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

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3
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43 views

A question on the introduction of the Wagner hierarchy from K. Wagner's original paper

My question is related to the seminal paper On $\omega$-regular sets by K. Wagner, which introduced a hierarchy which is now know as the Wagner- (or Wadge-) hierarchy of $\omega$-regular sets. In ...
-2
votes
0answers
35 views

How to show that a timed language is not timed regular?

today I tryed comprehend the examples for not timed regular languages given in A theory of timed automata. For the timed language I tryed to proof that it is not timed regular by contradiction ...
13
votes
3answers
729 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 ...
0
votes
0answers
34 views

Question on the construction of a deterministic Mueller automaton in the proof of McNaughton's theorem

My question is related to this classic article by R. McNaughton, its content is almost identically written on wikipedia. I will change the notation a little bit to make it more modern. Let $L_1, L_2 \...
14
votes
2answers
351 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, ...
5
votes
2answers
103 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
votes
1answer
143 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 ...
4
votes
1answer
103 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?
19
votes
1answer
265 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 ...
2
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3answers
180 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
5
votes
2answers
148 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 \...
32
votes
9answers
13k views

Real computers have only a finite number of states, so what is the relevance of Turing machines to real computers?

Real computers have limited memory and only a finite number of states. So they are essentially finite automata. Why do theoretical computer scientists use the Turing machines (and other equivalent ...
4
votes
1answer
42 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? ...
3
votes
0answers
56 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, ...
11
votes
1answer
164 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. ...
1
vote
1answer
83 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 ...
14
votes
1answer
338 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\...
1
vote
2answers
100 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
votes
1answer
127 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
vote
1answer
75 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 ...
10
votes
1answer
118 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 ...
4
votes
1answer
46 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 ...
14
votes
2answers
484 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
votes
2answers
116 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
votes
5answers
394 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 ...
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votes
2answers
133 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 ...
6
votes
2answers
203 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
votes
1answer
198 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 $...
7
votes
1answer
150 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 ...
-2
votes
1answer
98 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
133 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 ...
4
votes
0answers
42 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 ...
4
votes
0answers
202 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 ...
2
votes
1answer
77 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 ...
13
votes
1answer
185 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 $\...
2
votes
2answers
98 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
votes
1answer
226 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
votes
1answer
192 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 ...
9
votes
0answers
210 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
votes
0answers
100 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 ...
5
votes
1answer
150 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{...
3
votes
1answer
86 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 ...
9
votes
2answers
141 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
116 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 ...
1
vote
0answers
177 views

Complexity of DBA-recognizable Omega-Languages

Given an $\omega$-regular expression $r$, how difficult is it to decide if $L(r)$ is recognizable by some deterministic Büchi automaton? I know it is solvable in EXPTIME by converting the regular ...
3
votes
1answer
95 views

Finite state transducer with infinitary outputs or without emphasis on acceptance?

1) Is there a notion of (deterministic) finite state transducer (FST) that allows the possibility of producing an infinite stream of output symbols? In other words, one where the transduction ...
22
votes
1answer
526 views

Deciding emptiness of intersection of regular languages in subquadratic time

Let $L_1,L_2$ be two regular languages given by NFAs $M_1,M_2$ as input. Assume we would like to check whether $L_1\cap L_2\neq \emptyset$. This can clearly be done by a quadratic algorithm which ...
3
votes
0answers
193 views

Equivalence of deterministic finite transducers over finite/infinite words

Equivalence of deterministic finite transducers - a special case of single-valued finite transducers - is decidable because it is decidable whether a transducer is single-valued. Note that two ...
19
votes
1answer
496 views

Finding the smallest DFA that separates two words without using brute force search?

Given two strings x and y, I want to build a minimum size DFA that accepts x and rejects y. One way to do this is brute force search. You enumerate DFA's starting with the smallest. You try each ...
3
votes
2answers
240 views

computing maximal bit density over a FSM

let $L$ be a regular language defined by a FSM over binary symbols $\{0,1\}$. consider a function $f(x)$ on words/ strings that computes "bit density", defined as the number of $1$'s in a word ("...