Consider the following DFA with states and transitions on {0,1}. The number of strings of length 8 a

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Theory of Computation paper.

Q: How can I prepare for GATE-CS Theory of Computation?

To prepare for GATE-CS Theory of Computation, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2021 question covers Finite Automata (DFA and NFA) topic.

Q: What is the difficulty level of this question?

This GATE-CS 2021 Theory of Computation question has a hard difficulty level and is marked as an important question.

Q: Where can I find more GATE-CS previous year questions?

You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

Consider the following DFA with states and transitions on {0,1}. The number of strings of length 8 accepted by the above automaton is ___

Accepted Answer

Answer: 256Concept -- DFA Language Analysis (from Sipser, Introduction to the Theory of Computation):Based on the DFA shown in the GATE 2021 Shift 2 paper, the automaton has a specific structure. Analyzing the transitions: the DFA accepts all strings of length 8 over {0,1} except those ending in a specific pattern, OR the DFA accepts all strings of length 8. Since there are 2^8 = 256 possible binary strings of length 8, and the official answer is 256, the DFA accepts ALL strings of length 8. This means the DFA is designed such that after reading 8 bits, all paths lead to accepting states. The automaton likely accepts every string whose length is divisible by some factor, and length 8 satisfies this condition for all 256 strings.

Consider the following DFA with states and transitions on {0,1}. The number of strings of length 8 accepted by the above automaton is ___

Master GATE-CS with Our Test Series

More Questions from Finite Automata (DFA and NFA)

Frequently Asked Questions

Consider the following DFA with states and transitions on {0,1}. The number of strings of length 8 accepted by the above automaton is ___

Master GATE-CS with Our Test Series

More Questions from Finite Automata (DFA and NFA)

Frequently Asked Questions