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Apr
20
comment prove that set of palindroms such that $\#_0(w)=\#_1(w)$ is not CFG
@user220688 Perhaps there is, but this seems by far the simplest one.
Apr
20
comment prove that set of palindroms such that $\#_0(w)=\#_1(w)$ is not CFG
I'm missing something here. Observe that $|ww^r|_0 = 2\cdot |w|_0$ and same for $1$'s, so $|ww^r|_0 = |ww^r|_1$ implies $|w|_0=|w|_1$ (and the other implication does hold as well).
Apr
20
answered prove that set of palindroms such that $\#_0(w)=\#_1(w)$ is not CFG
Apr
16
revised Difference : subsequences and substrings
added 194 characters in body
Apr
16
answered Difference : subsequences and substrings
Apr
15
comment Can I embed $\mathbb R^{\mathbb N}$ with a partial order into $^\ast\mathbb{R}$ with the linear order?
@Regret It seems these are hyperreal numbers.
Apr
14
comment Euler walk by joinning subgraphs
If you have issues with multigraphs, instead of adding just edges, you can add edges with dummy vertices in the middle, so that the result of transformation will be just a simple graph.
Apr
8
comment Structure for first order language
Perhaps it should be interpreted as $f\big(g(x,y),c\big)$, see here.
Mar
31
revised What does continuity *in general* mean?
added 12 characters in body
Mar
30
revised monoids of injections and surjections
added 252 characters in body
Mar
30
comment Weakly connected graph test
Where did your definition come from?
Mar
30
comment Weakly connected graph test
I'm not sure that your approach works with the definition in the question. Please see my post, in particular observe how your algorithm would act on the example graph when started from vertex $1$.
Mar
30
answered Weakly connected graph test
Mar
30
comment how to prove that the ceiling(x) = floor(x) + 1?
It's only true for $x \notin \mathbb{Z}$. For example $\lceil 0 \rceil = 0 \neq 1 = 0 + 1 = \lfloor 0 \rfloor + 1$.
Mar
28
comment Are these languages Regular or Non-regular?
@Aniq Going back to the pumping lemma, your subword $w$ should be $b^p$, with $uwv = a^pa^5b^p$ (see here).
Mar
28
comment Are these languages Regular or Non-regular?
@Aniq Suppose that there is an automaton with $k$ states that recognizes $L$, consider the word $a^{k+1}a^5b^{k+1}$. Because the automaton has $k < k+1$ states, then when parsing $b$'s some state has to happen at least twice. That means that there is a loop and you can use it any number of turns you want, so for any number $x$ there is $y > x$ such that your automaton accepts $a^{k+1}a^5b^{y}$. Surely you can find $y$ so that that word shouldn't be in $L$.
Mar
28
answered Are these languages Regular or Non-regular?
Mar
25
answered monoids of injections and surjections
Mar
24
comment Relationship between parameters in graph
@LookingForKnowledge Yes, there are $k$ vertices in the path and another $n-k$ connected directly to one of the ends.
Mar
23
revised Relationship between parameters in graph
added 3 characters in body