# Is the Language $L = \{a^n b^m c^k d^q e^r \,|\, n, m, k, q, r \geq 0\}$ a Valid Regular Language?

I am inquiring about the nature of language L. It appears that L is not categorized as a regular language due to its unique characteristics, which involve the need to count occurrences of multiple characters ('a', 'b', 'c', 'd', 'e'). Regular grammars, which are bound by the limitations of regular expressions and finite automata, are unable to handle such complexities. They are primarily designed to identify patterns but are incapable of keeping track of character counts or maintaining a balance between different symbols, such as 'a', 'b', 'c', 'd', and 'e', as required by this language.

I am seeking confirmation and insights regarding whether L can indeed be classified as a regular language or not. If it does not meet the criteria for regularity, I am interested in understanding the formalism or theoretical framework necessary to represent it accurately. I appreciate your assistance in shedding light on this matter.

• Maybe try a simpler example first: $\{a^nb^m\mid m,n\ge 0\}$. Or if that is still too hard, $\{a^n\mid n\ge 0\}$.
– MJD
Sep 26, 2023 at 13:29
• @MJD both are the Regular Language , as no memory is required
– Tips
Sep 26, 2023 at 13:31
• Why did you start your post with the assertion The language $L$ is not a regular language, and then ask Can someone confirm if $L$ is indeed a regular language ? Sep 26, 2023 at 13:42
• Did you intend do start your post by saying something like Perhaps $L$ is not a regular language? Sep 26, 2023 at 13:43
• Okay, what about $\{a^nb^mc^k\mid n,m,k\ge 0\}$?
– MJD
Sep 26, 2023 at 14:07

Your language is better described by the regular expression $$a^*b^*c^*d^*e^*$$ and hence is regular.