Information about Cs419 lec5 lexical analysis using dfa

FINITE AUTOMATA FA Its goal is to act as a recognizer for specific language/pattern. Any problem can be presented in form of decidable problem that can be answered by Yes/No. Hence FA (machine with limited memory) can solve any problem. FA used to be hard wired devices like controller of a lift. Dr. Hussien M. Sharaf 2

IMPLEMENTATION OF FINITE AUTOMATA IN CODE 1. 2. Possible ways: Use the position in the code (nested within tests) to maintain the state implicitly. Use a variable to maintain the current state and write transitions as doubly nested case statements inside a loop, where the first case statement tests current state and the nested second level tests the input character, given the state or vice versa. Dr. Hussien M. Sharaf 3

EXAMPLE FOR METHOD 1 The position in the code to maintain the state Implicitly. Dr. Hussien M. Sharaf 4

CODE 1 Dr. Hussien M. Sharaf 5

EXAMPLE FOR METHOD 2 A variable to maintain the current state. Dr. Hussien M. Sharaf 6

CODE 2 Dr. Hussien M. Sharaf 7

DETERMINISTIC FINITE AUTOMATA DFA There is a fixed number of states and the DFA can only be in one state at a time. DFA = “a 5-tuple “ (Q, Σ, , q0, F) Q: {q0, q1, q2, …} is set of states. Σ: {a, b, …} set of alphabet. (delta): A transition function, which is a total function from Q x Σ to Q, this function: Takes a state and input symbol as arguments. Returns a single state. : Q x Σ→Q q0 Q is the start state. F Q is the set of final/accepting states. Dr. Hussien M. Sharaf 8

TRANSITION FUNCTION : Q x Σ→Q Maps from domain of (states, letters) to range of states. (q0, a) (q2, b) q2 (q1, b) Dr. Hussien M. Sharaf q1 q3 9

EXAMPLE1.1 Build an FA that accepts at two a’s followed by one b L = {aab} S1 - S2 a b b S3 a a S5 Dr. Hussien M. Sharaf b a,b S4 + S1 S2 S3 S4 a S2 S3 S5 S5 b S5 S5 S4 S5 10

EXAMPLE1.2 Build a DFA that accepts only aab DFA that is not well defined. S1 - a S2 a S3 b S4 + S1 S2 S3 S4 Dr. Hussien M. Sharaf a S2 S3 ? ? b ? ? ? ? 11

EX2 (a+b)* ± a, b Dr. Hussien M. Sharaf 12

FA ACCEPTING NOTHING 1. FA with no final states b a a,b 2. FA with disconnected graph. Start state does not have a path to the final state. b + a Dr. Hussien M. Sharaf a,b b 13

EX3 All words with even count of letters. ((a+b)(a+b))* a, b 1± 2 a, b Dr. Hussien M. Sharaf 14

EX4.1 All words that start with “a” a(a+b)* b a,b b 2 2 1- 1- a 3+ a,b a 3+ a,b Does not accept all inputs Dr. Hussien M. Sharaf 15

EX4.2 All words that start with “a” a(a+b)* a,b b 2 a,b 1- a 3+ a,b 4+ Special accept state for string “a”, might give better performance in hardware implementation Dr. Hussien M. Sharaf 16

ASSIGNMENT2 Compilers_DFA_Sheet_2.pdf Deadline is 7 March-2013 Dr. Hussien M. Sharaf 17

EX5 All words that start with triple letter (aaa+bbb)(a+b)* a 2 a a 3 1- 6+ b Dr. Hussien M. Sharaf 4 b 5 a,b b 18

EX6 + a - a,b a,b b b 5 {aa, ba, baba, aaaa, bbba, abba, aaabaa, …} All words with even count of letters and ends with “a”. (a+b)a ((a+b)a (b(a+b)a)* )* Dr. Hussien M. Sharaf 19

EX7 a,b - {aa, ba, baba, aaaa, ab, bb, bababa, aaba, …} All words with even count of letters having “a” in an even position from the start, where the first letter is letter number one. (a+b)a((a+b)a)* Dr. Hussien M. Sharaf 20

EX8 COMPILERS CONSTRUCTION PAGE 50 Consider the following FA: •Accepts identifiers where symbols are not acceptded with error handling. •An identifier must start with a letter. letter [a-zA-Z] Other =~letter Other# = ~(letter|digit) Dr. Hussien M. Sharaf — other letter letter digit Other# error any 21

EX9 COMPILERS CONSTRUCTION PAGE 52 Integer constants digit — digit digit other other error Dr. Hussien M. Sharaf 22

EX10 COMPILERS CONSTRUCTION PAGE 52 Decimal/floating constants digit — digit digit other . other digit digit other error Dr. Hussien M. Sharaf 23

THANK YOU Dr. Hussien M. Sharaf 24

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