved]: Optimal upper bound on the number of states in the complement of an NFA
Problem Detail: I have my own version of lex and I would like to add the complement operation. Derived from that I can then add the intersection and difference also. My version also supports the generation of NFAs (Non-deterministic Finite Automaton) Read More …
[Solved]: What is a fixed point in the context of Roger’s fixed-point theorem?
Problem Detail: In the Wikipedia article on Rogers’ theorem, it is stated that all total computable functions have a fixed point. The notation is a little hard for me to understand; a symbol is used that is used to denote “semantic Read More …
[Solved]: What does it mean to say that there doesn’t exist an algorithm from a TM point of view?
Problem Detail: A TM for a recursive language corresponds to our informal notion of an algorithm. as per Automata Theory, Languages and Computation by Ullman et al. Then there are languages called RE and $L_d$, where there exist TM that Read More …
