Questions tagged [automata-theory]

Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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27
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2answers
1k views

Conditions for NFA universality

Consider a nondeterministic finite automata $A = (Q, \Sigma, \delta, q_0, F)$, and a function $f(n)$. Additionally we define $\Sigma^{\leq k} = \bigcup_{i \leq k} \Sigma^i$. Now lets analyze the ...
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1answer
753 views

Are variables in RHS of Chomsky Normal Form productions distinct?

I'm wondering if it is permitted for production rules in a context-free grammar (CFG) in Chomsky Normal Form (CNF) to have multiple occurences of the same variable in the right-hand side of the ...
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2answers
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Status of Cerny Conjecture?

A DFA has a synchronizing word if there is a string that sends any state of the DFA to a single state. In ‘The Cerny Conjecture for Aperiodic Automata” by A. N. Trahtman (Discrete Mathematics and ...
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2answers
498 views

Taxonomy of notable regular expression automata

I'm trying to draw up a taxonomy of algorithms for transforming regular expressions into automata so as to perform some empirical tests of their complexity properties in specific domains. I'm aware ...
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1answer
1k views

Question about Mapping Reductions (Clarify Example)

I cannot for the life of me wrap my head around these reductions. Specifically, the example I'm wrestling with: ...
26
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4answers
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Is there a non Turing-complete model of computation whose halting problem is undecidable?

I cannot think of any such model, maybe some form of typed lambda calculus? some elementary cellular automaton? This would almost disprove Wolfram's "Principle of Computational Equivalence": ...
7
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1answer
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Photo of «Introduction to automata…» by Hopcroft and Ullman '79 cover?

Where can I get the photo of “Introduction to automata theory, languages and computation” by Hopcroft and Ullman '79 (first edition) cover in order to be able to read all the phrases placed on the ...
25
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2answers
1k views

Context Sensitive Grammars and Types

1) What, if any, is the relationship between static typing and formal grammars? 2) In particular, would it be possible for a linear bounded automaton to check whether, say, a C++ or SML program was ...
43
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5answers
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Is the Chomsky-hierarchy outdated?

The Chomsky(–Schützenberger) hierarchy is used in textbooks of theoretical computer science, but it obviously only covers a very small fraction of formal languages (REG, CFL, CSL, RE) compared to the ...
8
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1answer
439 views

Tool for translating PDAs to CFGs

We know that all push down automata are representable using context-free grammars. Furthermore, there is an algorithm to construct a CFG from any PDA (e.g. Sipser's proof in intro to theory of ...
9
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2answers
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Are there families of formal languages known to be truly PAC learnable?

I specifically mean language families that admit arbitrarily long strings -- not conjunctions over n bits or decision lists or any other "simple" language contained in {0,1}^n. I am asking about "...
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2answers
271 views

Why may the right hand sides in Chomsky Hierachy type 1 be larger?

I'm shaking my head because of this question, my Prof. didn't explain it. We have linear space limited automata and they have to satisfy for rules a -> b that |a| <= |b|. Why? I would have said, ...
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3answers
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Proving the set of powers of 2 over ternary alphabet to be non regular.

It's simple to see that the powers of 2 over alphabet {0,1} is regular because $10^*$ is a regular expression for it. But the powers of 2 represented in ternary appears to be non regular. Pumping ...
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11answers
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Books on automata theory for self-study

I need a finite automata theory book with lots of examples that I can use for self-study and to prepare for exams.
30
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2answers
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Is {$a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} non-context-free?

Is the language {$a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} context-free or not? I realized that I have encountered almost all variants of this question with different conditions about the ...
11
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1answer
489 views

Ehrenfeucht-Fraïssé games (Ajtai-Fagin in fact) for regular languages.

Immerman (Descriptive Complexity, 1999) presents the EF games for existential monadic second order (Ajtai-Fagin games) on page 127. As $\exists$MSO on words is equivalent to regular languages, the ...
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3answers
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Properties of Random Directed Graphs with Fixed Out-Degree

I am interested in properties of random directed graphs with fixed out-degree $d$. I am imagining a random graph model where each vertex chooses d neighbors (say, with replacement) u.a.r. ...
30
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4answers
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Are there “small” machines which can efficiently match regular expressions?

It's well-known that a regular expression can be recognized by a nondeterministic finite automaton of size proportional to the regular expression, or by a deterministic FA which is potentially ...
13
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1answer
453 views

Fast sparse boolean matrix chain product

So, I've got about 100-200 very sparse square boolean matrices with side length ~several dozens, and I need to compute their product. I know that if I multiply them serially, the product will usually ...
19
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4answers
3k views

Where do most REGEX implementations fall on the complexity scale?

Most modern implementations of regular expressions, such as the ones in perl or .NET, go beyond the classical computer science definition of REGEXes with features like lookahead and lookbehind. Do ...
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5answers
3k views

Automata Theory / Formal Language Thesis Topic

Hey All, I'm currently trying to find a solid masters thesis topic pertaining to some branch of automata theory or related to formal languages. I'm trying to generate some good ideas for what an ...
38
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9answers
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What is the difference between non-determinism and randomness?

I recently heard this - "A non-deterministic machine is not the same as a probabilistic machine. In crude terms, a non-deterministic machine is a probabilistic machine in which probabilities for ...
35
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6answers
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Regular expressions aren't

Ask even someone with a background in computer science what a regular expression is, and the answer is likely to go beyond the constraint of being within reach of a finite-state automaton. For ...
6
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3answers
529 views

Can words in regular languages be generated by automata in a unique way?

If $L\subset \Sigma^\ast$ is a regular language then it is known that we can find a directed graph (aka automaton) $G$ with edges labelled with symbols from $\Sigma$, an ‘initial’ vertex, and a set of ...
16
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1answer
332 views

Compared growth of the number of syntactic classes and Nerode classes.

For a language L ⊆ Σ^*, define the syntactic congruence ≡ of L as the least congruence on Σ^* that saturates L, i.e. : u ≡ v ⇔ (∀ x, y)[xuy ∈ L ↔ xvy ∈ L]. Now define the Nerode equivalence as the ...
25
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4answers
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DFA intersection in subquadratic space?

The intersection of two (minimal) DFAs with n states can be computed using O(n2) time and space. This is optimal in general, since the resulting (minimal) DFA may have n2 states. However, if the ...
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2answers
379 views

Can every non-deterministic finite automate be changed into one with only one acceptance state? [closed]

How can an arbitrary non-deterministic finite automate be converted into one with only one accept stage? If so, what is the proof that this can always be done?
18
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0answers
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To what extent MSO = WS1S, when adding relations?

[This question has been asked on MathOverflow with no luck a month ago.] Let me first clarify my definitions. For a word $w \in \Sigma^*$, with $\Sigma =\{a_1, \ldots, a_n\}$, I define two ...