19 votes 19 votes What is the type of the language $L$, where $L=\{a^n b^n \mid 0 < n < 327 \text{-th prime number} \}$ Theory of Computation gate1988 normal descriptive theory-of-computation identify-class-language + – go_editor asked Dec 18, 2016 • recategorized Apr 16, 2021 by Lakshman Bhaiya go_editor 3.0k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Rishav Kumar Singh commented Oct 27, 2018 reply Follow Share Here n is finite and finite language must be regular Languages. # If n >0 and n not mentioned prime only then it would be DCFL. # if n>0 and prime then it would be CSL 5 votes 5 votes Shiva Sagar Rao commented Jan 30, 2021 reply Follow Share Why does this question contain algorithms tag? 0 votes 0 votes Please log in or register to add a comment.
Best answer 27 votes 27 votes Here $n$ is finite and finite language must be regular. If $n$ is not restricted, then it would be DCFL. kirti singh answered Dec 18, 2016 • edited Jun 15, 2018 by Milicevic3306 kirti singh comment Share Follow See all 14 Comments See all 14 14 Comments reply Show 11 previous comments Satbir commented Sep 17, 2019 reply Follow Share Yes...it is also correct. 0 votes 0 votes iwasifirshad commented Jul 4, 2020 i edited by JAINchiNMay Nov 20, 2022 reply Follow Share But sir here, 'n' is a power of both 'a' and 'b' and we know that Regular Language uses Finite Automata, but FA doesn't have memory to store n.HOW CAN IT BE 'REGULAR LANGUAGE'? 0 votes 0 votes Gupta731 commented Aug 31, 2020 reply Follow Share @iwasifirshad But as you see $n$ is restricted to $0<n<327$th prime number, which makes the language finite. Hence Regular. 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes Regular language rishu_darkshadow answered Oct 5, 2017 rishu_darkshadow comment Share Follow See all 4 Comments See all 4 4 Comments reply Puja Mishra commented Nov 19, 2017 reply Follow Share Explain .... 0 votes 0 votes rishu_darkshadow commented Nov 23, 2017 reply Follow Share Because it is finite and every finite language is regular.... 1 votes 1 votes Puja Mishra commented Jan 15, 2018 reply Follow Share Finite and u can think it as union of regular language .... Specific ... 1 votes 1 votes raja11sep commented Jul 19, 2021 reply Follow Share Finite union 0 votes 0 votes Please log in or register to add a comment.