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bio website liafa.univ-paris-diderot.fr/…
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visits member for 2 years, 11 months
seen Dec 23 at 0:16

Jul
15
comment An extension of the real semiring with multiple degrees of infinity
It is not exactly the same framework, but maybe you will be interested in this: computer.org/csdl/proceedings/lics/2013/5020/00/… It is also related with weighted automata and different orders of "infinity"
Jul
2
awarded  Curious
May
14
comment Is it possible to classify all the inequivalent classes of first order sentence with quantifier rank fixed
See this question: math.stackexchange.com/questions/773942/…
May
13
comment Two sets of strings resulted from a set represented by binary and decimal code are in the same class of languages?
To detail the answer of Benjamin Steinberg: you have a transducer (i.e. an finite-state machine) that can change between binary and decimal representation. All the classes of languages you mentioned are preserved by applying a transducer, so the answer to your question is yes.
Apr
6
awarded  Popular Question
Mar
29
comment Convergence of iterated stochastic matrices
I don't get the first line of your answer. Why the $n^{th}$ powers of the matrices $M_n$ would form a subsequence? It seems to be plain wrong, for instance for $1\times 1$ size, the constant sequence $1/2$ converges to $M=1/2$, but $1/2^n\to 0$ and $M\neq 0$.
Feb
20
comment How do you prove that a subset of L is regular is L is regular?
in fact I cannot delete because it's accepted...
Feb
20
comment How do you prove that a subset of L is regular is L is regular?
@BenjaminSteinberg ok I'll adopt this behaviour in the future, and delete the answer here.
Feb
20
comment How do you prove that a subset of L is regular is L is regular?
@BenjaminSteinberg I thought it would be migrated to math.se together with my answer, I don't have the power to do so..
Feb
20
revised How do you prove that a subset of L is regular is L is regular?
added 390 characters in body
Feb
20
comment How do you prove that a subset of L is regular is L is regular?
Ok I will edit the answer more precisely.
Feb
20
comment How do you prove that a subset of L is regular is L is regular?
This construction works in general, for any regular $L$.
Feb
20
answered How do you prove that a subset of L is regular is L is regular?
Feb
18
comment Proof of conjecture that permutation-free automata restrict the possible states visitable from a stringset sharing prefixes and infixes
It seems $R=\{q_0\}$ and $k=1$ yields easy counter-examples.
Feb
18
answered Separating infinite words sharing factors by automata
Feb
4
answered Transfinite induction vs induction in mathematics
Feb
1
awarded  Yearling
Jan
26
comment Are algebraic structures uniquely identifed by their free objects?
thanks this is useful. So in this case how do you show that the free object indeed has the universal property?
Jan
26
comment Are algebraic structures uniquely identifed by their free objects?
@AndrejBauer the plan was to take for $x^\omega$ all the identities that are true for the idempotent power in finite structures (axioms (A')), and maybe additionally (A)
Jan
26
comment Are algebraic structures uniquely identifed by their free objects?
@ToddTrimble It is probably what I'm looking for, but I'm not very familiar with category theory. If I understand your comment, you are saying that having a free object is given almost for free according to category theory, as long as you are a monad. I tried to understand what a monad is on wikipedia, but it seems circular, because it looks like it is the structures having free objects... Also you mention varieties, but here it's not a variety, because axioms are not restricted to identities.