Prove that if L is a regular language over an alphabet , then, in first-order statement,...

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Prove that if L is a regular language over an alphabet Σ, then, in first-order statement, Vy * positive integers m, n [(m > n) ^ \z € Σ* (ym z € L if and only if y" z € L)]. Use the above result to study the regularity of the following languages: (a) L₁ = {0¹² | i > 0}. (b) L₂ = {uurv | u, v = (a + b)+}. Prove that if L is a regular language over an alphabet Σ, then, in first-order statement, Vy * positive integers m, n [(m > n) ^ \z € Σ* (ym z € L if and only if y" z € L)]. Use the above result to study the regularity of the following languages: (a) L₁ = {0¹² | i > 0}. (b) L₂ = {uurv | u, v = (a + b)+}.

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Solution Let That it L is a alphabet Then Now thing this E positive integers mnmon y ZCL if and ... View the full answer