Lab for Automated Reasoning and Analysis LARA

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

sav08:recursive_set [2008/03/18 18:03]
vkuncak created
sav08:recursive_set [2008/03/18 18:04] (current)
vkuncak
Line 1: Line 1:
 ====== Recursive Set ====== ====== Recursive Set ======
  
-We say that a set $S$ is //​recursive//​ if there exists an algorithm that, given an element $x$ determines whether $x \in S$ holds.+We say that a set $S$ is //​recursive// ​(decidable) ​if there exists an algorithm that, given an element $x$ determines whether $x \in S$.
  
 Example: the set of even numbers is recursive. ​ The algorithm takes $x$ represented in binary and checks whether its least signifficant digit is 0. Example: the set of even numbers is recursive. ​ The algorithm takes $x$ represented in binary and checks whether its least signifficant digit is 0.
Line 7: Line 7:
 Example: the set of all pairs $(T,x)$ such that $T$ is a representation of Turing machine and $x$ is an input such that $T$ terminates on input $x$, is not recursive. Example: the set of all pairs $(T,x)$ such that $T$ is a representation of Turing machine and $x$ is an input such that $T$ terminates on input $x$, is not recursive.
  
 +Example: the set of encodings of all valid first-order logic formulas is not recursive.
 +
 +Example: the set of all valid formulas of Presburger arithmetic is recursive.
  
 
sav08/recursive_set.txt · Last modified: 2008/03/18 18:04 by vkuncak
 
© EPFL 2018 - Legal notice