Language of prefixes of regular language is regular language
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Let there be L which is a regular language and let there be M which is a Finite Automaton for it. How is it possible to prove that a language L2 containing all prefixes of the L language is a regular language.
Through some books and of course this forum I found some examples.
Example 1: If there is a M FA then we can make a Non Deterministic FA which will have final states for every state that leads to the final state in the first M FA and there will be none 'garbage non acceptance' state. And lets add a new state S0 which will jump towards the first acceptance state with lambda. This way i think that we will get all the sub strings ( prefixes ) of the first regular language.(Please correct me if I am wrong)
Is there any way that I can prove that L2 is indeed a regular language using the operations between sets , like intersection, union , complement and etc?
proof-verification formal-languages regular-language
asked Nov 24 at 23:47
LexByte
163
add a comment |
up vote
-1
down vote
favorite
Let there be L which is a regular language and let there be M which is a Finite Automaton for it. How is it possible to prove that a language L2 containing all prefixes of the L language is a regular language.
Through some books and of course this forum I found some examples.
Example 1: If there is a M FA then we can make a Non Deterministic FA which will have final states for every state that leads to the final state in the first M FA and there will be none 'garbage non acceptance' state. And lets add a new state S0 which will jump towards the first acceptance state with lambda. This way i think that we will get all the sub strings ( prefixes ) of the first regular language.(Please correct me if I am wrong)
Is there any way that I can prove that L2 is indeed a regular language using the operations between sets , like intersection, union , complement and etc?
proof-verification formal-languages regular-language
asked Nov 24 at 23:47
LexByte
163
It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let there be L which is a regular language and let there be M which is a Finite Automaton for it. How is it possible to prove that a language L2 containing all prefixes of the L language is a regular language.
Through some books and of course this forum I found some examples.
Example 1: If there is a M FA then we can make a Non Deterministic FA which will have final states for every state that leads to the final state in the first M FA and there will be none 'garbage non acceptance' state. And lets add a new state S0 which will jump towards the first acceptance state with lambda. This way i think that we will get all the sub strings ( prefixes ) of the first regular language.(Please correct me if I am wrong)
Is there any way that I can prove that L2 is indeed a regular language using the operations between sets , like intersection, union , complement and etc?
proof-verification formal-languages regular-language
asked Nov 24 at 23:47
LexByte
163
Let there be L which is a regular language and let there be M which is a Finite Automaton for it. How is it possible to prove that a language L2 containing all prefixes of the L language is a regular language.
Through some books and of course this forum I found some examples.
Example 1: If there is a M FA then we can make a Non Deterministic FA which will have final states for every state that leads to the final state in the first M FA and there will be none 'garbage non acceptance' state. And lets add a new state S0 which will jump towards the first acceptance state with lambda. This way i think that we will get all the sub strings ( prefixes ) of the first regular language.(Please correct me if I am wrong)
Is there any way that I can prove that L2 is indeed a regular language using the operations between sets , like intersection, union , complement and etc?
proof-verification formal-languages regular-language
proof-verification formal-languages regular-language
asked Nov 24 at 23:47
LexByte
163
asked Nov 24 at 23:47
LexByte
163
asked Nov 24 at 23:47
LexByte
163
asked Nov 24 at 23:47
LexByte
163
asked Nov 24 at 23:47
LexByte
163
163
It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55
add a comment |
It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55
It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55
add a comment |
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It seems to me that the proof you sketch is correct, and elegant. Why muck about with set operations?
– saulspatz
Nov 25 at 0:03
Possible duplicate of Language of prefixes of regular language is regular.
– Joey Kilpatrick
Nov 25 at 3:53
@JoeyKilpatrick as i stated in the question the example is from a book and from this forum. I am looking for a answer if its actually right for prefixes and also if there any way i can use operations on sets to prove this concept.
– LexByte
Nov 25 at 3:55