# Questions tagged [automata-theory]

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88
questions

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### decidability of regularity of a language depending on representation

It is well known that many decision problems for regular languages are decidable. However, the proofs seem to rely on a witness of the regularity of said language, be it an automaton, a grammar, a ...

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60 views

### What a generating function for a language tells us about the language [closed]

What a generating function for a language tells us about the language .I need its answer in base of automata?

**15**

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**2**answers

464 views

### Is Post's tag system solved?

Has the 3-tag system investigated by Emil Post $(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any)...

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**1**answer

127 views

### Embedding Turing machine [closed]

I have some questions about Turing machines. Is there an embedding method where you embed Turing machines, finite automata into continuous space or graphs? Or are there geometrical approaches to ...

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24 views

### Probabilistic timed automata transition

I am kind of new to timed automata and I have a question related to their correctness and synchronisation.
Assume that I have three states, A, B and C. I have also two clocks, $x$ and $y$ that are ...

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138 views

### Errors in Waksman's Solution to Cellular Automaton Firing Squad Problem?

Recently, a student and I have been working through Waksman's paper ``An Optimum Solution to the Firing Squad Synchronization Problem.'' The paper claims that for any value of $n$, the proposed ...

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**1**answer

50 views

### For synchronizing eulerian finite state machines every proper subset of states has some larger state set leads to this subset

Suppose we have a deterministic complete finite automaton which is synchronized, meaning we have a reset word, i.e. a word which resets the automaton to a definite state, regardless from which state ...

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91 views

### Why can a least fixed point operator only be expanded finitely many times?

If we expand modal logic with least and greatest fix point operators $\mu$ and $\nu$, respectively, we obtain the logic $L_\mu$.
An alternating automaton on infinite trees has a state space that is ...

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251 views

### Characterization of non-Zeno functions $f:\mathbb{R}\rightarrow \{0,1\}$

[Edit: I tried to integrate Nate's comments (see below).]
In the context of automata over continuous time, consider Boolean-valued functions $f:\mathbb{R}\rightarrow \{0,1\}$. There are uncountably ...

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36 views

### Sampling non-isomorphic Moore automata

Consider the set of Moore machines with input alphabet $A$, output alphabet $B$, and state set $S$. Let $\langle f, g \rangle$ be a machine with transition function $f : A \rightarrow S \rightarrow S$ ...

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79 views

### Minimal DFA of L* [closed]

I'm learning how to minimize DFAs.
Are the number of states in the minimal DFA of L, is equal to the number of states
in the minimal DFA of L*?
I'm trying for hours to think of examples but couldn't ...

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86 views

### Intersection of cone types

Let $G$ be a finitely generated hyperbolic group with the word metric; fix a symmetric generating set $S$ and let $\mathcal{G}$ be the Cayley graph of $G$ w.r.t. $S$. Define the cone of an element $x\...

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57 views

### If a timed automaton always terminates, does there exist a trace with a maximum length?

I have a theoretical question regarding timed automata and I would like to know if someone has already given an answer to it, since that would be useful for my research. So my question is the ...

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136 views

### What does homomorphism between languages mean to the correspoding Turing Machines?

According to the article: every c.e.language over $\Sigma^*$can be formed by homomorphism from a Dyck language over $\Sigma^{'}$ intersection with a minimal linear language over $\Sigma^{'}$ to the ...

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273 views

### Unique words in dihedral groups

Suppose $x$ is a word over the alphabet $\{0,1\}$.
Let $a$, $b$ be elements of the group Dih$_k$ for some $k$.
Let $\varphi=\varphi_{a,b,k}$ be the map from words over $\{0,1\}$ to elements of the ...

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**4**answers

1k views

### Is there a physically realizable inductive turing machine that can solve Hilbert's $10$th problem and can it overcome Church-Turing Hypothesis?

There is a claim on https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines that 'Simple inductive Turing machines are equivalent to other models of computation such as ...

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192 views

### Verification of Turing-equivalent automata

Correct me if I slept in my computer science studium: If an automaton is Turing-equivalent, the Halting problem shows that there are programs we can not verify (since we can't even predict their ...

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262 views

### Life. Intermediate stages

My question is pure mathematics when restricted to the cellular automata theory.
John von Neumann got the grasp of and defined life. Many years later biologists supported von Neumann's definition of ...

