Problem Detail: I’m having trouble generating the set of strings, which a regular expressions describe. A typical regular expression can look like this: [atom_0] atom_1 (atom_2 | atorm_3 | … | atom_n-1) <var> [atom_n] Or any other combination of the following: Read More …
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[Solved]: Difference between graph-partitioning and graph-clustering
Problem Detail: What is the difference between graph-partitioning and graph-clustering in graph theory? Asked By : suhas bhairav Answered By : Yuval Filmus Graph partitioning and graph clustering are informal concepts, which (usually) mean partitioning the vertex set under some constraints (for example, Read More …
[Solved]: Building functionally complete boolean circuits out of trinary logic
Problem Detail: There are some not-very-commonly considered forms of trinary logic using 3 truth values. Even entire (unusual/rare) ternary computers have been built from it. Is there some knowledge or reference of how to convert some trinary logic systems into functionally Read More …
[Solved]: The use of multiset ordering in proving termination
Problem Detail: Based on the definition of a multiset and the information in this paper, why do we use multisets in proving the termination of a program? Is not the well-founded order enough? Asked By : M.M Answered By : Dmitri Chubarov As Read More …
[Solved]: Deciding Countability of Languages
Problem Detail: Suppose we have given $Sigma={a,b}$, Which one of the following set is not countable (a) Set of all languages over $Sigma$ (b) Set of all regular languages over $Sigma$ (c) Set of all languages over $Sigma$ accepted by Turing Read More …
[Solved]: Given 2 regular languages and their DFA’s, how to construct the DFA of the union?
Problem Detail: Suppose $L1, L2$ are both regular languages and $A1, A2$ are their corresponding DFA’s. How can I construct a new DFA for the regular language $L1 cup L2$? Asked By : slallum Answered By : Patrick87 Let’s denote the sets of Read More …
[Solved]: Creating bigger controlled nots from single qubit, Toffoli, and CNOT gates, without workspace
Problem Detail: Exercise 4.29 from Quantum Computation and Quantum Information by Nielsen and Chuang has me stumped. Find a circuit containing $O(n^2)$ Toffoli, CNOT and single qubit gates which implements a $C^n(X)$ gate (for $n > 3$), using no work qubits. Read More …
[Solved]: Dijkstras Shortest Path with Distance and Quality
Problem Detail: I want to write up a shortest as well as optimal path program for indoor navigation for people with disabilities. For the initial part of the assignment i wish to test my program through graph traversal. My application is Read More …
[Solved]: pumping lemma for $L={a^n b^m c^k mid n = m vee mneq k}$
Problem Detail: Using pumping lemma, how can I prove that $L={a^n b^m c^k mid n = m vee mneq k}$ is not regular?. If I choose $w= a^m b^m c^m$ and pump up with $i=2$, if have $a^m=1 b^m c^m$ but Read More …
[Solved]: Proving iff statement with reductions
Problem Detail: I have a statement I am trying to prove, and I’m very close, but I think I’m missing a couple of key concepts about regular and context-free languages. Question: Let $ A = { ww | w epsilon Sigma^{*} Read More …
