**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 do we need to remove the productions in the form of A -> B or A -> λ 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?

As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost other parts in the next question. (1) Regular Grammar: A grammar is regular if it has rules of form A → a or A → aB or A → ɛ where ɛ is a special symbol called NULL. Regular Grammar(Type-3 grammars) generate regular languages. Type-3 grammars must have a single non-terminal on the left-hand side and a right-hand side consisting of a single terminal or single terminal followed by a single non-terminal. The productions must be in the form X → a or X → aY where X, Y ∈ N (Non-terminal) and a ∈ T (Terminal) The rule S → ε is allowed if S does not appear on the right side of any rule. Example X → ε X → a | aYY → b Context-free Grammar - A context-free grammar (CFG) consisting of a finite set of grammar rules is a quadruple (N, T, P, S) where N is a set of non-terminal symbols. T is a set of terminals where N ∩ T = NULL. P is a set of rules, P: N → (N ∪ T)*, i.e., the left-hand side of the production rule P does have any right context or left context. S is the start symbol. (Type-2 grammars) generate context-free languages. The productions must be in the form A → γ where A ∈ N (Non-terminal) and γ ∈ (T ∪ N)* (String of terminals and non-terminals). These languages generated by these grammars are be recognized by a non-deterministic pushdown automaton. Example S → X a X → a X → aX X → abc X → ε(2) Context-free language The language of grammar G=(V,∑,R,S) is the set L(G)={w∈∑* : S*⇒w} of all terminal-symbol strings derivable from the start symbol. A language L is said to be a context-free language (CFL), if there exists a CFG G, such that L=L(G). Context-free Grammar− A context-free grammar (CFG) consisting of a finite set of grammar rules is a quadruple (N, T, P, S) where N is a set of non-terminal symbols. T is a set of terminals where N∩T = NULL. P is a set of rules, P:N→(N∪T)* i.e., the left-hand side of the production rule P does have any right context or left context. S is the start symbol. AUTOMATA Non-deterministic pushdown automata(PDA) recognize exactly the context-free languages. A PDA can remember an infinite amount of information. Pushdown automata is simply an NFA augmented with an "external stack memory". The addition of stack is used to provide a last-in-first-out memory management capability to Pushdown automata. Pushdown automata can store an unbounded amount of information on the stack. It can access a limited amount of information on the stack. A PDA can push an element onto the top of the stack and pop off an element from the top of the stack. To read an element into the stack, the top elements must be popped off and are lost. PDA Components: Input tape: The input tape is divided into a number of cells. The input head is read-only and only move from left to right, and one symbol at a time. Finite control: The finite control has some pointer that points to the current symbol which is to be read. Stack: The stack is a structure in which we can push and remove the items from one end only. It has infinite size. In PDA, the stack is used to store the items temporarily. The formal definition of PDA: The PDA can be defined as a collection of 7 components: Q : the finite set of states ∑ : the input set Γ : a stacked symbol that can be pushed and popped from the stack q0 : the initial state Z : a start symbol which is in Γ. F : a set of final states δ : mapping function which is used for moving from current state to next state.(3) Consider the grammar S → ABCd (1)A → BC (2)B → bB | λ (3) C → cC | λ (4) Add the first production. Then, create all the possible combinations that can be formed by replacing the nullable variables with λ. Therefore (1) now becomes 'S → ABCd | ABd | ACd | BCd | Ad | Bd |Cd | d ’. Apply the same rule to (2) but do not add ‘A → λ’ even though it is a possible combination. We remove all the productions of type ‘V → λ’. So the new grammar becomes: S → ABCd | ABd | ACd | BCd | Ad | Bd |Cd | dA → BC | B | CB → bB | bC → cC | c

Engineering

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(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?

(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?

Database System Concepts

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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

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Question

**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 do we need to remove the productions in the form of A -> B or A -> λ 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?

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