Problem Detail: According to wikipedia, every finite set is computable. Definition: set $S subset N$ is computable if there exists an algorithm which defines in finite time if a given number $n$ is in Set. Question: what is wrong with this Read More …
Category: Uncategorized
[Solved]: Viterbi algorithm recursive justification
Problem Detail: I have a question regarding recursion in Viterbi algorithm. Define $pi(k; u; v)$ which is the maximum probability for any sequence of length $k$, ending in the tag bigram $(u; v)$. The base case if obvious $pi(0,*,*)=1$ The general Read More …
[Solved]: Is SAT in P if there are exponentially many clauses in the number of variables?
Problem Detail: I define a long CNF to contain at least $2^frac{n}{2}$ clauses, where $n$ is the number of its variables. Let $text{Long-SAT}={phi: phi$ is a satisfiable long CNF formula$}$. I’d like to know why $text{Long-SAT} in P$. First I thought Read More …
[Solved]: Shifting subset sum solution by constant positive integer
Problem Detail: While reading the Wikipedia article about the subset sum problem I came across this example: “is there a non-empty subset whose sum is zero? For example, given the set ${ −7, −3, −2, 5, 8 }$, the answer is Read More …
[Solved]: Example for a non-trivial PCP verifier for an NP-complete problem
Problem Detail: During my involvement in a course on dealing with NP-hard problems I have encountered the PCP theorem, stating $qquaddisplaystyle mathsf{NP} = mathsf{PCP}(log n, 1)$. I understand the technical definition of a PCP verifier, so I know in principle what Read More …
[Solved]: Relation between space and time complexity for machines with write once read many (WORM) memory
Problem Detail: While thinking about different calculi for predicate logic (like natural deduction and sequent calculus), I noticed that these calculi are (often) presented in a form suitable for “human computers”. A “human computer” is limited to use write once read Read More …
[Solved]: Compression functions are only practical because “The bit strings which occur in practice are far from random”?
Problem Detail: I would have made a comment, as this pertains to Andrej Bauer’s answer in this thread; however, I believe it is worth a question. Andrej explains that given the set of all bit strings of length 3 or less, Read More …
[Solved]: Abstract Syntax Tree of Pure Lambda Calculus
Problem Detail: I was wondering if anyone had any good references or book recommendations that cover abstract syntax trees (ASTs). Specifically, I am interested in the abstract syntax trees of different evaluation strategies (call by value vs. call by name) of Read More …
[Solved]: How do we derive the runtime cost of Karatsuba’s algorithm?
Problem Detail: I’ve read the Wikipedia article explaining the complexity analysis of the Karatsuba algorithm, but I’m not fully grasping it. I seem to have gotten about 75% of the way to the solution on my own, but lack the last Read More …
[Solved]: Simple explanation of Simon’s Problem
Problem Detail: I just read the Wiki article for Simon’s Problem but I don’t fully understand it because I don’t follow the symbolic notation used to describe functions (I am not a computer scientist). Can someone just briefly explain it in Read More …
