The Gateway to Computer Science Excellence
0 votes
9 views

Let $L_{1},L_{2},\cdot\cdot\cdot,L_{k}$ be a collection of languages over alphbet $\Sigma$ such that:

  1. For all $i\neq j$, $L_{i}\cap L_{j}=\phi$; i.e., no string is in two of the languages.
  2. $L_{1}\cup L_{2}\cup\cdot\cdot\cdot\cup L_{k} = \Sigma^{\ast}$;i.e., every string is in one of the languages.
  3. Each of the languages $L_{i}$, for $i=1,2,\cdot\cdot\cdot,k$ is recursively enumerable.

Prove that each of the languages is therefore recursive.

in Theory of Computation by Veteran (54.9k points) | 9 views

Please log in or register to answer this question.

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,644 questions
56,511 answers
195,559 comments
101,073 users