All Questions
7 questions
2
votes
1
answer
70
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 ...
- 798
0
votes
0
answers
105
views
Counting path generating sentences in a specific formal language
Given a formal grammar of a language or an Turing machine of the language, can we count the path that generating sentences of the language?
For example, we know that if the grammar is context-free ...
- 3,094
6
votes
1
answer
165
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 ...
- 798
6
votes
1
answer
135
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-...
- 798
5
votes
1
answer
346
views
What prefix and factors determine a ultimately periodic word uniquely
Let $\xi$ be an ultimately periodic sequence, i.e. there exists finite sequences $p, q \in X^*$ such that $\xi = pq^{\omega}$. Does there exists a $n > 0$ such that the prefix of length $n$ and all ...
- 798
0
votes
0
answers
154
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 \...
- 798
20
votes
5
answers
1k
views
Is there a natural family of languages whose generating functions are holonomic (i.e. D-finite)?
Let $L$ be a language on a finite alphabet and let $L_n$ be the number of words of length $n$. Let $f_L(x) = \sum_{n \ge 0} L_n x^n$. The following are well-known:
If $L$ is regular, then $f_L$ is ...
- 118k