Problem Detail: These lecture slides sketch a proof that $L={ a^n b^n mid n geq 0 } cup { a^n b^{2n} mid n geq 0 }$ cannot be accepted by any Deterministic Pushdown Automaton. Unfortunately, the slides give no references as Read More …
Author: ignougroup
[Solved]: Is DSPACE properly contained in NSPACE?
Problem Detail: It may be a dumb question, but is $mathsf{DSPACE}(f(n)) subset mathsf{NSPACE}(f(n))$ or is $mathsf{DSPACE}(f(n)) subseteq mathsf{NSPACE}(f(n))$? In other words, is the containment relation proper or not? Wikipedia says the first one, while the ComplexityZoo says the other one. Asked Read More …
[Solved]: How to partition a set into a given number of disjoint subsets subject to some conditions?
Problem Detail: I am given a set $Atriangleq{1,ldots,k}$, an integer $sleqslant k$, and non-negative integers $a_{ij}$. My problem is to find $s$ disjoint subsets $S_j$ of ${1,ldots,k}$ such that: $bigcup_{j=1}^s S_j=A$; and $|S_j|leqslant a_{ij}$ for all $iin S_j$ and $j=1,ldots,s$. How Read More …
[Solved]: What’s the difference between clock replacement & LRU replacement?
Problem Detail: As title. When we want to request following page numbers 2,4,4,2,5,2,1,1,3,1, is clock replacement better? What are the advantages and disadvantages of them? Thanks~ Asked By : Echo0831 Answered By : Rick Decker Coincidentally, for your reference string, both LRU and Read More …
[Solved]: Proof of Karp-Lipton theorem
Problem Detail: I am trying to understand the proof of the Karp-Lipton theorem as stated in the book “Computational Complexity: A modern approach” (2009). In particular, this book states the following: Karp-Lipton theorem If NP $subseteq$ $P_{backslash poly}$, then PH $= Read More …
[Solved]: Probabilistic algorithm with two-sided error
Problem Detail: I am currently studying probabilistic algorithms and came across three major complexity classes: BPP: worst-case polynomial time, two-sided error RP: worst-case polynomial time, one-sided error ZPP: average-case polynomial time, no error At first I couldn’t understand why one would Read More …
[Solved]: Counter example to graph coloring heuristic using BFS
Problem Detail: I am considering the following heuristic for the graph coloring problem (i.e. to color a graph $G$ using a minimal number of colors so that no two adjacent vertices have the same color): Explore the vertices of $G$ in Read More …
[Solved]: Complement of CFL is Recursive
Problem Detail: If CFL are not closed under complementation, it means that if a language ‘$L$’ is CFL then its compliment $L^C$ is not CFL. Then how can we discuss about $L^C$ being recursive? My doubt arose because I think if Read More …
[Solved]: Why does quicksort work well with virtual memory?
Problem Detail: Introduction to Algorithms said that quicksort “works well even in virtual-memory environments,” but didn’t explain why. I’ve tried looking an Wikipedia and Stack Exchange, but found no reason why. Is it just because quicksort sorts in place? Asked By Read More …
[Solved]: Number of Hamiltonian cycles on a Sierpiński graph
Problem Detail: I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you Read More …
