Which languages represented by the following regular expressions are in L 1 E 1

Which languages represented by the following regular

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Which languages represented by the following regular expressions are in L * ? 1) E 1 = a * + ba , 2) E 2 = b * + a * aba * , 3) E 3 = aab + cab * ac , 4) E 4 = b ( ca + ac )( aa ) * + a * ( a + b ) , 5) E 5 = ( a 4 ba 3 ) 2 * c , 6) E 6 = b + ac ( b + = bb * ), 7) E 7 = ( b + c ) ab + ba ( c + ab ) * , 8) E 8 = ( b + c ) * ab + a ( c + a ) * .
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Automata HTNguyen, NAKhuong LHTrang Contents Motivation Alphabets, words and languages Regular expression or rationnal expression Non-deterministic finite automata Deterministic finite automata Recognized languages Determinisation Minimization DFAs combination Some applications 3.19 Exercise Let Σ = { a, b, c } and L = { ab, aa, b, ca, bac } Which languages represented by the following regular expressions are in L * ? 1) E 1 = a * + ba , 2) E 2 = b * + a * aba * , 3) E 3 = aab + cab * ac , 4) E 4 = b ( ca + ac )( aa ) * + a * ( a + b ) , 5) E 5 = ( a 4 ba 3 ) 2 * c , 6) E 6 = b + ac ( b + = bb * ), 7) E 7 = ( b + c ) ab + ba ( c + ab ) * , 8) E 8 = ( b + c ) * ab + a ( c + a ) * . Define a (simple) regular expression representing the language L * .
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Automata HTNguyen, NAKhuong LHTrang Contents Motivation Alphabets, words and languages Regular expression or rationnal expression Non-deterministic finite automata Deterministic finite automata Recognized languages Determinisation Minimization DFAs combination Some applications 3.20 Exercise Simplify each of the following regular expressions 1) E 1 = ε + ab + abab ( ab ) * , 2) E 2 = aa ( b * + a ) + a ( ab * + aa ) , 3) E 3 = a ( a + b ) * + aa ( a + b ) * + aaa ( a + b ) * .
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Automata HTNguyen, NAKhuong LHTrang Contents Motivation Alphabets, words and languages Regular expression or rationnal expression Non-deterministic finite automata Deterministic finite automata Recognized languages Determinisation Minimization DFAs combination Some applications 3.21 Finite automata Finite automata (Automat hoeu h/n) The aim is representation of a process system. It consists of states (including an initial state and one or several (or one) final/accepting states ) and transitions (events). The number of states must be finite.
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Automata HTNguyen, NAKhuong LHTrang Contents Motivation Alphabets, words and languages Regular expression or rationnal expression Non-deterministic finite automata Deterministic finite automata Recognized languages Determinisation Minimization DFAs combination Some applications 3.21 Finite automata Finite automata (Automat hoeu h/n) The aim is representation of a process system. It consists of states (including an initial state and one or several (or one) final/accepting states ) and transitions (events). The number of states must be finite. q 0 q 1 b a, b Regular expression b * ( a + b )
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Automata HTNguyen, NAKhuong LHTrang Contents Motivation Alphabets, words and languages Regular expression or rationnal expression Non-deterministic finite automata Deterministic finite automata Recognized languages Determinisation Minimization DFAs combination Some applications 3.22 Exercise Let Σ = { a, b } Which of the strings 1) a 3 b , 2) aba 2 b , 3) a 4 b 2 ab 3 a , 4) a 4 ba 4 , 5) ab 4 a 9 b , 6) ba 5 ba 4 b , 7) ba 5 b 2 , 8) bab 2 a are accepted by the following finite automata?
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  • Fall '13
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  • Regular expression, Nondeterministic finite state machine, Automata theory, Formal Languages and Automata, language L

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