Problem Detail: I know it’s possible to build a Finite State Transducer for converting numbers from base 2 to base 4 or 8 or other powers of 2 (translating from base N to base N^M is easy). However I’ve never seen Read More …
Category: Uncategorized
[Solved]: Why don’t nodes carry as many pointers as possible in a skip list?
Problem Detail: From this main picture explaining how skip lists work from Wikipedia, we see that some nodes carry different amounts of pointers to other parts of the list: Wouldn’t it make more sense to have every node carry 4 pointers Read More …
[Solved]: Are there problems that are polynomial-time equivalent to factoring composites?
Problem Detail: It seems that factoring a number known to be composite is in its own interesting little complexity class, e.g. polynomial time using quantum computing even though no one has proved $mathsf{P} = mathsf{NP}$ for quantum computing. Are there interesting, Read More …
[Solved]: Reconstructing a data table from cross-tabulation frequencies
Problem Detail: Say there is a data table $D$ that we cannot see, with $M$ columns. We are given exact cross-tabulation frequencies for all ${M choose 2}$ pairs of columns, that is how often each combination of two values occurs. From Read More …
[Solved]: Does the normal form theorem imply that every partially computabe function is primitive recursive?
Problem Detail: This is Normal Form Theorem (Second Edition of Computability, Complexity, and Languages written by Martin Davis page 75): Let $f(x_1,…,x_n)$ be a partially computable function. Then there is a primitive recursive predicate $R(x_1,…,x_n,y)$ such that: $f(x_1,…,x_n) = L(min R(x_1,…,x_n,z)_z)$ Read More …
[Solved]: Does a regular expression model the empty language if it contains symbols not in the alphabet?
Problem Detail: Suppose $Sigma = { a,b }$ and the regular expression $(a^*b+dc)^*(b^*d + ad)^*$. Is it equal to $varnothing$? So I have a regular expression like this: $(a^*b+dc)^*$. As only $(a,b) in Sigma$, I see that: $dc=varnothing$ So $(a^*b+dc)^*=(a^*b)^*$. Then: Read More …
[Solved]: Removing arbitrary element from Max Heap
Problem Detail: Which of the following strategies is more feasible? Strategy 1: Remove the element from the array, compress the array and reheapify. Strategy 2: Update the value of this node to the current maximum value in the heap + 1, Read More …
[Solved]: MGU and Variable Standardization – CNF
Problem Detail: I have been reading on converting first order logic sentences to conjunctive normal form, and then performing resolution. One of the steps of converting to CNF, is to Standardize variables: rename all variables so that each quantifier has its Read More …
[Solved]: How do I classify my emulator input optimization problem, and with which algorithm should I approach it?
Problem Detail: Due to the nature of the question, I have to include lots of background information (because my question is: how do I narrow this down?) That said, it can be summarized (to the best of my knowledge) as: What Read More …
[Solved]: Maximum independent nodes subset algorithm with strong constraint
Problem Detail: I’ve a tree with weighed nodes, the problem is to flag a subset of nodes with the following constraints: The selected nodes must be the optimal solution (maximal sum of weight). If one node is flagged no adjacent nodes Read More …
