SlideShare a Scribd company logo
1 of 1
How to determine whether a language is regular or not using Myhill-Nerode theorem?
I already have got this notes from my lectures, so I don't want a theoretical answer something
that repeats the same thing:
Here are the steps to prove that a language is not regular using the Myhill-Nerode theorem:
1) Define the relation L on the language L as follows:
For any two strings x and y in *, x L y if and only if, for any string z in *, either all of xz and yz
are in L, or neither of them are in L.
2) Construct an infinite set of pairwise distinguishable strings {w1, w2, w3, ...} such that for any
i and j, if i j, then w i and w j are not equivalent under the relation L.
To show that the set of strings is pairwise distinguishable, you need to show that for any two
distinct strings w i and w j , there exists a string z such that either w i z is in L and w j z is not in L,
or w j z is in L and w i z is not in L. This can be done by constructing such a string z for each pair
of strings.
3) Show that there are an infinite number of equivalence classes of strings under L, which
implies that the language L is not regular.
If you can successfully perform these steps and show that there are an infinite number of
equivalence classes, you can conclude that the language L is not regular. Language is regular if
and only if there are a finite number of equivalence classes of strings under a certain relation.
I want an explanation with some examples (regular language and non-regular language) to get an
understanding of this.

More Related Content

Similar to How to determine whether a language is regular or not using Myhill-Ner.docx

6.3 Equivalences versus partitions
6.3 Equivalences versus partitions6.3 Equivalences versus partitions
6.3 Equivalences versus partitionsJan Plaza
 
形式言語理論への 測度論的アプローチ
形式言語理論への 測度論的アプローチ形式言語理論への 測度論的アプローチ
形式言語理論への 測度論的アプローチRyoma Sin'ya
 
Ilja state2014expressivity
Ilja state2014expressivityIlja state2014expressivity
Ilja state2014expressivitymaartenmarx
 
Final formal languages
Final formal languagesFinal formal languages
Final formal languagesMegha Khanna
 

Similar to How to determine whether a language is regular or not using Myhill-Ner.docx (10)

Regular expression
Regular expressionRegular expression
Regular expression
 
rs1.ppt
rs1.pptrs1.ppt
rs1.ppt
 
draft
draftdraft
draft
 
6.3 Equivalences versus partitions
6.3 Equivalences versus partitions6.3 Equivalences versus partitions
6.3 Equivalences versus partitions
 
Lexical analyzer
Lexical analyzerLexical analyzer
Lexical analyzer
 
Syntactic Structures
Syntactic StructuresSyntactic Structures
Syntactic Structures
 
形式言語理論への 測度論的アプローチ
形式言語理論への 測度論的アプローチ形式言語理論への 測度論的アプローチ
形式言語理論への 測度論的アプローチ
 
Ilja state2014expressivity
Ilja state2014expressivityIlja state2014expressivity
Ilja state2014expressivity
 
Final formal languages
Final formal languagesFinal formal languages
Final formal languages
 
Prosodic Morphology
Prosodic MorphologyProsodic Morphology
Prosodic Morphology
 

More from Isaac9LjWelchq

help 4- A ray of light is sent in a random direction towards the x-axi.docx
help 4- A ray of light is sent in a random direction towards the x-axi.docxhelp 4- A ray of light is sent in a random direction towards the x-axi.docx
help 4- A ray of light is sent in a random direction towards the x-axi.docxIsaac9LjWelchq
 
hello- please dont just copy from other answers- the following is the.docx
hello- please dont just copy from other answers- the following is the.docxhello- please dont just copy from other answers- the following is the.docx
hello- please dont just copy from other answers- the following is the.docxIsaac9LjWelchq
 
Hello- I am working on writing a penetration test plan for a fictitiou.docx
Hello- I am working on writing a penetration test plan for a fictitiou.docxHello- I am working on writing a penetration test plan for a fictitiou.docx
Hello- I am working on writing a penetration test plan for a fictitiou.docxIsaac9LjWelchq
 
