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 Oct 6 awarded Nice Answer Oct 5 answered Essays and thoughts on mathematics Mar 10 awarded Enlightened Mar 10 awarded Nice Answer Feb 1 awarded Yearling 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