This document proposes economic solutions to limit the increasing size of blockchain states. It suggests transaction fees should be proportional to the storage space and time outputs occupy in the blockchain state. This includes prepaid outputs that rent state space for a maximum number of blocks, postpaid outputs where fees are paid when spent based on actual space-time used, and scheduled payments that periodically decrease output values. Estimates show such an approach can limit state size growth, provide a constant mining reward, and recirculate lost coins back into the economy over time.

1. On Space-Scarce Economy
In Blockchain Systems
Dmitry Meshkov1,2
, Alexander Chepurnoy1,2
1. Ergo platform
2. IOHK Research

2. Motivation
● Despite of a blockchain, nodes in
cryptocurrencies store a State
● State is required to validate transactions
● When transaction create an output, miners
commits that they will keep it forever
● State size continuously increasing (especially
during attacks)

3. Problems for users:
● Can’t validate blocks on low-end hardware
● Long validation on commodity hardware
=>
● Users move to centralized services
Possible solution[3]:
● Authenticate state
● Provide a proof of transaction correctness
Big state problem
3. Reyzin L. et al. Improving authenticated dynamic dictionaries, with applications
to cryptocurrencies

4. ● Miners should validate transactions efficiently
They can:
● Keep State in RAM => Mining centralization
● Do not keep State => SPV mining
Possible solution:
● Limit state size economically
Big state problem

5. Fee types
Transaction utilize different node resources:
fee = F(feen,feec,fees)
Cost Proportional to Dominant in
Network Transaction size Blockchain for money
Computation CPU utilization Blockchain for contracts
Storage State size changes Blockchain for database

6. Prior work: network fee
Addition of a new transaction to a block leads to
● Increased block reward
● Increased chance to get nothing
● There should have maximum somewhere
● Maximum may be at 0 in case of big fixed block
reward
1. P. R. Rizun, A transaction fee market exists without a block size limit.

7. Prior work: computation fee
● Important for blockchains with heavy
computations in transactions
● Required to prevent DoS attacks
● Miners have an incentive to include as heavy
transactions, as possible[2]
● This may change if other miners will be rational
and will be able to estimate required
calculations before contract evaluation
2. Luu L. et al. Demystifying incentives in the consensus computer

8. Storage fee

9. Storage fee
● User should pay for space-time multiplication
of State utilization
fees = K · Osize · Olifetime
where
● K – miner defined price for keeping 1 byte of
data for 1 block in a State
● Osize - output size in byte
● Olifetime - number of blocks output will be stored
in a State

10. Storage fee
Problem:
● When transaction creates an output, block
when it will be spent is unknown, so Olifetime is not
defined

11. Storage fee: prepaid
Prepaid Outputs:
● Rent a box in State of size Osize for at most Lmax
blocks, pay in advance
● When rent time is out – anyone can spend
output script:
(regular_script) (Height > O.height + L∨ max)

12. Storage fee: postpaid
Postpaid Outputs:
● Pay for resources you actually used when you
spend output
● For output value V, a height Hmax exists when the
whole output value will be consumed by fee
output script:
(regular_script) (Height > O.height + H∨ max)

13. Storage fee: scheduled
Scheduled payments:
● Decrease output value periodically
● After some duration Ds anyone can spend output,
putting money - fee back to the same script
output script:
(regular_script) (Height > (O.height + D∨ s) ∧
((O.value K · B · Ds tx.has_output(value =≤ ∨
out.value − K · B · Ds, script = O.script)))

14. State size
● Block size is limited Sblock
● State can increase for at most Sblock per block
● When the adversary tries to increase State, he
should pay for all previously created outputs
resulting State size:
S=
√2∗Sblock∗Ncoins
K

15. Mining reward
● Constant per-block reward is important [4]
● Releasing outputs will provide it forever
● Additional block reward Ssize*K
● Higher in prepaid model
4. Carlsten M. et al. On the instability of bitcoin without the block reward

16. Lost coin recirculation
● Possible coin supply is known but actual supply
is unknown due to lost keys
● Space-time fee provide a way to return coins
into circulation
where
● Nlost – number of lost keys
● Voutput – average output value
Rpostpaid=Rscheduled =∑
i=1
N lost
K·Osizei
Rprepaid =∑
i=1
N lost
Voutputi
Lmaxi

17. Estimations
Based on Bitcoin stats
● K=10-9 BTC/(Byte*Block)
● Rpostpaid=Rschedule≈0.036 BTC/Block
● Rprepaid≈20 Rpostpaid (for 10 years lifetime)
● Supper=183Gb

18. Contacts
● dmitry.meshkov@iohk.io
● https://twitter.com/DmitryMeshkov
● https://www.slideshare.net/DmitryMeshkov
● https://ergoplatform.org
● https://iohk.io