8. Construct Turing machines that will accept the following languages on \(\{\mathrm{a}, \mathrm{b}\}\)
(c) \(L=\{w:|w|\) is a multiple of 4\(\}\).
(g) \(L=\left\{a^{n} b^{n} a^{n} b^{n}: n \neq 0\right\}\).
(h) \(\left.L=a^{n} b^{2 n}: n \geq 1\right\}\).
Construct Turing machines that will accept the following languages on {a, b}:
5. 20 Points Draw transition diagrams for standard Turing machines that accept the following languages. In each case, give a brief description in English of your strategy. (a) Ls {ww w e {a, b}*} (b) Le wu w, и € fа, b}*, |u| 3D lul}
(a) Turing Machines can easily be designed to recognize regular languages. Construct either a Turing Machine that accepts the language denoted by the regular expression 0^*1 for the alphabet Σ = {0, 1}. Choose a random string in the language and trace through it (step by step) using your machine
Suppose L1, L2, and L3 are languages and T1, T2, and T3 are Turing machines such that L(T1) = L1, L(T2) = L2, L(T3) = L3, knowing that T3 is recursive (always halts, either halts and accepts or halts and rejects) and both T1 and T2 are recursive enumerable so they may get stuck in an infinite loop for words they don't accept.. For each of the following languages, describe the Turing machine that would accept it, and state whether...
Give transition diagrams for Standard Turing Machines that accept the following language L = {ww : w ∈ {a, b} ∗}
Give state diagrams (pictures) for Turing Machines that decide the following languages over the alphabet {0.1}: 1. {w | w contains an equal number of 0s and 1s} 2. {w | w does not contain twice as many 0s as 1s}.
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
(9 pts 3 pts each) For each of the following languages, name the least powerful type of machine that will accept it, and prove your answer. (Hint: a finite state automata is less powerful than a pushdown automata, which in turn is less powerful than a Turing Machine.) For example, to prove a language needs a PDA to accept it, you would use the Pumping Lemma to show it is not regular, and then build the PDA or CFG that...
please solve the problems(True/False questions) 25. There is a problem solvable by Turing machines with two tapes but unsolvable by Turing machines with a single tape 26. The language L = {(M, w) | M halts on input w} is recursively enumerable 27. The language L = {(M,w) | M halts on input w is recursive ne language L = {a"o"c" | n 2 1} in linear time 24. Nondeterministic Turing machines have the same expres siveness as the standard...
4) For the alphabet S={a, b}, construct an FA that accepts the following languages. (d) L= {all strings with at least one a and exactly two b's} (e) L= {all strings with b as the third letter} (f) L={w, |w| mod 4 = 0} // the cardinality of the word is a multiple of 4
1. Construct a NESA with at least one s-moves to accept each of the following languages. (a) (we 10,1)* | w corresponds to the binary encoding of a positive integer that is (b)(a"ba" | m, n 20 and n%3 m%3} For instance, b, aba, aabaa, aaab, abaaaa, (c) (we (a,b* | w contains two consecutive b's that are not immediately followed by an divisible by 16 or is odd. aaaaabaa are in the language, but abãa is not. a'). For...