Is Bitcoin POW to POS the key?

[jeraldskie11]

People are thinking what's the best way to get rid of this blockchain network congestion.

Network congestion is a problem for us because it affects the fee. The normal fee is just around $1 but this month we are experiencing a very high fee which is unaffordable to most people.

We found out that the reason of this issue is because of brc-20 tokens, they use Bitcoin blockchain. And since Bitcoin's blockchain is only process 7-10 transactions per second which is not enough to manage all the transaction if we included the brc-20 tokens.

Now, is the problem will be fixed if brc-20 tokens will be removed?

Yes, very possible, but how? Brc20 tokens keeps improving and lot of brc20 token is being launch everyday.
The total confirmed market cap of brc20 tokens that is listed in Coinmarketcap is $3b with a $1b trading volume which is very difficult to stop.

The other solution to fix network congestion is to increase the block size. Is increasing the block size fix network congestion?
Definitely yes, and there is no need to eradicate brc20 tokens.

But in what way? Is it really possible to increase the block size of Bitcoin? For sure there's a reason why Nakamoto put only a very limited block size.


I have found another solution to remove this obstacle in Bitcoin but I don't know if this idea is acceptable to the majority. If you remember what happen to Ethereum way back 2017, it encountered this such problem.
They made Ethereum to POS from POW as a solution to this problem, and it's called ETH 2.0

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

[Charles-Tim]

It is true that Ethereum converted from PoW to PoS but the transaction fee did not reduce. So I do not know the problem you meant that Ethereum faced in the paste.

There are coins that make use of PoW that are cheaper than Ethereum transactions. Examples are litecoin, doge et cetera.

Converting from PoW to PoS is not the solution.

[Mia Chloe]

During a period of about 8 to 6 years ago, Bitcoin has always tended towards this bottle necked condition of conjestions in the mempool. Starting from 2018 when lightning network and SEGWIT became widely used as layer 2 solution and a backwards compatible upgrade respectively, Bitcoin still tended towards this situation of high mempool conjestions.

With the problem of ordinals, I suggest they should me removed from the network like devs. Because they seem to be producing more conjestions than the LN feature can solve. With the issues on ground, let us not be surprised to see fees become double of it is now, though we hope the go down.

With the popularity and adoption of Bitcoin growing vastly, fixing conjestion problems may not be easy.

[Upgrade00]

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

Overturning the Bitcoin protocol is not a solution to high fees. Bitcoiners use it cause of the value it has and much of that value comes from the security the network has and how decentralized it is, changing that up will make it just another altcoin out there.

Off chain channels now seem to be the best option to transact with less fees at the moment. In the future a better solution ma be implemented.

[Ojima-ojo]

Am much as I definitely will want to agree that shifting bitcoin from its pow protocol to POS protocol may very likely sold the problem of network congection with results in high transaction fees, I still will say that I do not think it's good idea.

Bitcoin is Satoshi legacy and there are some thing that we are supposed to allow to remain the way he(satoshi) made it to be, and the protocol or consensus to which bitcoin runs or operates is one of those.

We have the lightening network as a ready solution to the problems of high fees and delay in transaction confirmation on the bitcoin L1 blockchain network, my question now is, why are people not using lightening network for small bitcoin transfers and all that?

[DooMAD]

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more

I'd just use fiat if it came to that.  You don't "fix" it by taking away one of the things that made it worth having to begin with.

This is very much an instance of "people don't appreciate what they've got until it's gone".

[BitMaxz]

I don't think Bitcoin developers would switch from POW to POS-based consensus but that's a good alternative solution to the current network congestion.

However, this is impossible to happen. The only solution that I can see is to remove BRC20 or needs mass adoption of the lightning network or they need to add more ASIC units to increase the network hashtate because it can help confirm transactions fast.

[jeraldskie11]

It is true that Ethereum converted from PoW to PoS but the transaction fee did not reduce. So I do not know the problem you meant that Ethereum faced in the paste.

There are coins that make use of PoW that are cheaper than Ethereum transactions. Examples are litecoin, doge et cetera.

Converting from PoW to PoS is not the solution.

