Questions tagged [automata-theory]

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

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5
votes
1answer
210 views

Can emptiness of reversal-bounded counter languages be decided in time polynomial to the number of counters?

I was reading this paper, about the complexity of decision problems for reversal bounded counter machines. I got to Theorem 1 on Page 6. The theorem shows that there's a log-space NTM which can ...
15
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2answers
615 views

Is there a well-defined division operation on finite automata?

Background: Given two deterministic finite automata A and B, we form the product C by letting the states in C be the cartesian product of states in A and states in B. Then, we choose transitions, ...
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3answers
1k views

On the realisation of monoids as syntactic monoids of languages

Let $L \subseteq X^{\ast}$ be some language, then we define the syntactic congruence as $$ u \sim v :\Leftrightarrow \forall x, y\in X^{\ast} : xuy \in L \leftrightarrow xvy \in L $$ and the quotient ...
5
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2answers
125 views

Characterization of union of DCFLs

We know that DCFL is not closed under the union operation and CFL is closed under union and contains the union of DCFLs. Is there a characterization of finite unions of DCFLs?
5
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1answer
170 views

Useful equivalence relations on $X^{\ast}$ (like the Nerode and syntactic equivalence relations)

I want to have an overview of all the meaningful equivalence relations defined on $X^{\ast}$, in particular when the languages in question are regular. They typically arise in connection with the ...
2
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1answer
528 views

Kleene closure of DFA

Given an $n$-state DFA (over a binary or any fixed alphabet), what is the complexity of computing its Kleene closure DFA? What is the largest possible/known blow-up in the number of states?
2
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3answers
547 views

Current research topics in tree automata

What are current research topics connected with tree automata? I'm particularly interested with connection between automatas, logics and databases. Kind regards, XYZ
21
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1answer
354 views

For which regular expressions $\alpha$ is $\{ \beta \mid L(\alpha) = L(\beta) \}$ PSPACE-complete?

It is well known that the following problem is PSPACE-complete: Given regular expression $\beta$, does $L(\beta) = \Sigma^*$? What about determining equivalence to other (fixed) regular ...
1
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1answer
357 views

How to generate Extended Finite State Machines Randomly with some properties?

This is related to my academic project An extended finite state machine is a tuple $SM=(I,S,T)$ (simplified): $I$ is the set of identifiers and it's divided into two sets Inputs and outputs, for ...
12
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1answer
196 views

Is there a survey of the field of quantum automata?

I'm looking for a survey paper of the important concepts in the field of Quantum Automata. I've found Quantum Automata Theory -- A Review by Hirvensalo, but it sounds too succinct to grasp the topic. ...
3
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1answer
102 views

What is the simplest universal unidimensional interaction net system?

The Interaction Combinators are possibly the simplest multidimensional system of interaction nets that is Turing-complete. What about interaction nets with only 2 ports - 1 principal, 1 auxiliary? ...
2
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0answers
73 views

What is the class of the languages recognized by PCREs?

I have been considering building a tool that would convert regexes between the various syntaxes (BRE, ERE, PCRE). It is obvious that PCREs are too strong for the is-regular problem to be decidable, ...
5
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2answers
286 views

Simplest Machine Model Accepting $L = \{ww^Rw\;|\; w\in \Sigma^*\}$

Let $\Sigma$ be a finite alphabet. A trivial finite automaton can accept the language $L_1 = \{w\;|\;w\in \Sigma^*\}$. A simple pushdown automaton can accept the language $L_2 = \{ww^R\;|;w\in \...
14
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1answer
543 views

Novel proof of pumping lemma for regular languages

Let $\mathcal{L}$ be the family of all languages over $\Sigma$ satisfying the pumping property of regular languages. Namely: for each $L\in\mathcal{L}$, there is an $N\in\mathbb{N}$ s.t. every word $w\...
10
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2answers
641 views

Are regular languages closed under addition?

