Difference between revisions of "Theoretical Aspects of Lexical Analysis/Exercise 4"
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The non-deterministic finite automaton (NFA), built by applying Thompson's algorithm to the regular expression '''<nowiki>(a|b)*abb(a|b)*</nowiki>''' is the following: | The non-deterministic finite automaton (NFA), built by applying Thompson's algorithm to the regular expression '''<nowiki>(a|b)*abb(a|b)*</nowiki>''' is the following: | ||
{{CollapsedCode|NFA| | {{CollapsedCode|NFA| | ||
| − | < | + | <dot-hack> |
digraph nfa { | digraph nfa { | ||
{ node [shape=circle style=invis] s } | { node [shape=circle style=invis] s } | ||
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fontsize=10 | fontsize=10 | ||
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} | } | ||
| − | </ | + | </dot-hack> |
}} | }} | ||
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{{CollapsedCode|DFA| | {{CollapsedCode|DFA| | ||
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digraph dfa { | digraph dfa { | ||
{ node [shape=circle style=invis] s } | { node [shape=circle style=invis] s } | ||
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8 -> 6 [label="b",fontsize=10] | 8 -> 6 [label="b",fontsize=10] | ||
fontsize=10 | fontsize=10 | ||
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} | } | ||
| − | </ | + | </dot-hack> |
}} | }} | ||
The minimization tree is as follows: | The minimization tree is as follows: | ||
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{{CollapsedCode|Minimal DFA| | {{CollapsedCode|Minimal DFA| | ||
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digraph dfamin { | digraph dfamin { | ||
{ node [shape=circle style=invis] s } | { node [shape=circle style=invis] s } | ||
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45678 -> 45678 [label="b",fontsize=10] | 45678 -> 45678 [label="b",fontsize=10] | ||
fontsize=10 | fontsize=10 | ||
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} | } | ||
| − | </ | + | </dot-hack> |
}} | }} | ||
Latest revision as of 22:44, 11 February 2019
Contents |
Problem
Use Thompson's algorithm to build the NFA for the following regular expression. Build the corresponding DFA and minimize it.
- (a|b)*abb(a|b)*
Solution
The non-deterministic finite automaton (NFA), built by applying Thompson's algorithm to the regular expression (a|b)*abb(a|b)* is the following:
| NFA |
|---|
Applying the determination algorithm to the above NFA, the following determination table is obtained:
| Determination table | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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Graphically, the DFA is represented as follows:
| DFA |
|---|
The minimization tree is as follows:
| Minimization tree |
|---|
|
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Given the minimization tree above, the final minimal DFA is as follows:
| Minimal DFA |
|---|