à Consider the following pushdown automaton: 0, € → # 1, € →→ # D A €₂ € → $ B 1, € → € 0, # →→ € 1, #→→ € €, $→ € D 1. What is the input alphabet? What is the stack alphabet? Explain how you know. 2. What are the states and stack contents for processing the string 010? Is the string accepted? 3. What is the language accepted by this pushdown automata? 4. Justify why your answer about the accepted language is correct with several sentences. 3 Create a pushdown automaton to recognize the language L = {w/w is a word of Σ* of the form an+¹b" for some positive integer n}

à Consider the following pushdown automaton: 0, € → # 1, € →→ # D A €₂ € → $ B 1, € → € 0, # →→ € 1, #→→ € €, $→ € D 1. What is the input alphabet? What is the stack alphabet? Explain how you know. 2. What are the states and stack contents for processing the string 010? Is the string accepted? 3. What is the language accepted by this pushdown automata? 4. Justify why your answer about the accepted language is correct with several sentences. 3 Create a pushdown automaton to recognize the language L = {w/w is a word of Σ* of the form an+¹b" for some positive integer n}

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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A Consider the following pushdown automaton: 1, € → # A1 0, € →→ € 1, € →→ # A2 0, € →→ € 1, € → # A3 0, # →→ € A4 1. What is the input alphabet? What is the stack alphabet? Explain how you know. 2. What are the states and stack contents for processing the string 0011? Is the string accepted? 3. What is the language accepted by this pushdown automata? 4. Justify why your answer about the accepted language is correct with several sentences.
A Consider the following pushdown automaton: 0, € 0 1, € → 1 A €, € $ assume the alphabet is Σ accepts L. B = 1, € → € 0,0 € 1,1 →→ € C €, $ → € 0, € → € 1. What is the input alphabet? What is the stack alphabet? Explain how you know. 2. What are the states and stack contents for processing the string 0100? Is the string accepted? 3. What is the language accepted by this pushdown automata? 4. Justify why your answer about the accepted language is correct with several sentences. B Create a pushdown automaton to recognize the language D L = {w|w is a word of Σ* of the form ab"c" for some non-negative integers n} {a,b,c}. Write a sentence or two to justify why your pushdown automaton
Write a program that converts an infix expression into an equivalent postfix expression. The rules to convert an infix expression into an equivalent postfix expression are as follows: Suppose infx represents the infix expression and pfx represents the postfix expression. The rules to convert infx into pfx are as follows: a. Initialize pfx to an empty expression and initialize the stack. b. Get the next symbol, sym, from infx. b.1. If sym is an operand, append sym to pfx. b.2. If symis (, push sym into the stack. b.3. If sym is ), pop and append all the symbols from the stack until the most recent left parenthesis. Pop and discard the left parenthesis. b.4. If sym is an operator: b.4.1. Pop and append all the operators from the stack to pfx that are above the most recent left ( and have precedence greater than or equal to sym. b.4.2. Push sym onto the stack. c. After processing infx, some operators might be left in the stack. Pop and append to pfx everything from the stack. In this…
We wish to build the simplest deterministic PDA for the language L = {ambmcndn: m, n >0}. Recall we use a symbol Z for the bottom stack marker. What would be the size of the smallest stack alphabet needed to decide L? A. 1, i.e., r = {Z} B. 2, e.g., r = {Z,Y} C. 3, e.g., r = {Z, X, Y} D. 5, e.g., r = {Z, A, B, C, D }
Implement a c# program to illustrates why a stack is a useful data structure for many computational problems. When we convert a decimal number to another form, we start with the right-most digits and work our way to the left. Pushing each digit on the stack as we go works perfectly because when we finish, the converted digits are in the correct order.
8. Suppose you have a stack in which the values 1 through 5 must be pushed on the stack in that order, but that an item on the stack can be popped and printed at any time. So for example, the operations s.push (1) s.push (2) print s.pop() Track 1 FIGURE 7-18 Railroad switching system for Exercise 4 s.push(3) s.push (4) print s.pop() s.push(5) print s.pop() print s.pop() print s.pop() C. 1 4 35 2 Track 2 Track 3 produce the sequence 2 4 5 3 1. Based on the constraints mentioned above, give the list of operations that would produce each of the following sequences. If it is not possible, state so. a. 1 3 5 4 2 b. 2 3 4 5 1 d. 1 5 4 2 3 e. Are there sequences that cannot occur? Explain why or why not. Exercises 421
Suppose we have a PDA M that accepts a language L by final state. We want to build another PDA M' for the same language L but one that accepts by empty stack. Which of the following is true? A. This is not always possible for some PDA because some languages L cannot have a PDA that accepts by empty stack. B. We can always convert M into M' by just adding an extra state with some extra transitions for popping the remaining symbols on the stack.
Make a C# program to illustrates why a stack is a useful data structure for manycomputational problems. When we convert a decimal number to anotherform, we start with the right-most digits and work our way to the left. Pushingeach digit on the stack as we go works perfectly because when we finish, theconverted digits are in the correct order.
Consider a queue data structure, where the two operations of interest are enqueue (at the back of the queue) and dequeue (from the front of the queue). A queue is thus a FIFO (first in-first out) structure. Suppose we implement a queue by using two stacks, A and B, which support operations of push and pop, as follows: enqueue(x): push x onto stack A if B is not empty return x = pop B if B is empty repeat until A is empty x = pop A push x onto stack B return x = pop B dequeue: a) This implementation seems to correctly emulate a queue. Illustrate (by drawing the two stacks) how it works for the following sequence of enqueue and dequeue operations: enqueue 5 enqueue 7 dequeue enqueue 3 enqueue 6 enqueue 9 dequeue dequeue dequeue dequeue b) The actual cost of a push or a pop operation is 1 unit of work. What is the worst-case single operation possible after a sequence of n enqueue and dequeue operations, and what is its cost? c) Explain how a simplistic worst-case analysis would lead to…
Solve the following problems using Scala with Classic Akka Actors. For each problem, also implement client actors for sending the messages required for beginning the required computation. Use these client actors for testing your application actors. Recall the card shuffling problem. In a Faro shuffle, a stack of cards is broken up into two, and then combined so that a card from one sub-stack is followed by one from the other, and so on. A perfect Faro shuffle breaks up the stack into two sub-stacks of exactly the same size, and then combines them in the manner described above. An out-shuffle results in the top and the bottom cards of the stack remaining the same after the shuffle; an in-shuffle results in these cards becoming the second and the second last cards of the shuffled stack. Implement a shuffler actor which accepts a message containing a deck of cards as a list of even length, an integer indicating the number of times that the deck is to be shuffled, and a boolean…
Consider the Python program: def A(I, P): def B(): print (I) if I > 3: P() elif I > 2: A(4, P) elif I > 1: A (3, B) else: A(2, B) def C(): print (0) A(1, C) What does this program print? Explain your answer. Draw the run-time stack. You can use in Python print (P) and print (B) from within A to identify the procedures uniquely. 2.
Based on the below PDA (M), answer the following questions: a, &a b, a → E b,a → E E,$ → $ 90 92 93 24 Stack 1. Write in sequence the used Transition Functions for the input (aaabbb), In which you start from (q0) state. 2. What's left in the stack after consuming the input (aaabbb)? 3. Is the input Accepted or Rejected? 4 What is the Language of this machine (L(M)) that répresent