Closure Property of Language Families - Revision history

Arjun Suresh at 20:51, 7 December 2015

2015-12-07T20:51:18Z

2014-07-14T09:35:24Z

2014-06-08T08:55:42Z

2014-05-05T05:55:12Z

2014-02-26T17:55:29Z

2014-02-26T17:33:13Z

2014-02-26T13:55:23Z

2014-02-26T13:53:18Z

2014-02-26T13:50:12Z

2014-02-26T12:56:04Z

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 Now, while applying closure property do remember the language hierarchy.
   Regular <math>\subset</math> DCFL <math>\subset</math>CFL <math>\subset</math> REC <math>\subset</math> RE.
 So, if CFL is closed under Union, and <math>L_1</math> and <math>L_2</math> belong to CFL,  then <math>L_1\cup L_2</math> will be a CFL. But  '''<math>L_1 \cup L_2</math> can also be a regular language, which closure property can't tell'''. For this we need to see <math>L_1</math> and <math>L_2</math>.

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 {{Template:FBD}}
-[[Category: Automata Theory]]
+[[Category: Automata Theory Notes]]
 [[Category: Compact Notes for Reference of Understanding]]

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 So, if CFL is closed under Union, and <math>L_1</math> and <math>L_2</math> belong to CFL,  then <math>L_1\cup L_2</math> will be a CFL. But  '''<math>L_1 \cup L_2</math> can also be a regular language, which closure property can't tell'''. For this we need to see <math>L_1</math> and <math>L_2</math>.
-{{alert|Please don't byheart this table. This is just to check your understanding and some of them are not required for GATE|alert-danger}}
+{{alert|Please don't by heart this table. This is just to check your understanding and some of them are not required for GATE|alert-danger}}
 :{| class="wikitable"

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   Regular <math>\subset</math> DCFL <math>\subset</math>CFL <math>\subset</math> REC <math>\subset</math> RE.
 So, if CFL is closed under Union, and <math>L_1</math> and <math>L_2</math> belong to CFL,  then <math>L_1\cup L_2</math> will be a CFL. But  '''<math>L_1 \cup L_2</math> can also be a regular language, which closure property can't tell'''. For this we need to see <math>L_1</math> and <math>L_2</math>.
 :{| class="wikitable"

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 | {{Yes}}
 | {{Yes}}
-<!--
 |}

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 | {{Yes}}
 | {{Yes}}
 |-
 |Substitution (<math>\epsilon</math>-free)
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 | {{No}}
 | {{Yes}}
 |-
 |Inverse Homomorphism

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