Questions tagged [automata-theory]

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

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2
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1answer
255 views

Partition refinement in transition state systems (bisimulation contraction)

I am trying to understand bisimulation contraction of Kripke models. I have read these lecture slides and this Wikipedia page, but I still don't fully understand it. I can understand that the two ...
7
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1answer
338 views

Is this a regular relation?

I'm a linguist (and not a computer scientist!) investigating a new sort of linguistic formalism for mapping phonological strings into other strings - and I'm wondering if it's a regular relation that ...
3
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2answers
157 views

A property of suffix-free regular languages of maximal state complexity for the reverse operation

Let $L$ be a regular suffix-free language whose complete minimal automaton has $n$ states and that the minimal automaton of $L^R$ has exactly $2^{n-2}+1$ states. Let $p, q$ be two distinct states of ...
17
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2answers
261 views

A reference for a “more algebraic” approach to pushdown automata and CFLs?

In the Sakarovitch's book on automata theory, it is written in the introduction to the section on rationals in the free group that the material presented therein lays "the foundation of a truly ...
1
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0answers
168 views

Hysteresis in finite automata

The concept of hysteresis seems well suited to describe and distinguish finite automata: "Hysteresis is the dependence of the state of a system on its history." (Wikipedia, Hysteresis) "[The ...
6
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2answers
176 views

Finite Automata with succinct representation of chains of states

Consider a kind of automata similar to common DFAs or NFAs where it is possible to represent succinctly linear chains of states. In other words, an automaton like this: could be represented in this ...
14
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4answers
563 views

Hierarchies in regular languages

Is there any known "nice" hierarchy $L_0 \subseteq L_1 \subseteq L_2 \subseteq \dots$ (may be finite) inside the class of regular languages $L$? By nice here, the classes in each hierarchy capture ...
3
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0answers
183 views

Formal definition of Turing Completeness [closed]

Wikipedia states: In computability theory, a system of data-manipulation rules […] is said to be Turing complete or computationally universal if it can be used to simulate any single-taped Turing ...
12
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2answers
532 views

Non-isomorphic minimal non-deterministic finite automata

Can somebody provide an example of two equivalent (recognizing the same language) minimal non-deterministic automata (NFA) which are not isomorphic?
2
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1answer
51 views

Determining the Class of a given Cellular Automata structure

Is it possible to write an algorithm that can determine the class of a given cellular automata structure ? (ie. Wolfram's 4 Classes) Thank you Ricky
2
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2answers
224 views

Simplest Machine Model for a langauge $ L = \{(w\# )^{k}\;|\; w\in \Sigma^{*},\;k\in \mathbb{N}\}$

What is the simplest machine model accepting the following language? $$ L = \{(w\# )^{k}\;|\; w\in \Sigma^{*},\;k\in \mathbb{N}\}$$ In other words, $L$ is obtained by taking each string $w$ in $\...
11
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3answers
471 views

Are there non-constructive proofs of existence of “small” Turing machines / NFAs?

After reading a related question, about non-constructive existence proofs of algorithms, I was wondering if there are methods of showing existence of "small" (say, state-wise) computation machines ...
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0answers
107 views

Why is an automaton on finite words co-deterministic iff its transitions are co-deterministic

In the article Automata and semigroups recognizing infinite words an automaton is specified by $\mathcal A = (Q, A, E, I, F)$ where $I$ is a set of initial states and $F$ a set of final states, $Q$ ...
2
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0answers
84 views

Proof of the equivalence of Muller automata and Parity (or Rabin chain) automata

Let $A$ be some finite alphabet and $\mathcal A = (Q, \delta, q_0)$ be some determinisitic finite automaton. Then $\mathcal A$ accepts infinite words $\xi \in A^{\omega}$ according to the Muller ...
18
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2answers
6k views

Finite automata that accept binary strings divisible by n

I'm working on a problem set for a class, and thought of a question related to what I was working on. Is there a minimum number of states that a finite automaton must have in order to accept binary ...
13
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4answers
693 views

(N)DFA with same initial/accepting state(s)

What is known about the class of languages recognized by finite automata having the same initial and accepting state? This is a proper subset of the regular languages (since every such language ...
5
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1answer
224 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
662 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, ...
13
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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 ...
6
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2answers
131 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
174 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
590 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
626 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
383 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
378 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
198 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
110 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
77 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
310 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
558 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
690 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 ...
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2answers
154 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
103 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
170 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 ...
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2answers
208 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
78 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 ...
248
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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
567 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
291 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
833 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
votes
2answers
246 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
215 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
240 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 ...
38
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9answers
20k 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
249 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
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0answers
96 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
110 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 ...