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Apr
8
comment Making 7 vertices triangle free graph bipartite by deleting an edge
There's a trivial counter-example: the graph with $|V|=7$ and $|E|=0$.
Apr
7
comment Characterizing a certain set of matrices arising from binary trees
Your diagram doesn't look like a binary tree. It could be converted into a binary tree by inserting three non-leaf nodes, but if this is done symmetrically then the distances between leaf nodes would be $2$ and $4$. What is the actual tree structure?
Apr
4
comment Josephus Variant
You might want to check your results against oeis.org/A032434.
Apr
2
comment Minimal DFA for a given regular expression
Are you familiar with the Myhill-Nerode theorem?
Mar
29
comment Are there useful combinatorial constructions of grammars?
I don't have enough to make an answer, and you stand more chance of getting a more complete answer if I stick to comments. But Flajolet and Sedgewick's book on Analytic Combinatorics seems to address something related to context-free grammars, so you might want to try to find a copy.
Mar
28
comment Are there useful combinatorial constructions of grammars?
I think you need to be a bit more careful in distinguishing between a rule from a CFG and the CFG itself. I can understand that you might want to identify the CFG with the rule which defines its initial non-terminal, but things might become clearer if you define the size of a rule as the number of symbols in its definition and the size of a grammar as the sum of the sizes of the rules reachable from its initial non-terminal. For a start, that immediately highlights the importance of the transitive closure, and suggests looking at graph combinatorics.
Mar
22
comment Maximum board position in 2048 game
How is the score computed from the move sequence?
Mar
10
comment What is the pupose of using minute and seconds with degree?
Is your question a mathematical history question ("What's the history of base-60 being preferred to base-10?") or is it about present day usage? If the second, could you give examples of where you've encountered it?
Feb
27
comment Smullyan-To-Mock-a-Mockingbird, Find egocentric bird in L
The stack overflow was due to $LL(LL) \rightarrow_{\beta} L(LL(LL))$. Manually eliminating that case, I managed to run the others for tens of thousands of beta-expansions and stopped when the program was using 14GB of memory. They were all expanded to at least 3 times their starting size.
Feb
27
comment Smullyan-To-Mock-a-Mockingbird, Find egocentric bird in L
NB I've attempted to test all expressions of the form $BB$ where $|B| < 6$ by beta-expanding repeatedly (using a priority queue by size of expression) and checking for each expression $XY$ so reached whether both $X$ and $Y$ had previously been encountered. The program failed with a stack overflow when looking for beta-expansions in a 1001-$L$ expression. $(N_3 N_3)(N_3 N_3)$, on the other hand, succeeds at the first opportunity with a 24-$L$ expression. So certainly there's no smaller solution which behaves as nicely as $(N_3 N_3)(N_3 N_3)$.
Feb
24
comment Smullyan-To-Mock-a-Mockingbird, Find egocentric bird in L
@Snowball, the problem there is that checking whether two combinator expressions are equivalent is undecidable in the general case, and the behaviour of $L L (L L) = L (L L (L L)) = \lambda x. L L (L L) (x x)$ seems to rule out testing extensionality for small cases, looking for a counterexample, as a strategy.
Feb
23
comment Is it possible to build a circle with quadratic Bézier curves?
@JasonS, I took a screenshot of the linked PDF.
Feb
21
comment Check if a point is on a plane? (Minimize the use of multiplications and divisions)
Why do you think that multiplication is the source of your errors? I'm not an expert in numerical analysis, but one of the first things I learnt is that subtraction is one of the biggest sources of error. Your choice of which vertex to call $v_0$ might have a big effect.
Feb
13
comment Little O Bound, Combinatorics
You're asking us to read your mind. What's the property $S_k$?
Feb
11
comment i^i^i^i^… Is there a pattern?
@nayrb, since $(a^b)^c = a^{(bc)}$, the convention is that $a^{b^c} = a^{(b^c)}$.
Feb
11
comment Logic behind the ID checksum?
@Prakhar, it's one of the first things I do when trying to understand a mystery sequence of numbers. It's a good way of identifying polynomials (if you repeat the operation $n$ times then an order-$n$ polynomial will give a constant vector).
Feb
11
comment Logic behind the ID checksum?
@Prakhar, "take first differences" means taking each adjacent pair and subtracting one from the other. So $1 - 2 \equiv 10, 6 - 1 \equiv 5, 3 - 6 \equiv 8, \ldots$.
Feb
9
comment Combinatorics - falling ball through a labyrinth
And for $m \times n$ labyrinths it's $\binom{m+n}{m}$, being a simple manifestation of staircase walks.
Feb
4
comment Proving that a language is not context-free
I suggest using the pumping lemma to derive a contradiction. That's the way pumping lemmas are typically used to prove that languages don't fall into the relevant class.
Feb
4
comment Which are the most effective modern intuitive definitions of a vector?
@twirlobite, "direction" is a very ineffective intuition. It makes sense in Cartesian products over fields of characteristic zero, but what would it mean in vector spaces over fields of finite characteristic?