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Question 2 Given that a language is both Turing-Recognizable and co-Turing-Recognizable what can we say about the language? (Note: By best we mean the machine that will halt on the most possible strings) We can design a machine for the language such that it will halt on every string The best machine we can design for this language will possibly loop on rejected strings The language is decidable The language is undecidable The best machine we can design for this language will possibly loop on accepted strings Question 3 Which of the following is true regarding the following statements: L₁ and L2 are context free languages. L₁ L2 may be undecidable O False. CFLs are decidable, and L₁ L₂ is a subset of L₁ and L₂. Since L₁ L₂ is a subset of a decidable language, L₁ L2 must also be decidable. O None of the above O True, L₁ L2 may be co-Turing-recognizable and undecidable. O False, because CFLS are decidable, and decidable languages are closed under intersection. O True, since CFLs are not closed under intersection, L₁ L₂ might not be a CFL and may be an undecidable language. Question 4 According to Cantor's definition of size which is necessary to prove the sets A and B are the same size. O A function f maps A to B and is a one-to-one correspondence (bijection). O Some Turing-Machine should process the input for A in the same amount of steps as B. O A function of maps A to B and is an onto (surjective) function. O If two sets are infinite every element in A must exist in B. Otherwise their cardinalities must be the same. O A function f maps A to B and is a one-to-one (injective) function.

Question 2 Given that a language is both Turing-Recognizable and co-Turing-Recognizable what can we say about the language? (Note: By best we mean the machine that will halt on the most possible strings) We can design a machine for the language such that it will halt on every string The best machine we can design for this language will possibly loop on rejected strings The language is decidable The language is undecidable The best machine we can design for this language will possibly loop on accepted strings Question 3 Which of the following is true regarding the following statements: L₁ and L2 are context free languages. L₁ L2 may be undecidable O False. CFLs are decidable, and L₁ L₂ is a subset of L₁ and L₂. Since L₁ L₂ is a subset of a decidable language, L₁ L2 must also be decidable. O None of the above O True, L₁ L2 may be co-Turing-recognizable and undecidable. O False, because CFLS are decidable, and decidable languages are closed under intersection. O True, since CFLs are not closed under intersection, L₁ L₂ might not be a CFL and may be an undecidable language. Question 4 According to Cantor's definition of size which is necessary to prove the sets A and B are the same size. O A function f maps A to B and is a one-to-one correspondence (bijection). O Some Turing-Machine should process the input for A in the same amount of steps as B. O A function of maps A to B and is an onto (surjective) function. O If two sets are infinite every element in A must exist in B. Otherwise their cardinalities must be the same. O A function f maps A to B and is a one-to-one (injective) function.

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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Question 2 Given that a language is both Turing-Recognizable and co-Turing-Recognizable what can we say about the language? (Note: By best we mean the machine that will halt on the most possible strings) We can design a machine for the language such that it will halt on every string The best machine we can design for this language will possibly loop on rejected strings The language is decidable The language is undecidable The best machine we can design for this language will possibly loop on accepted strings Question 3 Which of the following is true regarding the following statements: L₁ and L2 are context free languages. L₁ L₂ may be undecidable False. CFLs are decidable, and L₁ L₂ is a subset of L₁ and L₂. Since L₁ L₂ is a subset of a decidable language, L₁ L2 must also be decidable. O None of the above O True, L₁ L₂ may be co-Turing-recognizable and undecidable. O False, because CFLs are decidable, and decidable languages are closed under intersection. O True, since CFLs are not closed under intersection, L₁ L₂ might not be a CFL and may be an undecidable language. Question 4 According to Cantor's definition of size which is necessary to prove the sets A and B are the same size. O A function f maps A to B and is a one-to-one correspondence (bijection). Some Turing-Machine should process the input for A in the same amount of steps as B. O A function of maps A to B and is an onto (surjective) function. O If two sets are infinite every element in A must exist in B. Otherwise their cardinalities must be the same. O A function f maps A to B and is a one-to-one (injective) function.
Transcribed Image Text:Question 2 Given that a language is both Turing-Recognizable and co-Turing-Recognizable what can we say about the language? (Note: By best we mean the machine that will halt on the most possible strings) We can design a machine for the language such that it will halt on every string The best machine we can design for this language will possibly loop on rejected strings The language is decidable The language is undecidable The best machine we can design for this language will possibly loop on accepted strings Question 3 Which of the following is true regarding the following statements: L₁ and L2 are context free languages. L₁ L₂ may be undecidable False. CFLs are decidable, and L₁ L₂ is a subset of L₁ and L₂. Since L₁ L₂ is a subset of a decidable language, L₁ L2 must also be decidable. O None of the above O True, L₁ L₂ may be co-Turing-recognizable and undecidable. O False, because CFLs are decidable, and decidable languages are closed under intersection. O True, since CFLs are not closed under intersection, L₁ L₂ might not be a CFL and may be an undecidable language. Question 4 According to Cantor's definition of size which is necessary to prove the sets A and B are the same size. O A function f maps A to B and is a one-to-one correspondence (bijection). Some Turing-Machine should process the input for A in the same amount of steps as B. O A function of maps A to B and is an onto (surjective) function. O If two sets are infinite every element in A must exist in B. Otherwise their cardinalities must be the same. O A function f maps A to B and is a one-to-one (injective) function.
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