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157 views

### Rabin's proofs of emptiness and complementation problems for automata on infinite trees

I have originally asked this question on Math.SE, but I think it is more suitable here.
I have been reading M. Rabin's 1969 article Decidability of Second-Order Theories and Automata on Infinite ...

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**1**answer

197 views

### Modal logic in combination with automata theory

I'm planning to write a paper about the possibility of describing modal logic and the multiple world aspect of it with techniques of automata theory. To not duplicate my work does anyone have more ...

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322 views

### Giving the same concept different names in the same paper

I found a seminal paper of renowned authors (Inference of Finite Automata Using Homing Sequences (1993) by Ron Rivest and Robert Schapire) in which the authors define the very same set-theoretic ...

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209 views

### A problem on automatic groups and geodesic paths on the Cayley graph

Let $\Gamma = \langle S \mid R \rangle$ be a finitely generated group, with the neutral element $e \not \in S= S^{-1}$.
Let $\ell : \Gamma \to \mathbb{N}$ be the world length related to $S$.
For ...

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**1**answer

112 views

### Understanding the paper: “Guarded Fixed Point Logic”

This question is specifically about the paper "Guarded Fixed Point Logic" by Gradel and Walukiewicz. Among other things they prove the decidability of the satisfiability problem for Fixpoint Loosely ...

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361 views

### Neighbourhood of a word and Levenshtein distance

The Levenshtein distance or Edit distance $$ lev(U,V) $$ between two strings $U$ and $V$ over a finite alphabet $\Sigma$ of size $ \left| \Sigma \right| = \sigma ,$ is the minimal number of insertions,...

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941 views

### Non-regular languages fulfilling the Pumping Lemma

Some non-regular languages don't yield to the Pumping Lemma ($L_1=a^nb^mc^m$ should work). But now consider the set of non-regular languages L only over the alphabet {a}. (Like $L_2=a^{n^2}$ or ...

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**1**answer

119 views

### How one can use a real math function on transaction in Hybrid Petri Net fundamental equation?

Say we have a simple HPN with 2 continuous places $A$ and $B$ and one transition. We want a transition not only add and substract $N$ marks from $A$ and add $M$ to $B$ but use mathematical function $...

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**1**answer

256 views

### Deterministic Finite Automata question [closed]

I am very new to finite automata, and I came across an issue in my professors lecture slides which I think is wrong, and I'd wonder if any of you could confirm:
Alphabet: {1}
Automata
Surely the ...

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**1**answer

236 views

### How does “inhibitor arc” fit into fundamental equation of Hybrid Petri Nets?

In "ON HYBRID PETRI NETS" by DAVID AND ALLA published in 2001 on page 26 is given an example of how fundamental equation solves a HPN for given start and end time values.
A system looks like
And ...

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**1**answer

122 views

### Computations with conetypes of hyperbolic groups

I'd like to know if there exists (and, in this case, where I can find it) some computer program/programming language/any kind of software that can find explicitly the conetypes of a hyperbolic group ...

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41 views

### Relation between indexed languages (OI-macro or context-free tree) and scattered context languages

I'm not sure about the relation between indexed languages (generated by indexed grammars--Aho) and scattered context languages (generated by
scattered context grammars--J Hopcroft).
I think that ...

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**1**answer

365 views

### K-fellow traveler property and automatic structure

I have been reading several articles about automatic groups and metric spaces of negative curvature. However it is not clear for me the relationship between automatic groups, hyperbolcity and the k-...

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215 views

### The automorphism groups of smallest grammars of a language string are isomorphic

Let $s \in \Sigma^*$ be a formal language string. Consider the automorphism group of $s$, defined to be the set of all permutations of positions of $s$ that leave $s$ fixed. For instance $G(abab) = \...

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204 views

### Estimating the growth rate of nondeterministic finite automata

Given a nondeterministic finite automaton $\mathcal{A}$ (or a regular expression, or a regular grammar), can we efficiently compute the number $|L_k(\mathcal{A})|$ of accepted words of length $k$?
No,...

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495 views

### Deterministic finite-state automaton driven by a Markov chain

I've stumbled on some problem, and I have the feeling that this is closed to something well-studied in dynamical systems. The problem is the following. Consider a finite-state automaton with state ...

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217 views

### LTL - Büchi-automaton Translation [closed]

I need some help in Generalized Büchi automaton ..
I do understand the translation of a LTL-formula ϕ into Generalized Büchi automaton A= (Q, Δ, I, F), with F= {F1,...,Fn}
My problem is F ..
I know ...

