II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: a. L = {w & 01m | n is 3 times the value of m, and m > 0} b. L = {w & a³n^m' | s is >= n, and n is >= r, and r >0} c. L = {w & animk | k is >= j, and j is >= i, and i > 0}

II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: a. L = {w & 01m | n is 3 times the value of m, and m > 0} b. L = {w & a³n^m' | s is >= n, and n is >= r, and r >0} c. L = {w & animk | k is >= j, and j is >= i, and i > 0}

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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II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: a. L = {w & 01m | n is 3 times the value of m, and m >0} b. L = {w & a³nºm' | s is >= n, and n is >= r, and r >0} c. L = {w & animk | k is >= j, and j is >= i, and i >0} General Instructions: No initial state, missing transitions, or transition symbols for a machine means that the machine will be marked as incorrect.
draw a Turing Machine that accepts strings in each of the languages below. Includethe septuple of the language with transition functions as well. a . L = { a n bn an bn : n ≥ 1 } b . L = { a n b m an+m: n ≥ 0, m ≥ 1} c . L = {w : w ∈ { a ,b}+ , |w| is a multiple of 4} d. L = {a n bm bn am : m ≥ 1 , n > m } e. L = {wcw : w ∈ { a ,b}* }
II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: b. L = {w & a³n^m' | s is >= n, and n is >= r, and r>0} General Instructions: No initial state, missing transitions, or transition symbols for a machine means that the machine will be marked as incorrect. PLEASE PUT EXPLANATIONS I WILL UPVOTE
(a) Construct deterministic finite automata accepting the following languages: {w e {0, 1}"| w is not in the regular language defined by 0"1"}; (ii) {w e (0, 1}"| w has an even number of O's or an odd number of l's) (pay attention to or in this definition); (ii (w E (0, 1}"|w ends with a subword 01, i.e., w = 101 for some word z}. (i)
6. Give the state diagram for a Turing machine that decides each of the following language over E = {0, 1}: a) L6= {w:w contains both the substrings 011 and 101} b) L7= {w:w contains at least two 0's and at most two 1's}
Apply the Paint Blue algorithm discussed in class to the following Finite Automata. a a a b b a a + a b Show the status of the Finite Automata at the conclusion of the Paint Blue Algorithm (mark the visited states with an X and only include edges that have not been followed).
Construct nondeterministic pushdown automata (PDA) to accept the following languages. L = {w#wR | w is any binary string}, wR is the reverse of w.
2. [15 points] Draw a state diagram of a Turing machine accepting the language L = {x#ry | x € {0,1}* and y E {0,1,#}*}, i.e., L consists of all strings which have a prefix of the form x#x with x E {0, 1}*. Assume the tape alphabet is I = {0, 1, #, &, -}.
Construct PDAs that accept each of the following languages : (a) L = {w : w = w R, that is, w is a palindrom in {a, b} ∗} (b) L = {w : w starts and ends with the same symbol, w ∈ {a, b} ∗} (c) L = {a i .bj .ck : i + k = j}
II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: d. L = { w & akb'gc | k> 0, f is 2 times the value of k, and c = k + f} e. L = {w & a b'gc | k> 0, f = k + c, and c >= k} f. L = {w & amb cºgº | m is >= c, and c>= d, and d > o, and o >0}. General Instructions: No initial state, missing transitions, or transition symbols for a machine means that the machine will be marked as incorrect. PLEASE PUT EXPLANATIONS I WILL UPVOTE
2. Give a deterministic pushdown automata (DPDA) that recognizes the language L = {x*y°w* zl | 0
A Turing machine variant T' with the stay option for its head works Turing machines except its head can stay at the current cell after the the same as the standard transition. More formally, T' = (Q', ',I¹,8', s ,, f', r') where 8' : Q'×T' → Q'×T' x {L, R, S} with S meaning the head stays at the current position after the transition. T' accepts an input string w by entering f'. Prove that this kind of Turing machine variants are equivalent to the standard Turing machines.