Talk:Regular language

message: A regular language is a formal language (i.e. a possibly infinite set of finite sequences of symbols from a finite alphabet) that has one of the following equivalent properties:
* (...)
*  it can be described by a regular expression.
Modern "regular" expressions can describe more languages than just regular ones.
Example: /([a-z]*)\\1/ (weird software problem - there should be 1 backslash there) --Taw
:Obviously, this refers to regular expressions in the sense used in the theory of computation, not Perl regular expressions etc. -- Schnee 12:16, 13 Jun 2004 (UTC)
thread_title: Regular expressions

message: '# it can be accepted by a deterministic finite state machine.' is superfluous. Every NFA has an equivalent DFA. So by requiring a regular language to be accepted by an NFA requires it to be accepted by a (the corrisponding DFA)
:That's not superfluous. All the properties listed are equivalent, after all, and to the uninitiated, it's not obvious that DFAs and NFAs are basically the same. -- Schnee 12:16, 13 Jun 2004 (UTC)
thread_title: NFA's

message: This article describes the properties of regular languages and gives a few examples, but I think a kind of formal definition was missing. I added a well-known recursive definition. I think it fits pretty well in the article. What do you think? --Alexandre 22:27, 25 Jun 2004 (UTC)
replies: text: The section Regular language#Examples says that ∅* yields {ε}. That was my reason to revert the edit of 21 Feb. I just looked it up: the definition of Aho.Hopcroft.Ullman.1974 (sect.9.1, p.318) agrees with the example. - Jochen Burghardt (talk) 21:36, 22 February 2016 (UTC)
thread_title: Formal definition

message: The recursive definition is quite nice.  There's something I don't understand here, though.  Why is the kleene star required in the recursive definition?  It seems to me that you can construct it by induction using concatenation. 
Here's a proof.  Is it incorrect somewhere?
Suppose L is regular.  If \{\epsilon\} \cup L \cup L^2 \cup \cdots \cup L^n is regular, then concatenate L to get that L \cup L^2 \cup \cdots \cup L^{n+1} is regular.  Union with \{\epsilon\}. Therefore L* is regular.
:The trick is that ordinary induction cannot "go to infinity". Your proof only establishes that the language \{\epsilon\} \cup L \cup L^2 \cup \cdots \cup L^n is regular for all integers n. But none of these languages includes all of L*, only their union does, and regular languages are not closed under infinite unions. (if they were, every countable language would be regular) Deco 21:56, 5 December 2005 (UTC)
thread_title:  Kleene star 

message: Can anybody talk about properties of non - regular languages? (unsigned, undated)
it would be of great help if some one could post more info about non regular languages  7 OCT 2007  —Preceding unsigned comment added by 64.234.33.191 (talk) 19:18, 7 October 2007 (UTC)
thread_title: Properties of non-regular languages

message: The Article first describes regular language as one that is accepted by a deterministic finite state machine.  Then it defines it using the recursive definition.  The point is that either one can be used as definition.  However, if one is used as definition, the other one must be proved as theorem.--CBKAtTopsails 16:20, 6 June 2007 (UTC)
replies: text: This is implied by the word "equivalent", but may deserve clarification. Dcoetzee 18:15, 11 September 2007 (UTC)
thread_title: More Than One Definition?

message: Um... I'm not exactly an expert on the subject, but doesn't it certainly not contain AC0?  I'm hesitant to take it out, because I don't really know what I'm talking about (not to mention that I don't want to say they're separate without a source, and just cutting it might imply to the casual reader that it does contain it), but it seems to me as though certain languages in AC0 being regular would allow you to use their DFAs to construct DFAs for L-hard languages, violating the space hierarchy theorem.  Twin Bird (talk) 04:40, 1 July 2011 (UTC)
thread_title:  "On the other hand, it is not known to contain AC0." 

message: I propose that Rational language (currently orphaned) be merged into Regular language. I think that the content in the rational language article can easily be explained in the context of regular languages, and this article is of a reasonable size that the merging of Rational language will not cause any problems as far as article size or undue weight is concerned. Hermel (talk) 22:01, 3 August 2013 (UTC)
replies: text: Are you proposing this just because the names are similar? Regular language is also a particular case of context-free language and a lot of others... That doesn't mean all notions more general than Regular should be merged into Regular. If anything should be done with Rational language is to merge it to rational series—its generating notion. JMP EAX (talk) 23:00, 17 August 2014 (UTC)
thread_title:  Merger proposal 

message: "the number of equivalence classes of its syntactic congruence is finite.[note 8][note 9] (This number equals the number of states of the minimal deterministic finite automaton accepting L.)"
I'm quite sure that the sentence in parentheses is not true. The number of equivalence classes of the syntactic congruence is the size of the syntactic monoid. This is also the size of the transition monoid of the minimal deterministic finite automaton accepting L. However, there are usually more elements in the monoid than states in the automaton.  — Preceding unsigned comment added by 81.218.76.25 (talk) 08:45, 6 October 2019 (UTC)
thread_title:  Mistake in "Equivalent formalisms" section 

message: We also have regular and rational languages in the domain of trace languages.  They are defined using different definitions that coincide for the free monoid of strings in an alphabet, namely recognition by DFAs and the purely algebraic definitions respectively, for not all rational trace languages are regular trace languages.  The bad boy example is (U+0F73 TIBETAN VOWEL SIGN II}* in the domain of Unicode strings under canonical equivalence, with decomposable characters treated as syntactic sugar.
Should we mention such divergences here, or just have a headnote redirecting the read to Trace monoid for the use of the terms with respect to trace languages?  That article doesn't yet have a section on these languages. --RichardW57m (talk) 12:02, 30 March 2022 (UTC)
replies: text: IMO this deserves a mention under the Generalizations section, but not elsewhere, and the main content related to this should go at trace monoid. Caleb Stanford (talk) 14:56, 30 March 2022 (UTC)
replies: text: The existence of a generalisation needs to be mentioned somewhere before the reader concludes that this article has nothing to say about these terms for traces. --RichardW57m (talk) 16:04, 30 March 2022 (UTC)
thread_title:  Trace Languages 

message: — Assignment last updated by Fedfed2 (talk) 00:53, 9 December 2023 (UTC)
thread_title: Wiki Education assignment: Linguistics in the Digital Age