I don't think so. Maybe you are using exchanges to transfer your ETH that's why the fee is so high, or maybe you are transferring erc-20 tokens.

I have tried transferring ETH to another wallet using non-custodial wallets such as myetherwallet and metamask but it only needs a very low fee.

Now, the problem we need to fix is the Bitcoin transaction fee to get back to normal, not in brc-20 tokens.

[thecodebear]

PoW is one of the things that makes Bitcoin so amazing. Trashing Bitcoin's value proposition is not how you solve the fact that sometimes the fees spike. Also PoS isn't any faster than PoW. Just look at Ethereum, the switch from PoW to PoS didn't make fees cheaper. That was simply an erroneous assumption that even Vitalik Buterin has many times pointed out is false.


So switching to PoS does not make fees cheaper. And Bitcoin would NEVER change away from PoW, as in it WILL.NEVER.HAPPEN. So OP you're offering an impossible solution that would not fix anything but would in effect destroy the value proposition of Bitcoin.

[criptoevangelista]

Have you ever stopped to think that what has been happening with bitcoin is an attack to force an update in this sense?

I was thinking about it and it seems they are reaching a point where it will be impossible to maintain it as it is.

Maybe the best thing is to let time pass and see that this wave of meaningless tokens is useless.

[lionheart78]

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

I do not think that there is a relation between converting to POS to the network congestion unless people leave BTC after it converts to POS.  The thing with POS is that, the security of the network is not as strong as POW.  Check this article[1] [2]for comparison.  The network congestion solution relies on the blocksize limit and the frequency of creating blocks.  That should be modified IMO if one wanted to solve the congestion of network.



[1] https://cointelegraph.com/learn/proof-of-stake-vs-proof-of-work:-differences-explained
[2] https://river.com/learn/proof-of-work-pow-vs-pos-proof-of-stake/

[AprilioMP]

I have found another solution to remove this obstacle in Bitcoin but I don't know if this idea is acceptable to the majority. If you remember what happen to Ethereum way back 2017, it encountered this such problem.
They made Ethereum to POS from POW as a solution to this problem, and it's called ETH 2.0

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

If Bitcoin switches to PoS from PoW, then Bitcoin is nothing more than an Altcoin and there is nothing special about it anymore.
From what I know so far, miners under PoW work to crack hashes, cryptographic numbers and verify transactions requiring rewards^[1]. This means that miners also need profits. If you switch to PoS, then you are no longer a miner but a validator and Bitcoin is no longer different from altcoins.

Even though someone has already said it, I will repeat it again because I think it is true that switching from PoW to PoS is not a solution.
Switching from PoW to PoS based on the whitepapers I read, it will never happen.
Whitepaper is the beginning of the launch of Bitcoin with a unique concept. 21 million Bitcoins is a great innovation from Satoshi that will never change.

Actually, this is beyond my capabilities, especially regarding the offer to remove BRC-20 which was proposed as a solution to high transaction fees.

p.s. correct me if I'm wrong

[noonesh]

People are thinking what's the best way to get rid of this blockchain network congestion.

Network congestion is a problem for us because it affects the fee. The normal fee is just around $1 but this month we are experiencing a very high fee which is unaffordable to most people.

We found out that the reason of this issue is because of brc-20 tokens, they use Bitcoin blockchain. And since Bitcoin's blockchain is only process 7-10 transactions per second which is not enough to manage all the transaction if we included the brc-20 tokens.

Now, is the problem will be fixed if brc-20 tokens will be removed?

Yes, very possible, but how? Brc20 tokens keeps improving and lot of brc20 token is being launch everyday.

It's not possible to removeBRC-20 tokens as a "hey, lets remove this kinds of transactions here and that's it".
It requires a consensus, most nodes running software that limits extra data size and that will limit the amount of shit that can be added to a transaction non-related with financial transfer from inputs to outputs.

Now this is not possible with Bitcoin Core because there is a bug that is been exploited, where Inscription can send more data and it will still be accepted by the nodes even if the node owner configured to accept only a limited amount of bytes as extra-data. Once this is fixed, if people update to the new version AND USE this option to limit extra-data size limit, then we can see a reduction in BRC-shit.

