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Questions tagged [automata]

In theoretical computer science, automata theory is the study of abstract 'mathematical' machines or systems and the computational problems that can be solved using these machines. These abstract machines are called automata. ("Automata", Wikipedia)

From Wikipedia,

Automata, or automata theory, is the study of mathematical objects called abstract machines or automata and the computational problems that can be solved using them. Automata comes from the Greek word αὐτόματα meaning "self-acting".

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How should Chomsky's Hierarchy and Turing Machines influence language design?

I'm currently studying for a discrete mathematics test in which we are learning Chomsky's hierarchy and the type of automatas that recognize each level of the hierarchy. I'm being taught that most computer languages fall within "level 2 and 1" of…
andandandand
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Context Free Language Question (Pumping Lemma)

I know this isn't directly related to programming, but I was wondering if anyone know how to apply the pumping lemma to the following proof: Show that L={(a^n)(b^n)(c^m) : n!=m} is not a context free language I'm pretty confident with applying…
Maixy
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What is the difference between (a+b)* and (a*b*)*?

Assuming that Σ = {a, b}, I want to find out the regular expression (RE) Σ* (that being the set of all possible strings over the alphabet Σ). I came up with below two possibilities: (a+b)* (a*b*)* However, I can't decide by myself which RE is…
Rurou2
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Automata Theory books

Please suggest me some good books on "Formal languages and Automata Theory". Thanks!
Prasoon Saurav
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Formal Context Free Grammar From Context Free Language

How can a formal context free grammar be generated for the following language: {ai bjck | i != j or j != k} I have following productions but can't understand it: S->AX | YC unequal b’s c’s or a’s b’s A-> aA | e …
Light
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Combining deterministic finite automata

I'm really new to this stuff so I apologize for the noobishness here. construct a Deterministic Finite Automaton DFA recognizing the following language: L= { w : w has at least two a's and an odd number of b's}. The automate for each part of…
Haskell
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What's the proper grammar for this language?

I have this language: {an bm | m+n is an even number} What's the proper grammar for this?
Nick.h
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What are the useful limits of Linear Bounded Automata compared to Turing Machines?

There are languages that a Turing machine can handle that an LBA can't, but are there any useful, practical problems that LBAs can't solve but TMs can? An LBA is just a Turing machine with a finite tape, and actual computers have finite storage, so…
Bribles
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Levenshtein DFA in .NET

Good afternoon, Does anyone know of an "out-of-the-box" implementation of Levenshtein DFA (deterministic finite automata) in .NET (or easily translatable to it)? I have a very big dictionary with more than 160000 different words, and I want to,…
Miguel
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Design a PDA of all strings of 0's and 1's so that the number of 1's is twice the number of 0's

While practicing for my final exams I found this question in Automata Theory, Language and Computation by J. Hopcroft, R. Motwani, J. Ullman on page 222. PDA should accept string in which the count of number of 1's is twice of number of 0's and if…
user3276435
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confusion in finding first and follow in left recursive grammar

Recently I faced the problem for finding first and follow S->cAd A->Ab|a Here I am confused with first of A which one is correct {a} , {empty,a} as there is left recursion in A's production . I am confused whether to include empty string in…
rajkumar
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Regular expression to match string of 0's and 1's without '011' substring

I'm working on a problem (from Introduction to Automata Theory, Languages and Computer by Hopcroft, Motwani and Ullman) to write a regular expression that defines a language consisting of all strings of 0s and 1s not containing the substring 011. Is…
Prasoon Saurav
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What is the concatenation of this language with itself?

Given the following language: L1 = { (ab)n | n ≥ 0 } That is, L1 = { ε ab, abab, ababab, abababab, ... } The question is to find what language L12 is. My guess is that it's equal to { (ab)2n | n ≥ 0 }. Is that correct? If so, how do I prove it?…
Rouki
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Can someone give a simple but non-toy example of a context-sensitive grammar?

I'm trying to understand context-sensitive grammars, and I understand why languages like {ww | w is a string} {an bn cn | a,b,c are symbols} are not context free, but what I'd like to know if a language similar to the untyped lambda calculus is…
BlueBomber
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Find longest common substring of multiple strings using factor oracle enhanced with LRS array

Can we use a factor-oracle with suffix link (paper here) to compute the longest common substring of multiple strings? Here, substring means any part of the original string. For example "abc" is the substring of "ffabcgg", while "abg" is not. I've…
Ray
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