He . means concatenation PROPERTIES 1. Associativity 1.1. R .pdf

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He . means concatenation PROPERTIES: 1. Associativity: 1.1. R + (S + T) = (R + S) + T 1.2. R.(S.T) = (R.S).T 2. Commutativity: R + S = S + R 3.Distributivity: 3.1. R.(S + T) = R.S + R.T 3.2. (S + T).R = S.R + T.R 4. Identity element: 4.1 R + = + R = R 4.2 R. = .R = R 5. Neutral element: R. = .R = 6. Idempotence: 6.1. R+R=R 6.2. (R^{})^{} = R^{} 7. Properties of the Kleene lock: 7.1. ^{}= 7.2. ^{} = 7.3. R^{+} = R R^{} = R^{} R 7.4. R^{}.R^{} = R^{} 7.5. R^{} = + R^{+} = R^{+} + 7.6. R? = R + = + R 7.7. (R + S)^{} = (R^{}.S^{} )^{} = (R^{}.S)^{}R^{} 7.8. (R.S)^{} = + R.(S.R)^{}.S 7.10. R.(S.R)^{} = (R.S)^{}.R 8. Conditional properties: 8.1. If L(R) L(S), then R + S = S 8.2. If L(R^{}) L(S^{}), then R^{}.S^{} = S^{} 8.3. If L(R^{}) L(S^{}), then (R + S)^{} = S^{} SOLVE: Select the number in those regular expressions that are equivalent: 1) R=(1+0+)01S=1?01 2) R=110?0S=1+(0+) 3) R=1+S=11 4) R=1+S= 5) R=0+1S=00(1+).

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$He . means concatenation PROPERTIES: 1. Associativity: 1.1. R + (S + T) = (R + S) + T 1.2. R.(S.T) = (R.S).T 2. Commutativity: R + S = S + R 3.Distributivity: 3.1. R.(S + T) = R.S + R.T 3.2. (S + T).R = S.R + T.R 4. Identity element: 4.1 R + = + R = R 4.2 R. = .R = R 5. Neutral element: R. = .R = 6. Idempotence: 6.1. R+R=R 6.2. (R^{})^{} = R^{} 7. Properties of the Kleene lock: 7.1. ^{}= 7.2. ^{} = 7.3. R^{+} = R R^{} = R^{} R 7.4. R^{}.R^{} = R^{} 7.5. R^{} = + R^{+} = R^{+} + 7.6. R? = R + = + R 7.7. (R + S)^{} = (R^{}.S^{} )^{} = (R^{}.S)^{}R^{} 7.8. (R.S)^{} = + R.(S.R)^{}.S 7.10. R.(S.R)^{} = (R.S)^{}.R 8. Conditional properties: 8.1. If L(R) L(S), then R + S = S 8.2. If L(R^{}) L(S^{}), then R^{}.S^{} = S^{} 8.3. If L(R^{}) L(S^{}), then (R + S)^{} = S^{} SOLVE: Select the number in those regular expressions that are equivalent: 1) R=(1+0+)01S=1?01 2) R=110?0S=1+(0+) 3) R=1+S=11 4) R=1+S= 5) R=0+1S=00(1+)$

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He . means concatenation PROPERTIES 1. Associativity 1.1. R .pdf

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