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Compiler Construction
Sohail Aslam Lecture 7 compiler: intro
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Table Encoding of FA b Transition table a a 1 2 a b 1 err 2
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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Simulating FA trans_table[NSTATES][NCHARS]; accept_states[NSTATES];
state = INITIAL; while(state != err){ c = input.read(); if(c == EOF ) break; state=trans_table[state][c]; } return accept_states[state];
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RE → Finite Automata Can we build a finite automaton for every regular expression? Yes, – build FA inductively based on the definition of Regular Expression
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NFA Nondeterministic Finite Automaton (NFA)
Can have multiple transitions for one input in a given state Can have e - moves
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Epsilon Moves ε – moves machine can move from state A to state B without consuming input e A B
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NFA operation of the automaton is not completely defined by input 1 1
1 A B C On input “11”, automaton could be in either state
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Execution of FA A NFA can choose Whether to make e-moves.
Which of multiple transitions to take for a single input.
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Acceptance of NFA NFA can get into multiple states
Rule: NFA accepts if it can get in a final state 1 1 A B C
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DFA and NFA Deterministic Finite Automata (DFA)
One transition per input per state. No e - moves
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Execution of FA A DFA can take only one path through the state graph.
Completely determined by input.
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NFA vs DFA NFAs and DFAs recognize the same set of languages (regular languages) DFAs are easier to implement – table driven.
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NFA vs DFA For a given language, the NFA can be simpler than the DFA.
DFA can be exponentially larger than NFA.
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NFA vs DFA NFAs are the key to automating RE → DFA construction.
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RE → NFA Construction Thompson’s construction (CACM 1968)
Build an NFA for each RE term. Combine NFAs with e-moves.
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RE → NFA Construction Subset construction NFA → DFA
Build the simulation. Minimize number of states in DFA (Hopcroft’s algorithm)
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RE → NFA Construction Key idea:
NFA pattern for each symbol and each operator. Join them with e-moves in precedence order.
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RE → NFA Construction a s0 s1 NFA for a a e b s0 s1 s3 s4 NFA for ab
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RE → NFA Construction a NFA for a s0 s1
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RE → NFA Construction a NFA for a s0 s1 b NFA for b s3 s4
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RE → NFA Construction a NFA for a s0 s1 b NFA for b s3 s4 a b s0 s1 s3
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RE → NFA Construction a NFA for a s0 s1 b NFA for b s3 s4 a e b s0 s1
NFA for ab
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RE → NFA Construction a s1 s2 e e s0 s5 b e s3 s4 e NFA for a | b
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RE → NFA Construction a s1 s2 NFA for a
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RE → NFA Construction a s1 s2 b s3 s4 NFA for a and b
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RE → NFA Construction a s1 s2 e e s0 s5 b e s3 s4 e NFA for a | b
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RE → NFA Construction e e a e s0 s1 s2 s4 e NFA for a*
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RE → NFA Construction a s1 s2 NFA for a
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RE → NFA Construction e e a e s0 s1 s2 s4 e NFA for a*
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Example RE → NFA s4 s5 s0 s1 s2 s3 s8 s9 s6 s7 NFA for a ( b|c )* e e
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Example RE → NFA building NFA for a ( b|c )* a s0 s1
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Example RE → NFA NFA for a, b and c b s4 s5 a s0 s1 c s6 s7
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Example RE → NFA s4 s5 s0 s1 s3 s8 s6 s7 NFA for a and b|c e e e e b a
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Example RE → NFA s4 s5 s0 s1 s2 s3 s8 s9 s6 s7 NFA for a and ( b|c )*
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Example RE → NFA s4 s5 s0 s1 s2 s3 s8 s9 s6 s7 NFA for a ( b|c )* e e
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