Hello- I am struggling with figuring out how to solve for this The hor.docx
Hello- I am struggling with figuring out how to solve for this The hor.docxHello- I am struggling with figuring out how to solve for this The hor.docx
Hello- I am struggling with figuring out how to solve for this The hor.docxIsaac9LjWelchq
 
Hello! I need help with below project-Thank You- Please name and expla.docx
Hello! I need help with below project-Thank You- Please name and expla.docxHello! I need help with below project-Thank You- Please name and expla.docx
Hello! I need help with below project-Thank You- Please name and expla.docxIsaac9LjWelchq
 
Hello I wanted to know if I can get help with my medical information c.docx
Hello I wanted to know if I can get help with my medical information c.docxHello I wanted to know if I can get help with my medical information c.docx
Hello I wanted to know if I can get help with my medical information c.docxIsaac9LjWelchq
 
Hector loved visiting and playing with his grandson- David- Today was.docx
Hector loved visiting and playing with his grandson- David- Today was.docxHector loved visiting and playing with his grandson- David- Today was.docx
Hector loved visiting and playing with his grandson- David- Today was.docxIsaac9LjWelchq
 
Health psychology is a(n) - based science because practitioners are tr.docx
Health psychology is a(n) - based science because practitioners are tr.docxHealth psychology is a(n) - based science because practitioners are tr.docx
Health psychology is a(n) - based science because practitioners are tr.docxIsaac9LjWelchq
 
Healthcare Operations Analysis Utilizing Information Technology Explai.docx
Healthcare Operations Analysis Utilizing Information Technology Explai.docxHealthcare Operations Analysis Utilizing Information Technology Explai.docx
Healthcare Operations Analysis Utilizing Information Technology Explai.docxIsaac9LjWelchq
 
Hearing 10- What is the function of each of the following anatomical f.docx
Hearing 10- What is the function of each of the following anatomical f.docxHearing 10- What is the function of each of the following anatomical f.docx
Hearing 10- What is the function of each of the following anatomical f.docxIsaac9LjWelchq
 
Health information is important to public health authorities during an.docx
Health information is important to public health authorities during an.docxHealth information is important to public health authorities during an.docx
Health information is important to public health authorities during an.docxIsaac9LjWelchq
 
he reflex and reaction lab helped us understand how different factors.docx
he reflex and reaction lab helped us understand how different factors.docxhe reflex and reaction lab helped us understand how different factors.docx
he reflex and reaction lab helped us understand how different factors.docxIsaac9LjWelchq
 
having trouble with my code I'm using VScode to code a javascript code.docx
having trouble with my code I'm using VScode to code a javascript code.docxhaving trouble with my code I'm using VScode to code a javascript code.docx
having trouble with my code I'm using VScode to code a javascript code.docxIsaac9LjWelchq
 
How they can live a more Eco-friendly- Sustainable and Community Engag.docx
How they can live a more Eco-friendly- Sustainable and Community Engag.docxHow they can live a more Eco-friendly- Sustainable and Community Engag.docx
How they can live a more Eco-friendly- Sustainable and Community Engag.docxIsaac9LjWelchq
 
How many references are there to the list that refers to after the fol.docx
How many references are there to the list that refers to after the fol.docxHow many references are there to the list that refers to after the fol.docx
How many references are there to the list that refers to after the fol.docxIsaac9LjWelchq
 
How is the protective group removed to allow the addition of nucleotid.docx
How is the protective group removed to allow the addition of nucleotid.docxHow is the protective group removed to allow the addition of nucleotid.docx
How is the protective group removed to allow the addition of nucleotid.docxIsaac9LjWelchq
 
Has it been shown in the lab that simple organic compounds have formed.docx
Has it been shown in the lab that simple organic compounds have formed.docxHas it been shown in the lab that simple organic compounds have formed.docx
Has it been shown in the lab that simple organic compounds have formed.docxIsaac9LjWelchq
 