Specifically what I mean by addition is, we define $\Sigma_i$ to be the alphabet $\{0, 1, 2, ..., i\}$. Given regular languages $A$ and $B$ under some alphabet $\Sigma_i$, look at $A\times B$. For ...
1
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2answers
146 views

Are equalizers of regular functions always regular languages? (My guess is no because PCP, but…)

Edit: I originally defined a regular function as a function computable by a Mealy machine, but Denis pointed out that that was a weaker model than what I was thinking of. So to be more precise, by a "...
7
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1answer
138 views

A word anticorrespondence problem

A problem instance is a finite list of 4-tuples $(\alpha_1, u_1, v_1, \beta_1), ..., (\alpha_N, u_N, v_N, \beta_N)$, where $\alpha_i, \beta_i \in X$ come from a finite set, and each $u_i,v_i \in A^*$ ...
1
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1answer
100 views

Normal form for deterministic (sub)sequential transducers with letter-by-letter outputs

For a project I'm working on, it would seem useful to have a normal form for deterministic (sub)sequential transducers in which the set of states, $Q$, is partitioned into states, $r \in Q_R$, that ...
9
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1answer
168 views

Do bounded-visit nondeterministic linear bounded automata recognize only regular languages?

Do bounded-visit nondeterministic linear bounded automata recognize only regular languages? By a nondeterministic linear bounded automaton (nLBA) I mean a single-tape nondeterministic Turing machine ...
-2
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2answers
188 views

An algorithm that determines if regular language accepts all string of its alphabet [closed]

Let $L$ be a regular language with the alphabet $\Sigma$. I'm trying to find an algorithm to tell whether $L=\Sigma^{*}$, whether $L$ accepts all strings in its alphabet. I think this algorithm uses ...
3
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1answer
69 views

An exponentially-ambiguous weighted automaton without an equivalent polynomially-ambiguous automaton

A min-plus weighted automaton (WFA) is a nondeterministic automaton with a weight function that assigns each transition a weight in $\mathbb{N}$. The weights along a run are summed, and the value of a ...
246
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11answers
95k views

What is the enlightenment I'm supposed to attain after studying finite automata?

I've been revising Theory of Computation for fun and this question has been nagging me for a while (funny never thought of it when I learnt Automata Theory in my undergrad). So "why" exactly do we ...
14
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2answers
558 views

Regular versus TC0

According to the Complexity Zoo, $\mathsf{Reg} \subseteq \mathsf{NC^1}$ and we know that $\mathsf{Reg}$ cannot count so $\mathsf{TC^0} \not\subseteq \mathsf{Reg}$. However it doesn't say if $\mathsf{...
9
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2answers
8k views

Why is non-determinism (Push-down automata) necessary?

I would like to know why for the recognition of context-free languages only non-deterministic push-down automata (DPA=NPDA) work. Why do deterministic push-down automata (DPDA) not recognize such ...
9
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2answers
275 views

Generalizing Brzozowski's DFA minimization algorithm to finite automata with different classes of accepting states?

Brzozowski's algorithm for converting a DFA into an equivalent minimum-state DFA is remarkably simple: if $R(D)$ denotes the NFA formed by reversing all the edges in a DFA $D$, making the old start ...
3
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5answers
763 views

How to constrain a finite automaton (NFA and DFA) to a tree?

I have a finite automaton by the standard model Hopcroft & Ullman define: $$ M = (Q, \Sigma, \delta, q_0, F) $$ Where $\delta$ is the transition function mapping $Q \times \Sigma \mapsto Q$, such ...
6
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2answers
241 views

FSM transducer sequential composition decidability

this is a followup/ sequel to this recent question which was answered, this one presumably significantly harder. consider a deterministic FSM transducer $F$ and its mapping $F(x)$ of an input word $x$....
10
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1answer
212 views

Is it decidable whether the output length of a transducer is bounded by the input length?

The transducers considered here are those Wikipedia calls finite state transducers. The behavior of a transducer $T$, that is, the relation it computes, is written $[T]$: a word $y$ is an output for $...
9
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1answer
233 views

Directed multigraphs as minimal automata

Given a regular language $L$ on alphabet $A$, its minimal deterministic automaton can be seen as a directed connected multigraph with constant out-degree $|A|$ and a marked initial state (by ...
37
votes
9answers
18k views

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 ...
-2
votes
1answer
210 views

Writing a regular expression for character set $\Sigma = \{a,b,(,)\}$ that not have a parenthesis inside a parenthesis [closed]

Let character set $\Sigma=\{a,b,(,)\}$. I want to write a regular expression for the language $L$ that does not have a parenthesis inside a parenthesis. For example, $(abaab)(bbbaa) \in L$, while $(...
6
votes
2answers
240 views

Deciding functionality of transducers over infinite words

Given a finite state transducer defining a rational relation over infinite words, it is known to be decidable whether or not the relation is a function, i.e. whether each infinite input word is ...
5
votes
0answers
93 views

Why do multi-stack visibly pushdown languages label each call/return with a particular stack?

