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1. Lexactly_one = {(M, x) : M is a TM, ï ¤ Σ*, L(M) = {x}} {{M,x): M is a TM, ¤ ¤ £†, |L(M)| ≤ dec(x)} 2. LAT MOST = X Note: dec(x) converts a binary string to its corresponding decimal number. For example dec(0110) = 6. 3. Lnot_EQ = {(M₁, M₂) : M₁, M2 are TMs, L(M₁) ‡ L(M2)}

1. Lexactly_one = {(M, x) : M is a TM, ï ¤ Σ*, L(M) = {x}} {{M,x): M is a TM, ¤ ¤ £†, |L(M)| ≤ dec(x)} 2. LAT MOST = X Note: dec(x) converts a binary string to its corresponding decimal number. For example dec(0110) = 6. 3. Lnot_EQ = {(M₁, M₂) : M₁, M2 are TMs, L(M₁) ‡ L(M2)}

Database System Concepts
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
Section: Chapter Questions
Problem 1PE
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Let Σ = {0, 1} and consider the following languages. Is this language decidable / undecidable but CE / undecidable but co-CE / neither CE nor co-CE? Explain the answer. 

1. LEXACTLY_ONE = {(M, x) : M is a TM, ¤ ¤ Σ*, L(M) = {x}} 2. LAT MOST = {(M,x): M is a TM, x € Σ+, |L(M)| ≤ dec(x)} Note: dec(x) converts a binary string to its corresponding decimal number. For example, dec(0110) = 6. 3. LNOT EQ = {(M₁, M₂): M₁, M₂ are TMs, L(M₁) ‡ L(M₂)}
Transcribed Image Text:1. LEXACTLY_ONE = {(M, x) : M is a TM, ¤ ¤ Σ*, L(M) = {x}} 2. LAT MOST = {(M,x): M is a TM, x € Σ+, |L(M)| ≤ dec(x)} Note: dec(x) converts a binary string to its corresponding decimal number. For example, dec(0110) = 6. 3. LNOT EQ = {(M₁, M₂): M₁, M₂ are TMs, L(M₁) ‡ L(M₂)}
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