Problem Detail: Let $G = (V,E)$ be a directed graph with a weight function $w$ such that there are no negative-weight cycles, and let $v in V$ be a vertex such that there is a path from $v$ to every other Read More …
Category: Uncategorized
[Solved]: Can one reduce a problem of unknown complexity to a hard problem to show hardness?
Problem Detail: In this paper (page 3 Theorem 1) the authors want to prove that their problem is NP-complete. Their method is as follows. Let their problem be known as $P$. They show that their problem can be written as a Read More …
[Solved]: Approximate Bayesian Computation VS Monte Carlo Simulation
Problem Detail: I am a little confused about the differences between Approximation Bayesian Computation (ABC) and Monte Carlo Methods (MCM). Citing from wikipedia: Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical Read More …
[Solved]: Formulate the Marriage Problem into a Maximum-flow problem (Graph theory)
Problem Detail: Suppose I have $M={1,ldots, n}$ men and $W = {1, ldots, n}$ women and $B ={1, ldots, m}$ brokers, such that each broker knows a subset of $M times W$ and for each pair in this subset a marriage Read More …
[Solved]: How to determine the set of numbers read by a DFA from one state to another?
Problem Detail: Using the Deterministic Finite Automaton (Q, Σ, Δ, q_0, F): Alphabet: Σ is {(0 0), (0 1), (1 0), (1 1)} Definition of Δ to strings recursively: Δ*(q, ε) = q for all q ∈ Q Δ*(q, xa) = Read More …
[Solved]: How long would it take a computer with twice the processing power to solve a polynomial time problem?
Problem Detail: Say I have some problem of $Oleft(n^kright)$ complexity. If I were to solve the problem on a computer $x$, it would take time $t$. Now I have a new computer $x’$, which has double the computing power of $x$. Read More …
[Solved]: What kinds of programming pitfalls modern languages are able to express?
Problem Detail: I often see claims that modern functional strictly-typed languages are ‘safer’ than others. These statement mostly linked with type systems and their ability to explicitly express the following sources of pitfalls: Alternatives in function result. Maybe and Either datatypes Read More …
[Solved]: Is the universe problem for one-counter automata with restricted alphabet size undecidable?
Problem Detail: Consider the following universe problem. The universe problem. Given a finite set $Sigma$ for a class of languages, and an automaton accepting the language $L$, decide if $L=Sigma^*$. In [1], it is stated and proved that the universe problem Read More …
[Solved]: Prove or disprove that $NL$ is closed under polynomial many-one reductions
Problem Detail: If $B in NL$ and there exists a Karp reduction (polynomial-time many-one reduction) from $A$ to $B$, then $A in NL$. Prove that the above claim is correct, incorrect, or equivalent to an open question. Trying to solve Read More …
[Solved]: When to use Djikstra or Bellman-Kallaba algorithm?
Problem Detail: This the answer that was accepted for the arrangement problem of a library: we have books with heights $H_n,$ $1 le n le N$ and widths $W_n,$ with heights in ascending order for each book, and we want to Read More …