In A Unifying Approach for Multistack Pushdown Automata, multistack visibly pushdown automata are defined in terms of an alphabet where each symbol is either a call or return for a particular stack or ...
3
votes
1answer
108 views

Deterministic Parity Automata require unbounded index

Deterministic parity automata $(Q, \Sigma, q_0, \Delta, c)$ are powerful enough to recognize all $\omega$-regular languages. However, the number of priorities they require for a language can become ...
6
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0answers
781 views

What would a PDA be with a queue instead of a stack?

A while ago it occurred to me that the stack data model in a push-down automaton could be exchanged for a queue or deque model. I've explored this a bit as a pet project and it looks like an automaton ...
15
votes
1answer
541 views

Are DPDAs without a $\epsilon$ moves as powerful as DPDAs with them?

In the formal description of Deterministic Pushdown Automata, they allow $\epsilon$ moves, where the machine can pop or push symbols onto the stack without reading a symbol from the input. If these $\...
35
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6answers
5k views

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 ...
2
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2answers
104 views

If the set of factors of an infinite word $\xi$ is regular, is this property stable under “shift's” of $\xi$?

Let $\xi$ be an infinite binary sequence, and denote by $T(\xi)$ the set of all factors (infixes) of $\xi$. Also if $w$ is some finite prefix of $\xi$, denote by $\xi/w$ the unique $\eta$ such that $w ...
10
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1answer
267 views

What is the state complexity of the copy language?

Let a number $n$ be given. Consider the following language $L_n = \{ \; ww \; \vert \; w \in \{0,1\}^{n} \; \}$. In words, $L_n$ is the set of copy strings of length $2n$. Consider the following ...
4
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1answer
1k views

Emptiness of PDA without constructing the corresponding CFG

The emptiness problem for Context free Grammars(CFG) is well studied. The same holds for the equivalence problem between Pushdown Automata (PDA) and CFGs. Therefore, given a PDA, the straightforward ...
26
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4answers
1k views

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": ...
23
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1answer
549 views

Languages recognized by polynomial-size DFAs

For a fixed finite alphabet $\Sigma$, a formal language $L$ over $\Sigma$ is regular if there exists a deterministic finite automaton (DFA) over $\Sigma$ which accepts exactly $L$. I am interested in ...
17
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1answer
2k views

computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
9
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0answers
433 views

What exactly are Moore machines?

Ok, don't be scared by the title - it is not that I don't know the concept of a Moore machine, or basic FSM concepts in general. However, I think that the term "Moore machine", despite being ...
5
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0answers
115 views

Learning Finite Automata Behavior by Experimentation

This conjecture is from an expert in Game Theory area, I post it here to draw more attentions of TCS experts. Discussions and comments are welcome. http://gtcenter.org/WCS_Call_for_papers.pdf An ...
6
votes
1answer
215 views

Who introduced nondeterministic M-automata, and proved that the finite ones recognize the rational sets over M?

Let $M$ be a monoid. The family $\operatorname{RAT}(M)$ of rational sets over $M$ is defined inductively: If $L$ is a finite subset of $M$, then $L\in\operatorname{RAT}(M)$. If $K,L\in\operatorname{...
4
votes
1answer
443 views

Decidability of membership in the fixed point of a rational relation

Given a finite alphabet $\Sigma$, a non-deterministic finite-state transducer representing rational a relation $T \subseteq \wp(\Sigma^* \times \Sigma^*)$, a finite state machine representing a ...
43
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5answers
6k views

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 ...
10
votes
2answers
182 views

Separating lists of words

There is an open problem in formal languages known as the Separating Problem; which is briefly stated as given two distinct strings of length $n$, how large of a DFA is required to "separate" them, ...
5
votes
1answer
138 views

When does automaton stay unchanged after string homomorphism?

Suppose we have a string homomorphism $\varphi: \Sigma \rightarrow \Sigma^*$. Consider the languages in $\varphi(\Sigma^*)$ whose letters are elements of $\varphi(\Sigma)$, so here I do not want to ...