The other solution to fix network congestion is to increase the block size. Is increasing the block size fix network congestion?
Definitely yes, and there is no need to eradicate brc20 tokens.
But in what way? Is it really possible to increase the block size of Bitcoin? For sure there's a reason why Nakamoto put only a very limited block size.

This is old, very old. It doesn't work, because increasing block size will increase Storage requirements on the nodes, and Bitcoin only is Bitcoin today because anyone can run a full node from their home pc. If the Blockchain start going t 1 TB or 2 TB in size, it will start excluding people. If the block comes to somthing like 100 Mb, only big companies will be able to afford paying storage disks to run a node, and then decentralization os gone, congratulations.

So, NO, thank you. Increasing block size was defeated back in 2017 or something and should be kept defeated.

I have found another solution to remove this obstacle in Bitcoin but I don't know if this idea is acceptable to the majority. If you remember what happen to Ethereum way back 2017, it encountered this such problem.
They made Ethereum to POS from POW as a solution to this problem, and it's called ETH 2.0

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

This is just not true, it doesn't consider any of the advantages of having PoW over PoS, its only based on one exemple that is just a joke, because Ethereum is a Shitcoin Joke.
A centralize shitcoin Ethereum adopts a solution that gives control over the network to a more centralized group of people and in some way this end up with the appearance of a good thing.

PoW is the only way to prevent double spend, make sure that the valid chain is the longer one, guarantee decentralization because miners can go any pool they want, also miners don't control consensus in a certain way, because node runners (relays) also have a say.
If miners simply go away to a non-consensus fork, Node Runners can start mining and the network recovers itself.

Not, PoS, you give power to those who have more money, now billionaires control the consensus, control the network, can censor transactions, can sensor addresses, can sensor wallet providers, and so on...

Also, PoS doesn't impact directly transaction fees in absolutely anyway, unless you are trying to make people stop using bitcoin cause its not bitcoin anymore, and for sure this chain will be a ghost chain as Bitcoin Cash is today, then you are right, fees are going to zero cause nobody will want this new shitcoin.

[franky1]

asic miners that do the actual PoW do not select the transactions(dont confuse asic PoW with pool management)
the network congestion is not the blame of asic PoW miners..

trying to blame miners is just a scapegoat to distract from the real instigators of the problem.. and that is the devs that opened up the exploit

secondly
changing to PoS wont change the junk being added to congest the network

the actual solution is nothing to do with mining at all

the two methods to fix the junk spam is either
a. re-disabled unconditioned opcodes
b. make usage of unconditioned opcodes pay the penalty of extremely high fee, rather then everyone equally penalised

[jrrsparkles]

It is true that Ethereum converted from PoW to PoS but the transaction fee did not reduce. So I do not know the problem you meant that Ethereum faced in the paste.

There are coins that make use of PoW that are cheaper than Ethereum transactions. Examples are litecoin, doge et cetera.

Converting from PoW to PoS is not the solution.

I don't think so. Maybe you are using exchanges to transfer your ETH that's why the fee is so high, or maybe you are transferring erc-20 tokens.

I have tried transferring ETH to another wallet using non-custodial wallets such as myetherwallet and metamask but it only needs a very low fee.

Now, the problem we need to fix is the Bitcoin transaction fee to get back to normal, not in brc-20 tokens.

After switching to POS, the gas fee on Ethereum network became cheaper but it's still on a higher scale compared to other networks the offers similar so its not a solution. And there is no way that Bitcoin will ever switch to PoS and if it does then there is no reason for people to trust Bitcoin anymore because its not going to be as decentralized as it used to be.

Also banning Brc20 junkies from the bitcoin network become questionable and people may argue why there is censorship coming up in true decentralization so its kind of uncertainty.

