1. Convert the following Right Linear grammar (RLG) into a non-deterministic Finite State Automaton (NFSA). S> abA/B A> bA / as B> aA / ba/ e 2. Give a Deterministic Finite State Automaton (DFSA) to decide the language of all strings that start with 'aa' and finish with 'ba'. 3. Draw a Right Linear Grammar (RLG) to decide the language of all strings that contain the start with 'aa' and finish with 'ba'.

1. Convert the following Right Linear grammar (RLG) into a non-deterministic Finite State Automaton (NFSA). S> abA/B A> bA / as B> aA / ba/ e 2. Give a Deterministic Finite State Automaton (DFSA) to decide the language of all strings that start with 'aa' and finish with 'ba'. 3. Draw a Right Linear Grammar (RLG) to decide the language of all strings that contain the start with 'aa' and finish with 'ba'.

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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answer the following and explain Establish that L is context-free by building a CF grammar for L = {0n1m: n does not equal 6m and n,m ≥0}
Consider the grammar G = ({S, A}, S, {a, b}, P) with the following set of production rules P: S → aS|baA|abaAA → aAbb|aAb|ε 1. Determine what the language generated by G is. You may only use set builder notation and/or language operators in your answer. A proof is not required. 2. Show that the grammar G is ambiguous by: (a) Providing two distinct leftmost derivations for the same string w ∈ L(G).(b) Providing two distinct parse trees for the same string w ∈ L(G).
(20 Points) Consider the following grammars where S is the start symbol and a, b, and c are terminal symbols and A, B, and C are non-terminal symbols.S ---> aA | bB | cCA --> aA | aB | aB --> bB | bC | bC --> cC | cExplain in your own words what the grammar generates. Which of the following sentences are in the language generated by the grammar? Show derivations. If a sentence cannot be generated by the grammar, explain why abcabcab aaaaaabb cccccaaaa bbbbbbbc aaaaaaccc
Consider the following simple Probabilistic Context-Free Grammar (PCFG), which we will use to parse the sentence “student types program with keyboard”. . Find each of the possible parses of the sentence using the grammar, and draw the parse tree for each of these parses. Show the probability at each node. b. For each parse, calculate its probability, which will be the product of the probabilities for all the rules used in generating it. Which one is the most probable and the most likely parse for a human reader?
Exercise 1 Consider the following BNF grammar for a language. Answer the questions below according to the grammar. <fun> -> <pon> <fun> -> <pon> + <fun> <ybu> -> <fun> <ybu> -> <fun> @ <ybu> <pon> -> A <pon> -> Y <pon> -> B <pon> -> U A. What is the associativity of the @ operator: left-right-neither B. What is the associativity of the + operator: left-right-neither C. Which operator has higher precedence: @-+-neither D. The grammar is left recursive-right recursive-both-neither
For each of these languages, give both a context-free grammar and a push down automaton. Briefly explain how your CFG and PDA work. Your CFG should be relatively simple and contain at most 6 variables. For this question, your PDA cannot be directly convertedfrom your CFG (a)L1={ x#y | x is a prefix of yR, and y∈{a,b}* } ,Σ ={a,b,#} Recall that wR is w written backwards, and u is a prefix of v if v=ut for some stringt.For example bb#abb is in L1, but a#ab is not. (b)L2={ aibjck | i ≥ j or j ≥ k } (c)L3 = {w∈{a,b}* | w contains an unequal number of a’s and b’s}
Consider the grammar:S →aAbB | CCA →a | CB | εB →bB | dC →aC | d | ε where S, A, B, and C are non-terminals, S is the start variable, and a, b, c, and d are terminals. Does the grammar have a predictive recursive descent parser? If the grammar has a predictive recursive descent parser, show that the conditions of predictive parsing apply for every non-terminal. On the other hand, if the grammar does not have a predictive recursive descent parser, then show ALL the conditions of predictive parsing that fail.
In Example 6.1, show a derivation tree for the string ababbac, using both the original and the modified grammar. EXAMPLE 6.1 Consider G = ({A, B}, {a, b, c}, A, P) with productions A→a|aaA|abBc,B→abbA|b.A→a|aaA|abBc,B→abbA|b. Using the suggested substitution for the variable B, we get the grammar Ĝ with productions A→a|aaA|ababbAc|abbc,B→abbA|b.A→a|aaA|ababbAc|abbc,B→abbA|b. The new grammar Ĝ is equivalent to G. The string aaabbc has the derivation A ⇒ aaA ⇒ aaabBc ⇒ aaabbc in G, and the corresponding derivation A ⇒ aaA ⇒ aaabbc in Ĝ. Notice that, in this case, the variable B and its associated productions are still in the grammar even though they can no longer play a part in any derivation. We will next show how such unnecessary productions can be removed from a grammar.
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Question 3 a) Consider the grammar E → E + E | E ∗ E | (E) | id. I. Change ambiguous grammar to non-ambiguous? II. Give a context-free grammar for generating the set of palindromes over the alphabet a,b. III. Give a context-free grammar for generating all strings over a,b such that | a |= 2∗ | b
4. Given the language L = {wxwR: w ∈ {a, b}*, x is a fixed terminal symbol}, answer the following questions: a) Write the context-free grammar that generates L b) Construct the pda that accepts L from the grammar of (a) c) Construct the pda that accepts L directly based on the similar skill used in wwR. d) Is this language a deterministic context-free language?