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   Shifty Skip (shiftyskip@social.linux.pizza)'s status on Wednesday, 26-Mar-2025 20:19:46 JST Shifty Skip

   • Abhiseck Paira :gnu:

   @redstarfish Yes. A DFA either accepts or rejects a given word, and the language it recognises is the set of accepted words.
   Therefore, languages A and B are both "the set of words that are accepted by M".

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     MortSinyx (cnx@awkward.place)'s status on Thursday, 27-Mar-2025 01:50:34 JST MortSinyx

     • Abhiseck Paira :gnu:

     :blobcat_murakamisan_yes: @redstarfish, as both are L(M).

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     Shifty Skip (shiftyskip@social.linux.pizza)'s status on Thursday, 27-Mar-2025 02:03:54 JST Shifty Skip

     • Shakil Akhtar 🇸🇦 🇵🇸
     • Abhiseck Paira :gnu:
     • MortSinyx

     @redstarfish @cnx @shakil_tcs When we say a DFA M "recognizes" a language A, it means M accepts every word in A, and rejects every word not in A.
     This means, in your example, M doesn't recognize A1, because it accepts words that aren't in A1 (those from A2 \ A1).
     M only recognizes the language C and no other.

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     Shakil Akhtar 🇸🇦 🇵🇸 (shakil_tcs@mstdn.starnix.network)'s status on Thursday, 27-Mar-2025 14:16:43 JST Shakil Akhtar 🇸🇦 🇵🇸

     • Abhiseck Paira :gnu:
     • MortSinyx

     @redstarfish @cnx M doesn't recognise A1, if A1 =/= A2. It recognises A1 union A2. Unless, you define recognising a language to mean just accepting the words in the language.
     However, the standard definition is accepting every word in the language and rejecting every word not in the language.