[franky1]

Also banning Brc20 junkies from the bitcoin network become questionable and people may argue why there is censorship coming up in true decentralization so its kind of uncertainty.

bitcoin always has rejected many transactions for many reasons. learn bitcoin code and the consensus rules
learn how things have become softened to become exploitable

bitcoin has never been this openly exploitable before. something needs to be done

if core devs and their religious acolytes think that legacy deserves a 4x premium just to promote their new feature. then they too can make their exploit 1000x more premium to deter people using the exploit for the same reason they dont want people using legacy

[Stalker22]

I agree. The actual miners running the proof-of-work hardware dont get to pick which transactions get processed.  They just do the number crunching assigned by the network. Switching over to proof-of-stake wont inherently fix the problem of junk transactions overloaded the system.  The real solution has little to do with how we handle the mining.  Its more about closing the exploits, limiting who can publish transactions and potentially rearchitecting how transactions get prioritized and processed.

[nakamura12]

If it is changed then it's no longer the Bitcoin that people is using starting from the time it is used by many people until this day and in the future. I think that if there is a mining rig that is much more powerful then I think it might help getting transactions confirmed much faster than the current speed the transactions are confirmed this time but sadly I don't think there is a mining rig that powerful yet so, I think the best solution is for brc-20 tokens not being used, removed or eradicate as you have said or use lightning network.

[EL MOHA]

After switching to POS, the gas fee on Ethereum network became cheaper but it's still on a higher scale compared to other networks the offers similar so its not a solution. And there is no way that Bitcoin will ever switch to PoS and if it does then there is no reason for people to trust Bitcoin anymore because its not going to be as decentralized as it used to be.

We are mixing this things up, Ethereum didn’t actually switch to POS to solve any scalability problem, but rather they we’re looking for a way to reduce the energy consumption by the POW method according to them. This switch resulted into to validators been the verifiers of transactions and this validators are selected base on the amount of ETH Staked, although they say they shuffle the validators but still instead of all node been able to verify transactions like bitcoin it still looks like a centralized system since it is a group of people doing it.

I don’t see bitcoin switching to POS been a good solution to improve its scalability because if it actually solves the problem ethereum wouldn’t be looking at going into danksharding as scalability solution

[nelson4lov]

POS is not a lasting solution for scalability. It has its own downsides. Ethereum took that route with the hope that it would resolve some of its issues involving transaction throughrout and faster time to consensus but in hindsight, that is not the case. Stopping Brc20 too isn't the case because for a long time, bitvoiners have always wished they could have compute on the chain instead of patronizing alternative chains but at what cost?

Compute is here to stay. Bitcoin Developers need to figure out another scalability option if at all smass adoption is still the end goal for Bitcoin.

[panganib999]

People are thinking what's the best way to get rid of this blockchain network congestion.

Network congestion is a problem for us because it affects the fee. The normal fee is just around $1 but this month we are experiencing a very high fee which is unaffordable to most people.

We found out that the reason of this issue is because of brc-20 tokens, they use Bitcoin blockchain. And since Bitcoin's blockchain is only process 7-10 transactions per second which is not enough to manage all the transaction if we included the brc-20 tokens.

Now, is the problem will be fixed if brc-20 tokens will be removed?

Yes, very possible, but how? Brc20 tokens keeps improving and lot of brc20 token is being launch everyday.
The total confirmed market cap of brc20 tokens that is listed in Coinmarketcap is $3b with a $1b trading volume which is very difficult to stop.

The other solution to fix network congestion is to increase the block size. Is increasing the block size fix network congestion?
Definitely yes, and there is no need to eradicate brc20 tokens.

But in what way? Is it really possible to increase the block size of Bitcoin? For sure there's a reason why Nakamoto put only a very limited block size.


I have found another solution to remove this obstacle in Bitcoin but I don't know if this idea is acceptable to the majority. If you remember what happen to Ethereum way back 2017, it encountered this such problem.
They made Ethereum to POS from POW as a solution to this problem, and it's called ETH 2.0

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

Honestly, I don't think the switch of consensus mechanism is going to do wonders for bitcoin. I mean there is a reason why all these years, bitcoin remained to be PoW instead of submitting to the Proof of Stake meta outside the bitcoin network.