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229 views

### Exponential objects in a category of abstract automata

I'm working with a more or less standard definition of the category Aut(C) of automata over a category C (where C has finite products) which has tuples $$
A=\langle I_{A},O_{A},S_{A},\sigma_{A}, \...

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181 views

### QBF of exponential length?

We consider a slightly extended version of a nondeterministic finite automaton, call it a "propositional nondeterministic finite automaton". It is defined as follows. Consider a fixed propositional ...

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53 views

### Question about link between non-terminals of grammars and variables of Diophantine equations

If we change the right arrow in the rewriting rules of grammar into equators , changes all terminals into x and keep the non-terminals unchanged,we get system of equations.In some cases,those ...

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492 views

### Computing the pro-solvable closure of a finitely generated subgroup of a free group

The pro-solvable topology on a group $G$ is the unique group topology such that the set of normal subgroups $N\lhd G$ with $G/N$ a finite solvable group is a fundamental system of neighborhoods of the ...

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145 views

### Separating infinite words sharing factors by automata

Two infinite words $\xi, \eta \in X^{\omega}$ are separated by an (Büchi-)automaton if it accepts one but not the other.
Denote by $F_n(\xi)$ the factors of length $n$ of an infinite word $\xi$ and ...

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**1**answer

221 views

### An extension of the real semiring with multiple degrees of infinity

Is it possible to define an extension of the probability semiring $(\mathbb{R}^+, +, \times, 0, 1)$ such that
Closure $a^* = 1 + a + a^2 + \ldots$ is defined for every element of the semiring, not ...

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108 views

### Generalising the adherence operator and its closure properties with regard to regular (rational) languages

Let $X$ be an alphabet and denote by $X^{\omega}$ the set of all infinite sequences (i.e. words) in $X$. A subset $L \subseteq X^{\omega}$ is called $\omega$-regular if it is acceptable by some Büchi-...

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134 views

### Representability of sets of infinite sequences sharing common prefixes and factors (i.e. infixes)

Here we are concerned with the space $X^{\omega}$ of infinite sequences. Denote by $F_n(\xi)$
the set of factors (consecutive finite subsequences) of length $n$ and consider the set
$$
K_n(\xi) = \xi[...

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131 views

### Proof of conjecture that permutation-free automata restrict the possible states visitable from a stringset sharing prefixes and infixes

An automaton $\mathcal A = (X, Q, \delta, q_0)$ is called permutation-free iff no word $w \in X^*$ induces a nontrivial permutation of a subset of the states of $\mathcal A$. More formally for any $R \...

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151 views

### Subsets of $\omega$-regular lanuages accepted by automata with special acceptance condition

Let $\mathcal A = (X, Q, \delta, q_0, F)$ be a deterministic finite automata with the following acceptance condition on infinite words:
The automata accepts $\xi \in X^{\omega}$ with respect to $F$ ...

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147 views

### Optimum control of a probabilistic automaton

Suppose we have a probabilistic automaton and we assign a weight to each state. An "interaction strategy" would be a fixed map from states to inputs. Any interaction strategy could be used to ...

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561 views

### Proof that the $\omega$-language consisting of all words containing every finite word as a factor is not rational/regular

Let $\eta$ be an $\omega$-word over $X = \{0,1\}$ and let $F_k(\eta)$ denote the factors of $\eta$ of length $k$. Define the following $\omega$-languages
$$
L_k := \{ \xi : F_k(\xi) = X^k \} = \{ \xi ...

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161 views

### Varieties of rational languages and (pseudo-)varieties of finite monoids, question regarding closure property

Let $\mathcal Rat(A)$ denote the class of rational (or regular) languages over the alphabet $A$, a subset $\mathcal V(A) \subseteq \mathcal Rat(A)$ is called a variety of (rational) languages iff
...

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1k views

### Isomorphism in category of finite automata

What does meanthat two finite automata is equivalent? I think that we must define category of finite automata, i.e. we must define $\mathrm{Hom}(A,B)$, where $A,B$ be an arbitrary finite automata. ...

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222 views

### What is this structure called?

(I'm not entirely sure what to tag this; feel free to retag.)
While thinking about automata (specifics below), I ran into the following phenomenon:
A cofunction system is a pair of sets $X, A$, ...