Given a finite-state automaton A with eventualstate function N* and given any states s and t in A, we say that s and t are k-equivalent if, and only if, .______

The condition that finite-state automaton A, should satisfy to be s sand t are k− equivalent where the eventual function is N* and s and t are states in A.

Given information:

Given s and t are two states and N is an eventual-state function for a finite-state automaton A.

Let two states s and t and w be an accepted string for the finite-state automaton A.

Suppose w is a string of inputs in the length is less than or equal to k where k≥0.

When w is applied on the state s, the automaton goes to an accepting state and

when w is applied on to the state t, the automaton goes to an accepting state according to an N eventual function, we call these states as k− equivalent