How many possible ways can you roll a seven- What is the probability o.docx
How many possible ways can you roll a seven- What is the probability o.docxHow many possible ways can you roll a seven- What is the probability o.docx
How many possible ways can you roll a seven- What is the probability o.docxIsaac9LjWelchq
 
have type O blood- (Round your answers to four decimal places-).docx
have type O blood- (Round your answers to four decimal places-).docxhave type O blood- (Round your answers to four decimal places-).docx
have type O blood- (Round your answers to four decimal places-).docxIsaac9LjWelchq
 
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docx
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docxHow many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docx
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docxIsaac9LjWelchq
 

More from Isaac9LjWelchq (20)

help 4- A ray of light is sent in a random direction towards the x-axi.docx
help 4- A ray of light is sent in a random direction towards the x-axi.docxhelp 4- A ray of light is sent in a random direction towards the x-axi.docx
help 4- A ray of light is sent in a random direction towards the x-axi.docx
 
hello- please dont just copy from other answers- the following is the.docx
hello- please dont just copy from other answers- the following is the.docxhello- please dont just copy from other answers- the following is the.docx
hello- please dont just copy from other answers- the following is the.docx
 
Hello- I am working on writing a penetration test plan for a fictitiou.docx
Hello- I am working on writing a penetration test plan for a fictitiou.docxHello- I am working on writing a penetration test plan for a fictitiou.docx
Hello- I am working on writing a penetration test plan for a fictitiou.docx
 
Hello- I am struggling with figuring out how to solve for this The hor.docx
Hello- I am struggling with figuring out how to solve for this The hor.docxHello- I am struggling with figuring out how to solve for this The hor.docx
Hello- I am struggling with figuring out how to solve for this The hor.docx
 
Hello! I need help with below project-Thank You- Please name and expla.docx
Hello! I need help with below project-Thank You- Please name and expla.docxHello! I need help with below project-Thank You- Please name and expla.docx
Hello! I need help with below project-Thank You- Please name and expla.docx
 
Hello I wanted to know if I can get help with my medical information c.docx
Hello I wanted to know if I can get help with my medical information c.docxHello I wanted to know if I can get help with my medical information c.docx
Hello I wanted to know if I can get help with my medical information c.docx
 
Hector loved visiting and playing with his grandson- David- Today was.docx
Hector loved visiting and playing with his grandson- David- Today was.docxHector loved visiting and playing with his grandson- David- Today was.docx
Hector loved visiting and playing with his grandson- David- Today was.docx
 
Health psychology is a(n) - based science because practitioners are tr.docx
Health psychology is a(n) - based science because practitioners are tr.docxHealth psychology is a(n) - based science because practitioners are tr.docx
Health psychology is a(n) - based science because practitioners are tr.docx
 
Healthcare Operations Analysis Utilizing Information Technology Explai.docx
Healthcare Operations Analysis Utilizing Information Technology Explai.docxHealthcare Operations Analysis Utilizing Information Technology Explai.docx
Healthcare Operations Analysis Utilizing Information Technology Explai.docx
 
Hearing 10- What is the function of each of the following anatomical f.docx
Hearing 10- What is the function of each of the following anatomical f.docxHearing 10- What is the function of each of the following anatomical f.docx
Hearing 10- What is the function of each of the following anatomical f.docx
 
Health information is important to public health authorities during an.docx
Health information is important to public health authorities during an.docxHealth information is important to public health authorities during an.docx
Health information is important to public health authorities during an.docx
 
he reflex and reaction lab helped us understand how different factors.docx
he reflex and reaction lab helped us understand how different factors.docxhe reflex and reaction lab helped us understand how different factors.docx
he reflex and reaction lab helped us understand how different factors.docx
 
having trouble with my code I'm using VScode to code a javascript code.docx
having trouble with my code I'm using VScode to code a javascript code.docxhaving trouble with my code I'm using VScode to code a javascript code.docx
having trouble with my code I'm using VScode to code a javascript code.docx
 
