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Questions tagged [automata-theory]

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15
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2answers
426 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)...
6
votes
1answer
87 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 ...
0
votes
0answers
23 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 ...
1
vote
1answer
125 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 ...
2
votes
1answer
46 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 ...
1
vote
0answers
86 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 ...
1
vote
0answers
248 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 ...
1
vote
0answers
31 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 $f : A \rightarrow S \rightarrow S$ ...
1
vote
1answer
76 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 ...
3
votes
0answers
57 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\...
2
votes
0answers
56 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 ...
1
vote
0answers
84 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 ...
11
votes
1answer
246 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 ...
2
votes
4answers
897 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 ...
0
votes
2answers
177 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 ...
3
votes
0answers
208 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 ...
5
votes
0answers
131 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 ...
1
vote
1answer
170 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 ...
4
votes
1answer
309 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 ...
4
votes
0answers
185 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 ...
2
votes
1answer
105 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 ...
6
votes
2answers
270 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,...
1
vote
1answer
558 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 ...
-2
votes
1answer
116 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 $...
-2
votes
1answer
246 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 ...
2
votes
1answer
212 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 ...
4
votes
1answer
119 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 ...
2
votes
0answers
39 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 ...
5
votes
1answer
291 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-...
3
votes
0answers
192 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,...
6
votes
2answers
460 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 ...
1
vote
0answers
210 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 ...
3
votes
1answer
211 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}, \...
2
votes
1answer
172 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 ...
1
vote
0answers
48 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 ...
6
votes
0answers
462 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 ...
6
votes
1answer
140 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 ...
-1
votes
1answer
217 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 ...
7
votes
1answer
105 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-...
2
votes
1answer
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[...
0
votes
0answers
125 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 \...
4
votes
1answer
147 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 $F$ ...
1
vote
1answer
145 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 ...
2
votes
1answer
399 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 ...
2
votes
1answer
152 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 ...
7
votes
2answers
852 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. ...
1
vote
0answers
217 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 $X, A$, ...
5
votes
1answer
244 views

Is it decidable whether the support of a rational $\mathbb{Z}$-series is a regular language?

Let $S \in \mathbb{Z}\langle\langle A\rangle\rangle$ be a rational series in noncommutative variables. The support of $S$ is the set of all words $u \in A^*$ such that $(S, u) \not= 0$. It is ...
1
vote
0answers
101 views

Schönhage's SMM with only one instruction

It is possible to implement $\lambda$-calculus in Schönhage's storage modification machine using an infinite set of nodes and one single program consisted exclusively of (about hundred) instructions ...
3
votes
2answers
722 views

Turing-complete primitive blind automata

Let $N$ be the set of natural numbers, $S$ be the set of finite binary sequences, and $Q = [N \rightarrow N] \times [N \rightarrow N],$ where $[N \rightarrow N]$ is the set of all computable ...