# Clarfication on “ network synchrounisation” in analyzing bitcoin protocol in a synchronous model

I am reading The Bitcoin Backbone Protocol:Analysis and Applications and i have no previous knowledge on different type of networks . And there is a term in paper " high network synchronicity " which i really can not understand.The paper is analyzing core of bitcoin protocol which it call it bitcoin backbone protocol . They analyze protocol in a synchronous model ( messages will be delivered at most at the beginning of next round). Here are some part of paper which is talking about synchronization .

n is number of parties running the protocol which is fixed and t is number of parties adversary controls and f is probability at least one honest party succeeds in finding a POW in a round.

Honest Majority Assumption : A number of t out of n parties are corrupted such that t ≤ (1−δ)(n−t), where 3f+ 3e < δ≤1

we describe and analyze the Bitcoin system as well as a more elaborate BA protocol, proving them secure assuming high network synchronicity and that the adversary’s hashing power is strictly less than 1/2, while the adversarial bound needed for security decreases as the network desynchronizes describe and analyze the Bitcoin system as well as a more elaborate BA protocol, proving them secure assuming high network synchronicity and that the adversary’s hashing power is strictly less than 1/2, while the adversarial bound needed for security decreases as the network desynchronizes

We assume that messages are eventually delivered and all parties in the network are able to synchronize in the course of a“round.”

The parameter f plays a critical role in the analysis of the property and should be small in order to approximate honest majority,i.e., allowing to be close to n/2. A small choice for f, suggests also that the network synchronizes significantly faster than the rate of finding POW’s. On the other hand, when the network “desynchronizes” and f gets closer to 1, achieving provably a common prefix requires almost all parties to be honest.

For both properties to hold we require an honest majority (i.e., that the adversary’s hashing power is strictly less than 50%) assuming high network synchronicity (i.e., the duration of a round in terms of the number of computational steps the parties take towards finding a POW is close to 0). If this is violated, Persistence requires stricter bounds on adversarial hashing power in order to be preserved following the bounds of the common prefix property.

In the context of Bitcoin, our analysis implies that the Bitcoin backbone provides an operational transaction ledger under the assumptions: (i) the adversary controls less than half of the total hashing power, and (ii) the network synchronizes much faster relative to the POW solution rate,(iii) digital signatures cannot be forged.

So my questions are :

1) what it means "low or high network synchronicity" ?

2) what it means "parties in the network are able to synchronize in the course of around." ?

3) more importantly what it means " A small choice for f, suggests also that the network synchronizes significantly faster than the rate of finding POW’s" or "the network synchronizes much faster relative to the POW solution rate" ?

I know my question might not be a good question and there might be obvious answers to questions but i really need some general clarification to help me fully understand the paper .