6
votes
1answer
118 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 ...
5
votes
1answer
72 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 ...
0
votes
0answers
68 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 ...
3
votes
1answer
101 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
0answers
92 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
528 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 ...
1
vote
1answer
508 views

Collatz conjecture— finite state machine transducer construction, origination?

wikipedia has an entry on the Collatz conjecture with a section on As an abstract machine that computes in base two. this apparently describes a construction of a FSM transducer computing sequential ...
4
votes
1answer
480 views

Deciding equivalence of regular languages

Given two regular expressions $R$ and $S$ on an alphabet $\Sigma$ it is possible to decide their equivalence as follows: build two finite automata $M_R$ and $M_S$ such that $L(R) = L(M_R)$ and $L(S) ...
3
votes
2answers
926 views

Is there an algorithm that can “reverse engineer” a Regular Expression?

Given a Regular language (represented as a black box to which one can apply inputs and get 0/1) Is there an algorithm that can find a finite deterministic automaton that produces that language?
5
votes
0answers
191 views

Büchi automata with acceptance strategy

I have already asked this question on cstheory.stackexchange, but without success. Maybe it is too close to an "open problem", although it is not a famous one. Anyway I try here, I can always remove ...
0
votes
1answer
244 views

Universality of blind graph rewriting

Let us consider $S(M) = \{(f_0, f_1) | f_0, f_1: M \rightarrow M\}$, where $M$ is a finite set. Each element of $S(M)$ is equivalent to a finite directed graph with the set of nodes $M$, which has ...
3
votes
1answer
625 views

Algebraic structure generated by primitive graph operations

Let $M$ be a finite set, and $S(M) = \{(f_0, f_1) | f_0, f_1: M → M\}$. Each element of $S(M)$ can be considered as a finite directed graph with the set of nodes $M$, which has exactly two arrows ...
3
votes
2answers
731 views

Certain type of regular languages

Dear All, there is one type of regular languages, over $\{a,b\}$, which appear naturally in what I am studying, so if anybody could recognise them, or say any sort of their characterisation, that ...
0
votes
1answer
457 views

Transition Graph per alphabet?

How do you determine how many different Transition Graphs are over a particular alphabet? For example How many TG's are over the alphabet {x, y}. I am taking a class with a similar question from ...
4
votes
1answer
329 views

Growth zeta-functions of regular languages

Dear All, my following question may be known and ought to be known, so in case it is folklore please could you give me the references. To start, it is obvious that growth of rational languages are ...
2
votes
1answer
263 views

Given a PDA M such that L(M) is in DCFL construct a DPDA N such that L(N) = L(M)

Is it possible to construct an algorithm which takes as input a pushdown automaton $M$ along with the information that the language accepted by this automaton $L(M)$ is a deterministic context-free ...