How they can live a more Eco-friendly- Sustainable and Community Engag.docx
How they can live a more Eco-friendly- Sustainable and Community Engag.docxHow they can live a more Eco-friendly- Sustainable and Community Engag.docx
How they can live a more Eco-friendly- Sustainable and Community Engag.docx
 
How many references are there to the list that refers to after the fol.docx
How many references are there to the list that refers to after the fol.docxHow many references are there to the list that refers to after the fol.docx
How many references are there to the list that refers to after the fol.docx
 
How is the protective group removed to allow the addition of nucleotid.docx
How is the protective group removed to allow the addition of nucleotid.docxHow is the protective group removed to allow the addition of nucleotid.docx
How is the protective group removed to allow the addition of nucleotid.docx
 
Has it been shown in the lab that simple organic compounds have formed.docx
Has it been shown in the lab that simple organic compounds have formed.docxHas it been shown in the lab that simple organic compounds have formed.docx
Has it been shown in the lab that simple organic compounds have formed.docx
 
How many possible ways can you roll a seven- What is the probability o.docx
How many possible ways can you roll a seven- What is the probability o.docxHow many possible ways can you roll a seven- What is the probability o.docx
How many possible ways can you roll a seven- What is the probability o.docx
 
have type O blood- (Round your answers to four decimal places-).docx
have type O blood- (Round your answers to four decimal places-).docxhave type O blood- (Round your answers to four decimal places-).docx
have type O blood- (Round your answers to four decimal places-).docx
 
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docx
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docxHow many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docx
How many ways can Marie choose 2 pizza toppings from a menu of 8 toppi.docx
 

Recently uploaded

Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17Celine George
 
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45MysoreMuleSoftMeetup
 
Morse OER Some Benefits and Challenges.pptx
Morse OER Some Benefits and Challenges.pptxMorse OER Some Benefits and Challenges.pptx
Morse OER Some Benefits and Challenges.pptxjmorse8
 
Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...Mark Carrigan
 
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General QuizPragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General QuizPragya - UEM Kolkata Quiz Club
 
Financial Accounting IFRS, 3rd Edition-dikompresi.pdf
Financial Accounting IFRS, 3rd Edition-dikompresi.pdfFinancial Accounting IFRS, 3rd Edition-dikompresi.pdf
Financial Accounting IFRS, 3rd Edition-dikompresi.pdfMinawBelay
 
Discover the Dark Web .pdf InfosecTrain
Discover the Dark Web .pdf  InfosecTrainDiscover the Dark Web .pdf  InfosecTrain
Discover the Dark Web .pdf InfosecTraininfosec train
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文中 央社
 
size separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceuticssize separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceuticspragatimahajan3
 
Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024CapitolTechU
 
How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17Celine George
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...Nguyen Thanh Tu Collection
 
Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Celine George
 
Championnat de France de Tennis de table/
Championnat de France de Tennis de table/Championnat de France de Tennis de table/
Championnat de France de Tennis de table/siemaillard
 
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdf
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdfINU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdf
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdfbu07226
 
Behavioral-sciences-dr-mowadat rana (1).pdf
Behavioral-sciences-dr-mowadat rana (1).pdfBehavioral-sciences-dr-mowadat rana (1).pdf
Behavioral-sciences-dr-mowadat rana (1).pdfaedhbteg
 
Essential Safety precautions during monsoon season
Essential Safety precautions during monsoon seasonEssential Safety precautions during monsoon season
Essential Safety precautions during monsoon seasonMayur Khatri
 
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfDanh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfQucHHunhnh
 

Recently uploaded (20)

Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 2 STEPS Using Odoo 17
 
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
Exploring Gemini AI and Integration with MuleSoft | MuleSoft Mysore Meetup #45
 
Post Exam Fun(da) Intra UEM General Quiz - Finals.pdf
Post Exam Fun(da) Intra UEM General Quiz - Finals.pdfPost Exam Fun(da) Intra UEM General Quiz - Finals.pdf
Post Exam Fun(da) Intra UEM General Quiz - Finals.pdf
 
Morse OER Some Benefits and Challenges.pptx
Morse OER Some Benefits and Challenges.pptxMorse OER Some Benefits and Challenges.pptx
Morse OER Some Benefits and Challenges.pptx
 
Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...Navigating the Misinformation Minefield: The Role of Higher Education in the ...
Navigating the Misinformation Minefield: The Role of Higher Education in the ...
 
