For each of the following languages, say whether it is decidable. Justify your answer in about 5-10 sentences. (a) L₁ = {(M, t) | Turing machine M accepts some input in at least t steps} (b) L₂ = {(M) | Turing machine M infinite loops on some input} (c) L3= {(M₁, M2) | M₁, M2 are Turing machines such that L(M₁) ‡ L(M₂)} (d) L₁ = {(M, t) | Turing machine M accepts every input in at most t steps}

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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For each of the following languages, say whether it is decidable. Justify your answer
in about 5-10 sentences.
(a) L₁ = {(M, t) | Turing machine M accepts some input in at least t steps}
(b) L2 =
{(M) | Turing machine M infinite loops on some input}
(c) L3 =
{(M₁, M2) | M₁, M2 are Turing machines such that L(M₁) ‡ L(M₂)}
(d) L₁ = {(M, t) | Turing machine M accepts every input in at most t steps}
Transcribed Image Text:For each of the following languages, say whether it is decidable. Justify your answer in about 5-10 sentences. (a) L₁ = {(M, t) | Turing machine M accepts some input in at least t steps} (b) L2 = {(M) | Turing machine M infinite loops on some input} (c) L3 = {(M₁, M2) | M₁, M2 are Turing machines such that L(M₁) ‡ L(M₂)} (d) L₁ = {(M, t) | Turing machine M accepts every input in at most t steps}
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