Given the following expression in language A(true op1 (false op2 true))Which of the following expressions in Language B has the same semantic meaning? (Assuming thatoperations occur left to right like the OpSem, I.E. e₁ op1 e2 is not the same as e2 op1 e1)op3 op4 true false trueop3 op4 false true trueop3 true op4 false trueop3 false op4 true trueNone of the above Recall that Operational Semantics gives meaning to expressions by the operations performed.Consider the two operational semantic rules for two languages A and B. OCaml will be the meta-language for both.Language AA; true trueA; falsefalseA; e1 ⇒v1A; e2 ⇒ V2A; (e1 opl e2)V3 =if v₁ then V2 else V1v3A; e1⇒v1A; e2 ⇒ V2 v3if v₁ then v₁ else v₂A; (e1 op2 e2)v3Language BA; true trueA; false=> falseA; e1 ⇒v1A; e2 ⇒ V2V3 = v₁ && v₂A; op3 e₁ e2V3A; e1 ⇒v1A; e2 ⇒ V2v3 = v1 || v2A; op4 e₁ e2 ⇒ V3

Answered: Given the following expression in…

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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Part A. Review the concepts by yourself: (1) Describe the difference between a regular grammar and a context-free grammar from their definitions focusing on the forms of productions. (2) Explain the definitions and relations among the language, grammar, and automata for context- free language. (3) Given a context-free grammar, why we need to remove the productions in form of A -> B or A - >1. to get an equivalent one? (4) Given a context-free grammar G, what is the relation L(G) and derivation tree? (5) What is the relation between Turing machine and our current computer? (6) What are the output of DFA/NFA, Pushdown Machine, and Turing Machine?
(b) Consider the following context-free grammar, partially augmented with semantic rules: {NP.sem(VP.sem)} + Det Nominal {Det.sem(Nominal.sem)} Nominal → Adj Nominal {Adj.sem(Nominal.sem)} {..} { ...} { ...} S → NP VP NP Det + every Det a → small Nominal → dog → barks Adj VP {...} Now consider the following two sentences, with their desired meaning represen- tations: A1 every dog barks A2 Vd Dog (d) =→ Je Barking (e) A Barker(e, d) B1 a small dog barks B2 3d Dog(d) A Small(d) ^ Je Barking(e) A Barker(e, d) Complete the above augmented grammar, by giving the semantics of 'every', 'a', 'small', 'dog', and barks', so that the desired meaning representations are obtained for A1 and B1. Show that your solution is correct, by first giving the lambda expressions obtained from A1 and B1 before any beta reductions, and then showing step-by-step that the beta reductions lead to A2 and B2.
1. Consider the following grammar and try to find out Operator Precedence and Associativity. Is the grammar Ambiguous? If so, find a string for which it is ambiguous and finally, convert to Unambiguous grammar without changing the original Language. S → S % A/ A A → B * A/ B В — В & C/С C → S/ id
1.Eliminate left recursion from the production rules that are given in below. E = E + T / T 2.Define context-free grammar. 3.Write down the characteristic of context-free grammar.
Assume that G is a Context Free Grammar as the 4-tuple (V,T,S,P) where V={S,A,B} set of non-terminal symbols, T={ab} set of terminal symbols, and S is the start symbol, and P is the set of the production rules. Select the correct statement(s). P is defined as {X→Y: such that XEV, YE(VUT)* } P is defined as {X→Y: such that XEV, YE(VUT)* } ☐ {S→ε} can not be a subset of P. ]{S→Aa|AB|bA} can be a subset of P.
subject theory of automata
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?
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
There is a significant conceptual divide between operational and denotational semantics that must be understood.
6 2. Construct a context-free grammar G to accept the set of strings over the alphabet {(,)} that are not balanced. Explain the role of the each nonterminal and state the language generated by each of them. Exhibit leftmost derivations for the strings w1 = ())(, w2 = ((()) and w3 = ) in your grammar G.
6) Please look at the attached image.
Question 2-Context-free Grammars Consider the alphabet = {A, V., (,), x, y, z) and the following grammar G = (V,E, R, F), defined by the rules: F (FAF) | (FVF) | (F) | P (a) Identify the set of variables and the set of terminal symbols of G. (b) Identify three words (of lengths between 10 and 20) that can be generated by the above grammar and show their derivations. (c) Consider a modified grammar G', where we remove the brackets '(' and ')' from the alphabet and the derivation rules. That is we set Σ'= {A, V., x, y, z) and we remove all occurrences of brackets in the derivation rules. Show that there are words that are derived ambiguously in G'

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