“O BEIJO” EM ARTE .
“O BEIJO” EM ARTE                       .“O BEIJO” EM ARTE                       .
“O BEIJO” EM ARTE .
 
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General QuizPragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
Pragya Champions Chalice 2024 Prelims & Finals Q/A set, General Quiz
 
Financial Accounting IFRS, 3rd Edition-dikompresi.pdf
Financial Accounting IFRS, 3rd Edition-dikompresi.pdfFinancial Accounting IFRS, 3rd Edition-dikompresi.pdf
Financial Accounting IFRS, 3rd Edition-dikompresi.pdf
 
Discover the Dark Web .pdf InfosecTrain
Discover the Dark Web .pdf  InfosecTrainDiscover the Dark Web .pdf  InfosecTrain
Discover the Dark Web .pdf InfosecTrain
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
 
size separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceuticssize separation d pharm 1st year pharmaceutics
size separation d pharm 1st year pharmaceutics
 
Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024Capitol Tech Univ Doctoral Presentation -May 2024
Capitol Tech Univ Doctoral Presentation -May 2024
 
How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17How to the fix Attribute Error in odoo 17
How to the fix Attribute Error in odoo 17
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT VẬT LÝ 2024 - TỪ CÁC TRƯỜNG, TRƯ...
 
Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17Features of Video Calls in the Discuss Module in Odoo 17
Features of Video Calls in the Discuss Module in Odoo 17
 
Championnat de France de Tennis de table/
Championnat de France de Tennis de table/Championnat de France de Tennis de table/
Championnat de France de Tennis de table/
 
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdf
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdfINU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdf
INU_CAPSTONEDESIGN_비밀번호486_업로드용 발표자료.pdf
 
Behavioral-sciences-dr-mowadat rana (1).pdf
Behavioral-sciences-dr-mowadat rana (1).pdfBehavioral-sciences-dr-mowadat rana (1).pdf
Behavioral-sciences-dr-mowadat rana (1).pdf
 
Essential Safety precautions during monsoon season
Essential Safety precautions during monsoon seasonEssential Safety precautions during monsoon season
Essential Safety precautions during monsoon season
 
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdfDanh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf
 

How to determine whether a language is regular or not using Myhill-Ner.docx

  • 1. How to determine whether a language is regular or not using Myhill-Nerode theorem? I already have got this notes from my lectures, so I don't want a theoretical answer something that repeats the same thing: Here are the steps to prove that a language is not regular using the Myhill-Nerode theorem: 1) Define the relation L on the language L as follows: For any two strings x and y in *, x L y if and only if, for any string z in *, either all of xz and yz are in L, or neither of them are in L. 2) Construct an infinite set of pairwise distinguishable strings {w1, w2, w3, ...} such that for any i and j, if i j, then w i and w j are not equivalent under the relation L. To show that the set of strings is pairwise distinguishable, you need to show that for any two distinct strings w i and w j , there exists a string z such that either w i z is in L and w j z is not in L, or w j z is in L and w i z is not in L. This can be done by constructing such a string z for each pair of strings. 3) Show that there are an infinite number of equivalence classes of strings under L, which implies that the language L is not regular. If you can successfully perform these steps and show that there are an infinite number of equivalence classes, you can conclude that the language L is not regular. Language is regular if and only if there are a finite number of equivalence classes of strings under a certain relation. I want an explanation with some examples (regular language and non-regular language) to get an understanding of this.