Consider Let Bindings in lettuce. Consider the following operational semantic rule: error eval(e₁,0)= U₁. eval(e2,0)= U₂, U₁ eval(Let(id, e₁,e₂), 0) = U₂ The remaining semantic rules are as in the "Lettuce-Let Language" notebook. Specifically, the semantics for Constants and Identifiers are recalled here: eval(Const(v), o) = xE domain(e) eval(Identix), e) = a(x) x (const-rule) a false What is the value of the following program under these semantics: let x-10 in O O b. 10 (ident-ok-rule) x@domain(e) eval(Ident(x), e) error (ident-nok-rule)

Consider Let Bindings in lettuce. Consider the following operational semantic rule: error eval(e₁,0)= U₁. eval(e2,0)= U₂, U₁ eval(Let(id, e₁,e₂), 0) = U₂ The remaining semantic rules are as in the "Lettuce-Let Language" notebook. Specifically, the semantics for Constants and Identifiers are recalled here: eval(Const(v), o) = xE domain(e) eval(Identix), e) = a(x) x (const-rule) a false What is the value of the following program under these semantics: let x-10 in O O b. 10 (ident-ok-rule) x@domain(e) eval(Ident(x), e) error (ident-nok-rule)

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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1. Prove that the language L(G) is not regular where G is the following context-free grammar: G = ({S,A,B,C}, {a,b}, {S->bB|C, A>b|C, B->Sb, C->aAa }, S). Note: You must first determine L(G).
3. Write a sentence that is true in an interpretation A if, and only if, the domain of A contains exactly two elements. 4. Write a sentence that is true in an interpretation A if, and only if, the domain of 2A contains exactly three elements.
Problem 3 Show that the following language is decidable: INFINITECEG = {(G) |G is a context-free grammar such that L(G) is infinite}
Prove that the following language is regular.L = {x | x ∈ {0, 1}∗, x does not contain five consecutive 0's or five consecutive 1's}Hint: You may take advantage of some closure properties.
Context-free grammars are sometimes used to model natural languages. In this problem you will model a fragment of the English language using context-free grammars. Consider the following English sentences: The girl is pretty. The girl that the boy likes is pretty. The girl that the boy that the clerk pushed likes is pretty. The girl that the boy that the clerk that the girl knows pushed likes is pretty. This is a special type of sentence built from a subject (The girl), a relative pronoun (that) followed by another sentence, a verb (is) and an adjective (pretty). Give a context-free grammar G that models this special type of sentence. Your terminals should be words or sequences of words like pretty or the girl. Is the language of G regular? If so, write a regular expression for it. If not, prove using the pumping lemma for regular languages. Can you give an example of a sentence that is in G but does not make sense in common English?
Question 4. Recursive Descending subroutine with EBNF rule, using C or Java syntax Type (Recursive-Descent Subprogram): -> while () ; The lex method to be used reads a single lexeme, and the lexemes' token code is in the nextToken variable. is to the left. Suppose that the defined tokens are respectively: while - WHILE_CODE left parantex - LEFTPAREN_CODE right parenthesis - RIGHTPAREN_CODE semicolon - SEMICOLON_ CODE If any error is caught, create the function that calls the error function.
1. Use the algorithm described in class that takes a CFG and converts it into a CNF (Chomsky Normal Form) grammar that generates the same language as the original grammar, except possibly for the string A, to answer the following question. As part of your answer, you should say which variables are nullable, and you should give the appropriate grammar after each step of the algorithm. There are four steps. Give a CFG (context-free grammar) in CNF (Chomsky Normal Form) that generates the same language, except possibly for the string A, as the following grammar: SAB AB →bAa A → aaB bb
Given the grammar G with following production rules: ? → ?|??|?? determine whether the following strings can be generated by the grammar G and where it can be generated, write the language for the grammar G.(i) ?????? (ii) ???????? (iii) ??????
NAT Lang processing: Please explain in detail Consider a CFG representing a phrase structure grammar for a natural language such as English, including the following rule (the period is part of the rule): S -> NP VP . In this rule, S, NP, and VP are non-terminal symbols, but we will assume that the period is a terminal symbol specifically representing a period (as opposed to some other end-of-sentence marker). So, we can interpret this rule as stating that a sentence can have the form of a noun phrase followed by a verb phrase followed by a period. (To implement a parser for grammars with rules like this, the tokenizer would have to treat periods as separate tokens.) Assume that you need to convert this grammar to Chomsky normal form (CNF), perhaps with the CKY parsing algorithm in mind. Using the procedure discussed in class, show the rules that might result from the conversion.
Businesses that engage in EDI with each other are called silent partners. O True O False
Complete the proof of Theorem 6.4. Theorem 6.4: Let G = (V, T, S, P) be any context-free grammar without λ-productions. Then there exists a context-free grammar bG = (bV , b T, S, b P) that does not have any unit-productions and that is equivalent to G. 1
For this exercise, we will work on a regular grammar to recognize a comment in a C++ or Java program. A comment starts with /* and ends with */ and anything else in between can be ignored. We won't consider the case of nested comments. Keep in mind that you can have any number of * characters at the beginning, at the end, and in between. • Write a regular grammar recognizing such comments. • Draw the finite state machine for this grammar. • Draw a table for this grammar such as the ones for table-driver scanners in the class notes and in the book.