For one, networks like Ethereum are known to be very versatile and all-encompassing. You got an idea, Ethereum can make it work for you. So do other networks that popped into existence in the past few years. Bitcoin's not really known for this since besides the fact that it has a very low scalability propensity, it also doesn't have that extra capability to handle projects with innovative motifs in them. Prime example being Ordinals. Besides that, it would seem as though the whole network, developers and consumers like us included, made it a point to not actually use bitcoin for anything other than investing, trading, and sending money from far off lands. Nothing wrong with it honestly, but it would signify the lack of need for us to switch to PoS and jeopardize bitcoin's otherwise robust security just so it could cater to a wider audience.

There are other ways we could integrate a solution that would make the bitcoin network faster and cheaper, employing a robust layer 2 off-chain that would facilitate transactions off the blockchain being one of the biggest examples I can think of right now. But if I were to rate consensus mechanism switch, I'd put it at the bottom of the solution's list.

[icalical]

.

Also banning Brc20 junkies from the bitcoin network become questionable and people may argue why there is censorship coming up in true decentralization so its kind of uncertainty.

Decentralized is not the same as anarchism, it doesn't mean that we couldn't have rules for Bitcoin. There has been several BIP (Bitcoin Improvement Proposals) implemented before, so there is no reason for a new BIP that reject ordinals transaction to be applied if 95% of the miners approved the new rules. It will still be decentralized, because even after 95% approve the BIP then community need to upgrade their Bitcoin core, if they are on the same page with miners.

[adaseb]

First of all, ETH didn’t move to POS to get cheaper fees, they did it mostly for environmental reasons and they didn’t like POW because it was a waste of energy. As soon as POS went live, the fees were pretty much identical.

BTC won’t switch to POS, there is nothing in its future about doing such a thing. Ethereum is different because ever since it’s launch in 2016, it’s goal was to go POS but it was never bitcoins future. So there will be no POS for bitcoin don’t worry.

[NotATether]

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

Read this, and then tell me whether you still think PoS is a good idea.

[pooya87]

Now, is the problem will be fixed if brc-20 tokens will be removed?

There is no such thing as BRC-20 in Bitcoin protocol. What they refer to on their centralized website is just arbitrary data on bitcoin blockchain.

Yes, very possible, but how? Brc20 tokens keeps improving and lot of brc20 token is being launch everyday.
The total confirmed market cap of brc20 tokens that is listed in Coinmarketcap is $3b with a $1b trading volume which is very difficult to stop.

Stopping an attack is never about how much money the attackers have at their disposal. It is always about methods the protocol uses to prevent it. For example if you have billions of dollars, you still wouldn't be able to perform a 51% attack on bitcoin because the protocol and the reality of the world (won't be able to get that much ASICs) prevents it.

The other solution to fix network congestion is to increase the block size.

Wrong. Increasing the block size fixes natural congestion caused by increased adoption. It will not do anything to prevent a congestion caused by an attack. In fact more capacity could mean cheaper and consequently much worse attack.

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

That would be like saying "my nose itches and as a solution I will saw off my left leg".

Proof of Stake is a flawed protocol and a flawed concept. Not to mention that it does absolutely nothing to prevent a spam attack! That's simply because no matter HOW you process the blocks, the abusers can still inject a large amount of junk into the chain as long as the consensus rules allows it!

The only reason why a centralized shitcoin like Ethereum switched to PoS was because the centralized authority behind this project held a massive premine of 72 million ethers and they wanted to both gain full control over the network and have a solid revenue without having to liquidate their premined bags.

[God bless u]

If there will be a Bitcoin 2.0 or a change of network from POW to POS then not only the network congestion is being fixed but many more, and also it can reduced the energy consumption.

I don't think Upgrading Bitcoin network into version 2.0 would solve these problems.
as you can see Ethereum Gas problem still there even after upgrading into 2.0 and becoming a POS.
other than that Ethereum have a Team behind, a group of developers. and Bitcoin is not controlled by anyone. I am not an expert, sorry if I am wrong but I think it is technically not possible to do that.
also what about all those miners who will go jobless after that?

[m2017]

It is true that Ethereum converted from PoW to PoS but the transaction fee did not reduce. So I do not know the problem you meant that Ethereum faced in the paste.

