## algorithms – Leader Election: Every bit-reversal ring is \$frac{1}{2}\$-symmetric

I have a proof that I need help with. Like the title says, the theorem is that every bit-reversal ring is $$frac{1}{2}$$-symmetric. The theorem is for Leader Election algorithm in synchronous ring. The things I know follow:

Bit reversal ring is defined as follows: We assign to each process $$i$$ the integer from $${0,ldots, n-1}$$ whose $$k$$ bit representation is the reverse of the $$k$$ bit representation of $$i$$. $$n$$ is also a power of two, $$n=2^{k}$$.

Two segments $$U$$ and $$V$$ are order equivalent if they are the same length $$k$$, and for all $$i$$ and $$j$$ such that $$1 leq i,j leq k$$ we have that $$u_{i} leq u_{j}$$ if and only if $$v_{i} leq v_{j}$$.

Ring $$R$$ is $$c$$-symmetric if for every segment $$S$$ of $$R$$ there are at least $$lfloor frac{cn}{l} rfloor$$ segments that are order equivalent to $$S$$, including $$S$$ itself, where $$l$$ is length of the segment, and this holds for every $$sqrt{n} leq l leq n$$.

So after plugging all I know into formulas I get that $$lfloor frac{2^{k-1}}{l} rfloor$$ is formula for number of segments and $$l$$ is such that $$2^{frac{k}{2}} leq l leq 2^{k}$$.

Any hint or piece of information would be much appreciated! Thank you.

## Do you think Donald Trump will win the election again?

If he doesn’t, we have a befuddled, senile old fool at the wheel at one of the most crucial times of American history.  So yes.  He is going to win BIGLY.  Trump is a student of the ancient Chinese philosopher Sun Tzu.  One of Sun Tzu’s key points is “When you are strong, show weakness.  When you are weak, show strength.”  Democrats have totally underestimated him for the last 3.5 years and I don’t expect them to stop.

## can we kick the cons out of the country once bunker boy loses the election?

No need. When Trump loses, all his supporters will use it as an excuse to start a race war. As a result the US military, which is 40% minorities, will be called on to suppress the pathetic rebellion and many of these clueless mouthy Red Hat Lovers will not survive. The future is looking good for decent Americans.

## Americans are scared of Biden’s election just like the Jews were scared of Hitlers election in 1933?

Really? Biden is like Hitler?   What about the orange blob in the Oval Office right now? The one who authorized placing children in cages, the one who wanted to sequester groups like Asians, Mexicans, etc- to keep them from immigrating into the US?  The one who says there were “Good people on both sides” when white supremacists marched in Charlotte?

## Will this time US be more prepared for Russia’s fake news bombardment to help Trump again in next election?

It’s not the fake news in 2016 that was the problem.  The problem arose when Russia successfully hacked into all 50 states vote tallying systems and altered the votes in a few key states.  And, yes, the states are more prepared now and that won’t happen again.

## Do you think the Democrat riots will hurt them in November’s election?

It really doesn’t matter that their shooting Black People in their Riots as long as they continue to kill Black People there will be an awakening to destroy their racist BLM hate group.

And it doesn’t matter what happens in November they still lose.

It would hurt Blacks the most if Biden wins in November though he’ll bring back Slavery putting Blacks back in chains.

## [ Politics ] Open Question : What are the odds Trump commits suicide when he loses the November election by a landslide?

[ Politics ] Open Question : What are the odds Trump commits suicide when he loses the November election by a landslide?

## Republicans: If George W Bush endorsed Biden, would that sway your vote in the upcoming election? Why or why not?

Absolutely not. Because he’s an open borders globalist who got my VOTE only because I thought Gore would have been even worse. I’m not so sure now. Then he had my SUPPORT because of 9/11, but proceeded to make a mess of the war.

I have done without a word of comfort or advice from George Bush for twelve years, so I don’t need his opinion now.

His spokespeople say he’s not going to get involved with presidential politics. We’ll see who’s lying.

## How do democrats cheat by implementing vote-by-mail election?

If you have a process then you add an extra step that must give you extra ways to cheat the system. It certainly can’t remove any.

One way is just to “lose” the returned votes for the party you do not like. Adding the mail-in step to the process gives you extra opportunities for losing those votes.

Do ballots ever go missing? One estimate is that 28.4 million have gon missing since 2012. https://www.breitbart.com/politics/2020/04/20/fede…

You can send out ballots to thousands of dead people. Naturally, you would not actually deliver them but you could complete them and post them back.

Some areas in the US already have over 120% voter turnout. No-one seems to find that suspicious. We think we have done quite well if we get a 70% turnout in the UK.

You could try pre-filling in the ballots then sending them out – to non-citizens. Yes, it’s been done: https://twitter.com/foxandfriends/status/105327152…

There are places where people discover they have voted but they knew nothing about it: https://bigleaguepolitics.com/fraud-numerous-new-y…

All that is on top of the vote stuffing, mis-calibrated voting machine screens, reprogrammed voting machines, people “finding” boxes stuffed with ballots after the initial count where they established how many extra votes their party would need.

One vote-stuffer was recently convicted of registering 22% of the votes all by himself!  https://www.phillyvoice.com/voter-fraud-south-phil…

People have been convicted of changing absentee ballots: https://news.yahoo.com/michigan-city-clerk-charged…

How you think you can trust the results of any election in the US beats me.

## Will Republicans ever win another election again?

There are many factors that play into this.

Increased immigration favors Democrats.

The current draconian policies that the Democratic governors of NY, MI, WA and VA have implemented will cost them long-term votes.

Especially if voters believe that current policies are based more on political considerations than on public safety.

Then we have the fact that the Democratic Party is being pushed further to the left by Democratic politicians like AOC.

There is growing discontent in the Democratic party, where the far left of the party does not want to play well with anyone.

That will likely cause a split in the Democratic party.

If this happens, Republicans may have a greater chance of being elected.