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Use the Myhill-Nerode theorem to prove that the language $\left\{a^i \mid i\right.$ is a perfect square $\}$ is not regular.

    Use the Myhill-Nerode theorem to prove that the language $\left\{a^i \mid i\right.$ is a perfect square $\}$ is not regular.

Languages and Machines: An Introduction to the Theory of Computer Science

Languages and Machines: An Introduction to the Theory of Computer Science

Thomas A. Sudkamp 2nd Edition

Chapter 7, Problem 23

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The language in question is \( L = \{a^i \mid i \text{ is a perfect square}\} \). The Myhill-Nerode theorem states that a language is regular if and only if there are a finite number of equivalence classes of the relation \( R_L \), where \( x R_L y \) if and only Show more…

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Use the Myhill-Nerode theorem to prove that the language $\left\{a^i \mid i\right.$ is a perfect square $\}$ is not regular.

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