Automata, Languages, and Computation
Design a Turing machine that recognizes the language For example, 0$01 e L, 10$010 E L, but 10081...
Design a Turing machine that recognizes the language L := {vSw : u, w E {0,1)" and u is a substring of u For example, 0801 E L' 10$010 E L, but i 00$10101 ¢ L. Describe the High Level algorithm informally and define the corresponding Turing Machine in details. Design a Turing machine that recognizes the language L := {vSw : u, w E {0,1)" and u is a substring of u For example, 0801 E L' 10$010 E...
Design a Turing machine that recognizes the language {a^i b^j c^k | i >= j >= k >= 0}
1. (25 points) Turing Machine Design: Design a Turing machine Mi that operates on inputs that are strings in 10, 1). Design Mi so that it recognizes the following language: fw E (0.1)l w ends in 10 or 111) a. Provide a high-level English prose description for the actions of Mi b. Provide an implementation-level description of M. c. List the parts of the formal 7-tuple for M d. Draw a detailed pictorial state diagram for M1 e. List the...
40 points) Please design a Turing machine T to recognize the union of the languages of two Turing machines Mi and M2. That is, T accepts an input string w, if and only if either Mi or M2 or both accept string w. Please describe the high-level idea (or algorithm) of your Turing machine T. You do not need to draw the low-level state transition diagram of your Turing machine. Note that the difficulty is that Mi or M2 may...
Specify a Turing machine with input alphabet Σ = {a, b} that recognizes the language L = { ww | w ∈ Σ ∗}. Is L decidable?
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,...
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}.
(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...
12. Design a Turing machine that computes the function: f(x) = x − 2 if x > 2 = 0 if x ≤ 2. I'm kind of having a little bit of a hard time understanding these concepts so it would be nice if you can explain thoroughly... thanks for the help! Formal Languages and Automata Question... 12. Design a Turing machine that computes the function f (x)x2 if x> 2 ifx<2 12. Design a Turing machine that computes the...
(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.