My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.

1d
comment How Graph Isomorphism is used to determine Graph Automorphism?
It is good that you care about graph automorphisms. Any permutation is a product of transpositions, but it can happen that you have two transpositions which are not automorphisms of the graph, but their product might still be an automorphism of the graph. But it is fine for me, if you say that the transposition was just an example, and that the idea also works for permutations which are not transpositions. On an unrelated note: Did you notice that the text said: "continue till an isomorphism is found"? So it only computes a single representative. Can you work out why a single rep. is enough?
2d
comment How Graph Isomorphism is used to determine Graph Automorphism?
"Now consider a transposition $\pi$ that moves $(i+1)$ th vertex to $j'$ th position where $i <j'\leq n$." Is it really sufficient to only look at transpositions $\pi$? What would happen, if you used this algorithm to compute the automorphism group of a directed circle (whose automorphism group doesn't contain any transposition)?
2d
reviewed Approve suggested edit on Prove multiple cell move instructions don't increase power of Turing Machines
2d
comment NL and NP compute different binary relations, so what?
@Raphael Especially if there is more than a single input string and more than a single output string, a transducer can compute relatively general relations. For nondeterministic transducers, the distinction between input and output can easily get blurred, so the operations available in the relational algebra might indeed describe quite well, how such relation can be combined to get new relations. But the reason why I added it was that there was neither a "binary relation" tag, nor a "function" tag, and anyway neither would have properly captured the intended subroutine notion.
2d
comment NL and NP compute different binary relations, so what?
I just noticed that the binary relations computed by $NL$ are not really closed under composition. Maybe I should have used $SAC^1=LOGCFL$ instead of $NL \subset SAC^1$, but the basic question "so what?" remains the same. (And I would need a new trivial example, because the binary relation $\{(1^n,ww^R):n\in\mathbb N, |w|\leq n\}$ won't do the job anymore.)
Feb
7
reviewed Approve suggested edit on Deleted data remains on a disk until?
Feb
6
asked NL and NP compute different binary relations, so what?
Feb
6
reviewed Edit suggested edit on Grammar ambiguous or not?
Feb
6
revised Grammar ambiguous or not?
LaTex edits
Feb
6
answered Relationship of algorithm complexity and automata class
Feb
4
revised Is a LBA with stack more powerful than a LBA without?
(3) ... nondeterministic -> deterministic
Feb
4
revised Smallest class of automata model whose corresponding language class contains CFL and is closed against (dis)allowing nondeterminism in the model
(3) ... nondeterministic -> deterministic
Feb
4
accepted An obvious approach to explaining NP != coNP, how far has it been pushed?
Feb
4
accepted Is the word problem for regular languages in ALogTime?
Feb
4
reviewed Approve suggested edit on Can a language have more than one DFA?
Feb
4
reviewed Approve suggested edit on Debug C code to prevent large file output
Feb
4
revised Turing reductions by NX ∩ coNX and binary relation problems
the Turing reduction -> a Turing reduction
Feb
3
revised Turing reductions by NX ∩ coNX and binary relation problems
improved terminology from from hugely non-standard to slightly non-standard
Feb
3
comment Turing reductions by NX ∩ coNX and binary relation problems
@RickyDemer The point with the complement is very good. It made me realize that the "it would be nice" items would indeed have been too nice (for quite obvious reasons). There are limits to how much I can clarify what I mean by "the Turing reduction" "of a complexity class" (I tried to explain it by analogy with the same notion for decision problem now), because in a certain sense the question exactly asks for "a good definition", i.e. a meaning of those words.
Feb
3
revised Turing reductions by NX ∩ coNX and binary relation problems
Hopefully addressed the issue raise by Ricky Demer's comment
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