The document discusses the design of lexical analyzer generators and state minimization of deterministic finite automata (DFAs). It covers the process of converting regular expressions to nondeterministic finite automata (NFAs) and then converting NFAs to equivalent DFAs. The key steps are: (1) defining an NFA for each regular expression operator, (2) simulating the NFA to obtain the states of the equivalent DFA, where each DFA state represents a set of NFA states, and (3) constructing the DFA transitions based on the reachable NFA states. Implementing the minimized DFA as a table makes lexical analysis very efficient.

1. System Software (5KS03)
Unit 1 : Introduction to Compiling
Lecture : 6 Design of lexical analyzer generator,
State minimization of a DFA
A S Kapse,
Assistant Professor,
Department Of Computer Sci. & Engineering
Anuradha Engineering College, Chikhli

2. Contents…
 Design of lexical analyzer generator,
 State minimization of a DFA

3. Objectives…
 Upon completion of this lecture, you will be able
 To understand the Lexical Analysis
 To understand Role of lexical analyses
 To understand input buffering & state minimization of
DFA

4. Review…./ Concepts
 What do you mean by State?
 What do you mean by NFA & DFA?
 What do you mean by Parse tree?

5. 5
Deterministic and Nondeterministic
Automata
 Deterministic Finite Automata (DFA)
 One transition per input per state
 No -moves
 Nondeterministic Finite Automata (NFA)
 Can have multiple transitions for one input in a given state
 Can have -moves
 Finite automata have finite memory
 Need only to encode the current state

6. 6
Execution of Finite Automata
 A DFA can take only one path through the state
graph
 Completely determined by input
 NFAs can choose
 Whether to make -moves
 Which of multiple transitions for a single input to take

7. 7
Acceptance of NFAs
 An NFA can get into multiple states
• Input:
0
1
1
0
1 0 1
• Rule: NFA accepts if it can get in a final state

8. 8
NFA vs. DFA (1)
 NFAs and DFAs recognize the same set of
languages (regular languages)
 DFAs are easier to implement
 There are no choices to consider

9. 9
NFA vs. DFA (2)
 For a given language the NFA can be simpler than
the DFA
0
1
0
0
0
1
0
1
0
1
NFA
DFA
• DFA can be exponentially larger than NFA

10. 10
Regular Expressions to Finite Automata
 High-level sketch
Regular
expressions
NFA
DFA
Lexical
Specification
Table-driven
Implementation of DFA

11. 11
Regular Expressions to NFA (1)
 For each kind of rexp, define an NFA
 Notation: NFA for rexp A
A
• For 

• For input a
a

12. 12
Regular Expressions to NFA (2)
 For AB
A B

• For A | B
A
B





13. 13
Regular Expressions to NFA (3)
 For A*
A




14. 14
Example of RegExp -> NFA conversion
 Consider the regular expression
(1 | 0)*1
 The NFA is

1C E
0D F


B


G



A H
1
I J

15. 15
Next
Regular
expressions
NFA
DFA
Lexical
Specification
Table-driven
Implementation of DFA

16. 16
NFA to DFA. The Trick
 Simulate the NFA
 Each state of resulting DFA
= a non-empty subset of states of the NFA
 Start state
= the set of NFA states reachable through -moves from
NFA start state
 Add a transition S a S’ to DFA iff
 S’ is the set of NFA states reachable from the states in S
after seeing the input a
 considering -moves as well

17. 17
NFA -> DFA Example
1
0
1
 






A B
C
D
E
F
G H I J
ABCDHI
FGABCDHI
EJGABCDHI
0
1
0
1
0 1

18. 18
NFA to DFA. Remark
 An NFA may be in many states at any time
 How many different states ?
 If there are N states, the NFA must be in some
subset of those N states
 How many non-empty subsets are there?
 2N - 1 = finitely many, but exponentially many

19. 19
Implementation
 A DFA can be implemented by a 2D table T
 One dimension is “states”
 Other dimension is “input symbols”
 For every transition Si a Sk define T[i,a] = k
 DFA “execution”
 If in state Si and input a, read T[i,a] = k and skip to state
Sk
 Very efficient

20. 20
Table Implementation of a DFA
S
T
U
0
1
0
1
0 1
0 1
S T U
T T U
U T U

21. 21
Implementation (Cont.)
 NFA -> DFA conversion is at the heart of tools such
as flex or jflex
 But, DFAs can be huge
 In practice, flex-like tools trade off speed for space in
the choice of NFA and DFA representations

22. Video on Compilers
1. Design of lexical analyzer generator,

23. Questions..
1. What are the steps associated with transformation from
NFA to DFA?
2.

24. Homework..
1. What is parser?
2. Define a translator and categorize it.