It would be good to analyze the changes that occurred in the Ethereum network after the conversion from PoW to PoS. Such as the number of active users, the total number of transactions, etc. Such statistics would help explain why transaction fee have not decreased.

There are coins that make use of PoW that are cheaper than Ethereum transactions. Examples are litecoin, doge et cetera.

Transactions in the networks of these coins are not only cheaper than Ethereum transactions, but these coins themselves are much cheaper than Ethereum (even their current total value).

Whether transactions in the networks of these coins will remain as cheap if their current value increases to the level of Ethereum (as well as the number of active users increases) is another question.

Converting from PoW to PoS is not the solution.

Was such a transition discussed in the BTC-community?

[goldkingcoiner]

DO NOT IMPLEMENT POS! It is a trap!

Do you guys have any idea of the irreversible damage this will do to Bitcoin? Especially now, with ETFs being brought out to the crowd of traditional investors by institutional investors? Bitcoin needs to remain free! A POS will ensure centralization immediately after implementation! It will not lower transaction fees as much as you hope!

Look at what happened to Ethereum straight after POS implementation: 2 addresses owned almost 50% of all ETH!

The moment 2 people have the right to decide on how the blockchain functions, just because they own the most coins, it becomes centralized. It becomes regulatable. It becomes a backdoor CBDC!

This is exactly what the government wants. They will be able to decide who gets to use it, and which transactions are valid and which are not!

[btc78]

Let us disregard first the fact that the switch from POW to POS could help the congestion, is it possible to change Bitcoin from POW to POS?

Well, yes but it will for sure face many difficulties and the community will be having some challenges i mean just with bitcoin’s size alone transitioning from POW to POS will already serve as a challenge in itself

If we were to change from POW to POS it would not be easy and we would have to rely to miners heavily

[franky1]

Let us disregard first the fact that the switch from POW to POS could help the congestion, is it possible to change Bitcoin from POW to POS?

Well, yes but it will for sure face many difficulties and the community will be having some challenges i mean just with bitcoin’s size alone transitioning from POW to POS will already serve as a challenge in itself

If we were to change from POW to POS it would not be easy and we would have to rely to miners heavily

asics do not choose transactions.. POOL managers do
convincing a mining pool that it can still select transactions, claim a reward but not need to then pay out individual mining asic owners could actually be a achievable thing..

not suggesting it should happen. just saying it is capable of happening
if core went completely numbskull to want to change code to make the bitcoin node software operate as such its more then possible as any other brand of node does not have the ability to counter propose or offer majority avoidance of core changes. so yes it is possible to change. though not recommended to change

.. changing to PoS wont change the transaction selection. because the transaction selection has never been related to PoW (sha256 hashing)

[coolcoinz]

The normal fee is just around $1 but this month we are experiencing a very high fee which is unaffordable to most people.

What is normal? In 2017 the average fee was already $3 so how did you come up with that idea that $1 is normal?  In 2015 "normal" was below $1, but in 2017 "normal" was $5. In a network that's constantly growing you can't expect the fees to stay at the same level.

Ordinals made it so that we're at least 4x the fee we would be paying if the fees were growing with the network, but even if we ban ordinals, don't expect fees to go back to $1.
In 2024 you can expect 2 things to happen. Bitcoin will go into another post-halving FOMO rally and fee will grow with as it went up in 2018 and 2021. It's more likely that $10 will become the new normal than $2. $1 fee? Forget about it.

[Charles-Tim]

Was such a transition discussed in the BTC-community?

I do not think so. The only PoS that is likely possible would be the Spiderchain which is also called the drive chain or something. The proposal is in a way the PoW and the onchain transaction will not be affected as it will also be like a side chain or a other layer 2. But for PoS to be proposed directly, there is nothing like that.

[DapanasFruit]

I am sure that the whole Bitcoin community would never give a nod to transform BTC from PoW to PoS as this is one of the strongest feature of Bitcoin we think should not be tinkered with. With the ongoing congestion and the resulting high fees happening again, developers should be looking for ways to somehow solve the ongoing problem and should have a roadmap for long-term solutions.