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Specify in detail a (deterministic) a Turing machine that accepts the language L = a* ba*...
Specify a Turing machine with input alphabet Σ = {a, b} that recognizes the language L...
Specify a Turing machine with input alphabet Σ = {a, b} that recognizes the language L = { ww | w ∈ Σ ∗}. Is L decidable?
(a) Give a high level description of a single-tape deterministic Turing machine that decides the language...
(a) Give a high level description of a single-tape deterministic Turing machine that decides the language L = {w#x#y | w ∈ {0, 1} ∗ , x ∈ {0, 1} ∗ , y ∈ {0, 1} ∗ , and |w| > |x| > |y|}, where the input alphabet is Σ = {0, 1}. (b) What is the running time (order notation) of your Turing machine? Justify your answer.
Draw the transition graph of a Standard Turing Machine (TM) that accepts the language: L =...
Draw the transition graph of a Standard Turing Machine (TM) that accepts the language: L = {(ba)^n cc: n greaterthanorequalto 1} Union {ab^m: m greaterthanorequalto 0} Write the sequence of moves done by the TM when the input string is w = bab. Is the string w accepted?
Give an informal description of a deterministic Turing machine for the language L = {w ∈...
Give an informal description of a deterministic Turing machine for the language L = {w ∈ {0, 1}* | w is not of the form (01)^n (10)^n for n ≥ 0}.
Construct a Turing Machine (TM) that accepts the following language, defined over the alphabet Σ =...
Construct a Turing Machine (TM) that accepts the following language, defined over the alphabet Σ = {0,1): at accepts the tollowing language, define [10] Give the transition diagram and explain the algorithm implemented by your TM.
a) What language is accepted by the Turing machine d(%-a)-(%-a, R), d(%-a)-(9-a, R). (5) Design a...
a) What language is accepted by the Turing machine d(%-a)-(%-a, R), d(%-a)-(9-a, R). (5) Design a Turing machine that will accept language OL-L6.a) (6) Design a Turing machine that will calculate fx)-3x. You must show the representation of s and 3x on the tape of Turing machine when the calculation starts and ends, respectively Extra Questions (20 points) 1. Fill the proper words in the blank (1) Given alphabet Σ, a language on Σ isa (2) Given a grammar G,...
Turing Machines - Models of Language and Computation 8. (7 points) Consider the deterministic Turing machine M (s, t, h), includes fa, b, u) and possibly other symbols, H following rules, along with...
Turing Machines - Models of Language and Computation
8. (7 points) Consider the deterministic Turing machine M (s, t, h), includes fa, b, u) and possibly other symbols, H following rules, along with possibly other rules: (K, Σ, δ, s,H), where K (h), and includes the 6(s,凵) = (t,-) δ(t, a) = (t,-) 6(r,L) = (h, a) Here凵represents a blank. Suppose M is started in the configuration 凵aababaa in the start state with the read write head scanning the blank...
. Please design a standard TM (i.e., a single semi-infinite tape, deterministic) for the laın gua...
. Please design a standard TM (i.e., a single semi-infinite tape, deterministic) for the laın guage of all palindromes over alphabet {a, b} . Please give both the high-level description (text description or pseudo-code algorithm) and the low-level state transition diagram. Please analyze how many steps (one transition is considered as a step) it takes to accept an input palindrome with n symbols . Please design a deterministic Turing machine with two semi-infinite tapes for the same language. Please give...
2. Let L = {hMi: M is a Turing machine that accepts at least two binary strings}. a) Define the notions of a recognisabl...
2. Let L = {hMi: M is a Turing machine that accepts at least two
binary strings}. a) Define the notions of a recognisable language
and an undecidable language. [5 marks] b) Is L Turing-recognisable?
Justify your answer with an informal argument. [5 marks] c) Prove
that L is undecidable. (Hint: use Rice’s theorem.) [20 marks] d)
Bonus: Justify with a formal proof your answer to b). [20
marks]
2. Let L-M M): M is a Turing machine that accepts...
Show that the language A = {<M1> | the language accepted by the Turing Machine M1...
Show that the language A = {<M1> | the language
accepted by the Turing Machine M1 is 1*} is
not decidable. Present your proof in the style of the proof of Th.
5.3, which shows below.
PROOF We let R be a TM that decides REGULARTm and construct TM S to decide ATM. Then S works in the following manner. S - "On input (M, w), where M is a TM and w is a string: 1. Construct the following...
Draw the transition graph of a Standard Turing Machine (TM) that accepts the language: L = {(ba)^n cc: n greaterthanorequalto 1} Union {ab^m: m greaterthanorequalto 0} Write the sequence of moves done by the TM when the input string is w = bab. Is the string w accepted?
Construct a Turing Machine (TM) that accepts the following language, defined over the alphabet Σ = {0,1): at accepts the tollowing language, define [10] Give the transition diagram and explain the algorithm implemented by your TM.
a) What language is accepted by the Turing machine d(%-a)-(%-a, R), d(%-a)-(9-a, R). (5) Design a Turing machine that will accept language OL-L6.a) (6) Design a Turing machine that will calculate fx)-3x. You must show the representation of s and 3x on the tape of Turing machine when the calculation starts and ends, respectively Extra Questions (20 points) 1. Fill the proper words in the blank (1) Given alphabet Σ, a language on Σ isa (2) Given a grammar G,...
Turing Machines - Models of Language and Computation
8. (7 points) Consider the deterministic Turing machine M (s, t, h), includes fa, b, u) and possibly other symbols, H following rules, along with possibly other rules: (K, Σ, δ, s,H), where K (h), and includes the 6(s,凵) = (t,-) δ(t, a) = (t,-) 6(r,L) = (h, a) Here凵represents a blank. Suppose M is started in the configuration 凵aababaa in the start state with the read write head scanning the blank...
. Please design a standard TM (i.e., a single semi-infinite tape, deterministic) for the laın guage of all palindromes over alphabet {a, b} . Please give both the high-level description (text description or pseudo-code algorithm) and the low-level state transition diagram. Please analyze how many steps (one transition is considered as a step) it takes to accept an input palindrome with n symbols . Please design a deterministic Turing machine with two semi-infinite tapes for the same language. Please give...
2. Let L = {hMi: M is a Turing machine that accepts at least two
binary strings}. a) Define the notions of a recognisable language
and an undecidable language. [5 marks] b) Is L Turing-recognisable?
Justify your answer with an informal argument. [5 marks] c) Prove
that L is undecidable. (Hint: use Rice’s theorem.) [20 marks] d)
Bonus: Justify with a formal proof your answer to b). [20
marks]
2. Let L-M M): M is a Turing machine that accepts...
Show that the language A = {<M1> | the language
accepted by the Turing Machine M1 is 1*} is
not decidable. Present your proof in the style of the proof of Th.
5.3, which shows below.
PROOF We let R be a TM that decides REGULARTm and construct TM S to decide ATM. Then S works in the following manner. S - "On input (M, w), where M is a TM and w is a string: 1. Construct the following...
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