For the next three questions, consider the subset construction, It is our first example of a fixed-point algorithm.
Assume that N is the original set of NFA states. The algorithm repeatedly applies a function f(set,char) where set is a set of NFA states and char is a character in the alphabet of the NFA. For a given set of NFA states and a given character, f(x,y) either produces one of two results:
a new set of NFA states that contains the NFA that can be reached from states in x by taking a transition on y followed by zero or more transitions on epsilon; OR
the empty set, which corresponds to the error state in the DFA.
The algorithm constructs an initial set of NFA states to represent the start state (specifically, {n0 U f(n0 , epsilon)} where n0 is the NFA's start state). It iterates over all the sets x in the collection and all of the letters y in the alphabet. If computes f(x,y) and, if that produces a new state, it adds the state to the collectioon. It stops when an iteration over all the states adds no new sets to the collection. We say that the construction has reached a fixed point when the collection stops changing.
The following questions contain a statement about some property of the subset algorithm. For each property, you are to state whether the property plays a role in the algorithm reaching a fixed point (that is, terminating). Answer "true" if the property helps ensure that the algorithm reaches a fixed point and "false" if the property is simply a technique that helps make the algorithm execute more quickly.
Again:
TRUE => the property helps ensure that the algorithm reaches a fixed point
FALSE => the property simply helps the implementation run more quickly
The iterated application of f adds new members to the collection of sets of NFA states but never removes a member from the collection.
Group of answer choices
True
False