Problem Detail: In the seminal distributed systems paper The Part Time Parliament (the Paxos protocol), Leslie Lamport names fictional legislators who are involved in the Paxon parliament protocol. According to this writing, he notes that: I gave the Greek legislators the Read More …
Category: Uncategorized
[Solved]: Showing that the set of TMs which visit the starting state twice on the empty input is undecidable
Problem Detail: I’m trying to prove that $L_1={langle Mrangle mid M text{ is a Turing machine and visits } q_0 text{ at least twice on } varepsilon} notin R$. I’m not sure whether to reduce the halting problem to it or Read More …
[Solved]: Partition partition with constraint of equal size
Problem Detail: I see the problem here which is the well know partition problem but with constraint that the size of both sets must be equal. I look at the answer and I don’t understand that why Colin said add max(S)⋅length(S), Read More …
[Solved]: What is wrong with this seeming contradiction with a paper about AND-compression of SAT?
Problem Detail: Got a simple construction seemingly contradicting a paper assuming plausible conjecture. Since it is unlikely the conjecture to be false, what is wrong with the argument? From a paper An AND-compression is a deterministic polynomial-time algorithm that maps a Read More …
[Solved]: Is Hidoku NP complete?
Problem Detail: A Hidoku is a $n times n$ grid with some pre-filled integers from 1 to $n^2$. The goal is to find a path of successive integers (from 1 to $n^2$) in the grid. More concrete, each cell of the Read More …
[Solved]: Bound on space for selection algorithm?
Problem Detail: There is a well known worst case $O(n)$ selection algorithm to find the $k$’th largest element in an array of integers. It uses a median-of-medians approach to find a good enough pivot, partitions the input array in place and Read More …
[Solved]: Unification vs. SAT solver
Problem Detail: I read on Wikipedia that unification is a process of solving the satisfability problem. At the same time, I know that such solvers are called “SAT solvers” or “SMT solvers”. So, are they different names for the same thing? Read More …
[Solved]: Wheel subgraph problem
Problem Detail: In the following two threads I specified the question in the wrong way (easier to solve that way). Proving that finding wheel subgraphs is NP-complete Reducing from Hamiltonian Cycle problem to the Graph Wheel problem My sincere apologies.. I Read More …
[Solved]: A list of n strings lexicographic order using the merge-sort algorithm. The worst case running time of this computation is
Problem Detail: A list of n strings, each of length n, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is __________. $O(n log n)$ $O(n^2 log n)$ $O(n^2 +log n)$ $O(n^2)$ My Read More …
[Solved]: Find a CFG for a language
Problem Detail: In an assignment I’ve been asked to find a CFG for $a^x b^y a^z b^w$, where, $x,y,z,w in mathbb{N}^+$, $y > x$, $z > w$, and $x+z = y+w$. A hint was given, think of the language as $(a^p Read More …
