OPTIMIZATION OF DFA-Based on Pattern Matchers

1. Compiler Design
Optimization of DFA-Based
Pattern Matchers
02/13/17 1
ANKUR SRIVASTAVA ASSISTANT
PROFESSOR JETGI

2. Optimization of DFA-Based Pattern Matchers
• It refers to detecting those states of a DFA whose
presence or absence in a DFA does not affect the
language accepted by the automata.
• These states can be eliminated from the automata
without affecting the language accepted by the
automata.
• SUCH STATES ARE:-
• Unreachable States:
• Dead States:
• Nondistinguishable States:
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ANKUR SRIVASTAVA ASSISTANT
PROFESSOR JETGI
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3. Contd…….
• Unreachable States: Unreachable states of a DFA are not
reachable from the initial state of DFA on any possible input
sequence.
• Dead States: A dead state is a nonfinal state of a DFA whose
transitions on every input symbol terminates on itself. For
example, q is a dead state if q is in Q F, and δ(q, a) = q for
every a in Σ.
• Nondistinguishable States: Nondistinguishable states are those
states of a DFA for which there exist no distinguishing strings;
hence, they cannot be distinguished from one another.
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PROFESSOR JETGI
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4. Contd……..
• Optimization entails:
• Detection of unreachable states and eliminating
them from DFA;
• Identification of nondistinguishable states, and
merging them together; and
• Detecting dead states and eliminating them from
the DFA.
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ANKUR SRIVASTAVA ASSISTANT
PROFESSOR JETGI
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5. Consider The Transition Diagram
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Fig: Partitioning down to a single state.

6. Contd……
• Initially, we have two groups, as shown below:
Group I Group II
Since
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A, B, C, E, F D

7. Contd…..
• Partitioning of Group I is not possible, because the
transitions from all the members of Group I go only to
Group I. But since
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state F is distinguishable from the rest of the members of Group I. Hence, we divide
Group I into two groups: one containing A, B, C, E, and the other containing F, as shown
below:

8. Contd……
Group I Group II Group III
Since
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A, B, C, E F D
partitioning of Group I is not possible, because the transitions from all the
members of Group I go only to Group I. But since

9. Contd…..
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states A and E are distinguishable from states B and C. Hence, we further divide Group
I into two groups: one containing A and E, and the other containing B and C, as shown
below:

10. Contd……
Group I Group II Group III Group IV
Since
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A, E B, C F D
state A is distinguishable from state E. Hence, we divide Group I into two groups:
one containing A and the other containing E, as shown below:

11. Contd……
Group I Group II Group III Group IV Group V
Since
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A E B, C D
partitioning of Group III is not possible, because the transitions from all the
members of Group III on a go to group III only. Similarly,
F

12. Contd…..
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partitioning of Group III is not possible, because the transitions from all the
members of Group III on b also only go to Group III.
Hence, B and C are nondistinguishable states; therefore, we merge B and C to
form a single state, B1, as shown in next Figure…

13. Contd……..
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PROFESSOR JETGI
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Fig. Merging nondistinguishable states B&C into a single state
B1.

14. THANKS
02/13/17 14
ANKUR SRIVASTAVA ASSISTANT
PROFESSOR JETGI