Compiler Design: Conversion of NFA to DFA, Minimization of DFA, and Syntax Analysis, Lecture notes of Compiler Design

Download Compiler Design: Conversion of NFA to DFA, Minimization of DFA, and Syntax Analysis and more Lecture notes Compiler Design in PDF only on Docsity!

COMPILER DESIGN

(BCSPC5010)

5 th^ Semester CSE (R-18)

Conversion of NFA to DFA

Lecture – 8 LEXICAL ANALYSIS

Start/Input a b

S0 S1 S

S1 S1 S

S2 S1 S

S3 S1 S

S4 S1 S

Syntax Analysis

Lecture – 9 Syntax Analysis

Overview of the previous Lecture

Syntax Analysis

Context Free Grammar

Derivation

Syntax Analysis

Source

Code

Lexical

Analyzer

(Scanner)

Syntax

Analyzer

(Parser)

Toke

n

Request for

next Token

Lexemes

Symbol Table

Error Handler

Semantic

Analyzer

Parse

Tree

Syntax Analysis

Lecture – 9 Syntax Analysis

Syntax analysis or parsing is the second phase of a compiler. In this chapter, we shall learn the basic concepts used in the construction of a parser. We have seen that a lexical analyzer can identify tokens with the help of regular expressions and pattern rules. But a lexical analyzer cannot check the syntax of a given sentence due to the limitations of the regular expressions. Regular expressions cannot check balancing tokens, such as parenthesis.

Lecture – 9 (^) Grammar Syntax Analysis

Grammars

Therefore, this phase uses context-free grammar (CFG), which is recognized by push-down automata. CFG, on the other hand, is a superset of Regular Grammar, as depicted below:

Lecture – 9 (^) Grammar Syntax Analysis

Grammars

Construct the CFG for the language having any number of a's over the set ∑= {a}. Solution : As we know the regular expression for the above language is a* Production rule for the Regular expression is as follows:

1. S → aS rule 1
2. S → ε rule 2

Example-2 Construct a CFG for the regular expression (0+1)* Solution : Production rule for the Regular expression is as follows:

3. S → 0S | 1S rule 1
4. S → ε rule 2

Lecture – 9 (^) CFG (Context-Free Grammar) Syntax Analysis

Example-

S is the start symbol and the set of terminal symbols is {0,1}. Here are the production rules:

• S → 1S
• S → 0S
• S → 0 What does the above context-free grammar describe? a) Strings that end in 0 b) Strings that have an odd number of 1’s c) Strings that have an equal number of 1’s and 0’s d) Strings that end in 1 e) Strings that have an even number of 1’s and 0’s

Question

Ans: a)

Lecture – 9 Syntax Analysis

Question

According to Noam Chomosky, there are four types of grammars − Type 0, Type 1, Type 2, and Type 3. The following table shows how they differ from each other

Grammar Type Grammar Accepted^ Language Accepted^ Automaton Type 0 Unrestricted grammar

Recursively enumerable language

Turing Machine

Type 1 Context-sensitive grammar

Context-sensitive language

Linear-bounded Non-deterministic automaton Type 2 Context-free grammar

Context-free language Non-deterministic Pushdown automaton Type 3 Regular grammar Regular language Finite state automaton

Lecture – 10 (^) Types of Grammars Syntax Analysis

Types of Grammars

Type-0 grammars generate recursively enumerable languages. The productions have no restrictions. They are any phase structure grammar including all formal grammars. They generate the languages that are recognized by a Turing machine. The productions can be in the form of αAβ → δ where α, β & δ are string of terminals and/or non-terminals. They can be empty.

Example S → ACaB Bc → acB CB → DB aD → Db

The productions can be in the form of: α → β where α is (V + T)* V (V + T)* and β is (V + T)*

V : Variables (Non-terminals) & T : Terminals.

Type – 0 (Unrestricted Grammars)

Type – 0 (Unrestricted Grammars)

Lecture – 9 Syntax Analysis

Type-2 grammars generate context-free languages. The productions must be in the form A → β where A ∈ N (Non terminal) and β ∈ (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

1. The productions can be in the form of α → β
2. First of all it should be Type 1.
3. Left hand side of production can have only one variable. |α| = 1 Their is no restriction on β.

Type – 2 (Context-Free Grammars)

Type – 2 (Context-Free Grammars)

Lecture – 9 Syntax Analysis

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 A → a or A → aB where A, B ∈ 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 A → ε A → a | aB B → b

Type 3 is most restricted form of grammar. Type 3 should be in the given form only :

V → VT* | T* (or) V → TV | T

Type – 3 (Regular Grammars)

Type – 3 (Regular Grammars)

Lecture – 9 Syntax Analysis

Left-most Derivation (Example)

Consider the following grammar and construct a Parse Tree for the string using LMD. 2 * ( 5 + 3 ) / 4 ▪ E -> E A E ▪ E -> ( E ) ▪ E -> id ▪ A -> + | - | * | / | ^ Left Most Derivation : E -> E A E E -> id A E E -> id * E E -> id * E A E E -> id * ( E ) A E

E -> id * ( E A E ) A E E -> id * ( id A E ) A E E -> id * ( id + E ) A E E -> id * ( id + id ) A E E -> id * ( id + id ) / E E -> id * ( id + id ) / id E -> 2 * ( 5 + 3) / 4

Lecture – 9 Syntax Analysis

Left-most Derivation (Example)

Parse Tree using Left-most Derivation (LMD)

Parse Tree using Left-most Derivation (LMD)

Lecture – 9 Syntax Analysis