When are 2 finite states equivalent?a)Same number of transitionsb)Same number of statesc)Same number of states as well as transitionsd)Both are final statesCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:

Two finite states can be considered equivalent if they have the same behavior, which means that they accept the same language. In order to determine whether two states are equivalent or not, we need to compare their transition functions. The transition function of a state is a function that maps each input symbol to a next state.

Criteria for Equivalence:

To determine whether two finite states are equivalent or not, we need to consider the following criteria:

Same number of states: Two finite states can be considered equivalent only if they have the same number of states. If the number of states is different, then the two states cannot be equivalent.

Same number of transitions: Two finite states can be considered equivalent if they have the same number of transitions. If the number of transitions is different, then the two states cannot be equivalent.

Same number of final states: Two finite states can be considered equivalent if they have the same number of final states. If the number of final states is different, then the two states cannot be equivalent.

Same language: Two finite states can be considered equivalent if they accept the same language. If the language accepted by the two states is different, then the two states cannot be equivalent.

Conclusion:

From the given options, option C is the correct answer as it states that two finite states are equivalent if they have the same number of states as well as transitions. This criteria is necessary but not sufficient to determine equivalence, as we also need to consider the language accepted by the two states.

Similar Computer Science Engineering (CSE) Doubts

When are 2 finite states equivalent?

There exists an initial state, 17 transition states, 7 final states and one dumping state, Predict the maximum number of states in its equivalent DFA?

If a string S is accepted by a finite state automaton, S=s1s2s3……snwhere si∑ and there exists a sequence of states r0, r1, r2…… rn such that δ(r(i), si+1) =ri+1for each 0, 1, …n-1, then r(n) is

Top Courses for Computer Science Engineering (CSE)View all

GATE Computer Science Engineering(CSE) 2025 Mock Test Series

Question Bank for GATE Computer Science Engineering

General Aptitude for GATE

Computer Networks

Programming and Data Structures

Top Courses for Computer Science Engineering (CSE)

Top Courses for Computer Science Engineering (CSE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company