First note that bitcoin nodes pass on blocks. So even if most machines in a country are cut off from the rest of the world it only takes one machine that can "see both sides" to keep the blocks flowing back and forth.
But what happens if an area is completely cut off from most of the world?
Miners on both sides of the cut will continue trying to find blocks. The probability of them finding them is determined by the current difficulty.
Assuming the "most of the world" side has most of the hashing power it will continue more or less as usual.
The "armenia" side on the other hand will experiance a massive drop in block rate. If they have 1% of the hashing power (and I doubt they have even that) then they will experience a one hundred fold drop in block rate.
If the isolation goes on long enough then the "target" on the "Armenia" side will adjust to restore the normal block rate but this will take a long time. The "target" only readjusts after every 2016 blocks and it only readjusts by a factor of up to four each time. Say that when the split happens we are halfway between difficulty readjustments, if the "Armenia" has one percent of the hashing capacity then it will take about 100 weeks (~two years) to reach it's first difficulty adjustment.
If and when connectivity is restored then any blocks mined on the "Armenia" side will be discarded as the chain from the "rest of world" side is much stronger. Transactions from the "Armenia" side may be re-included in new blocks if they are still valid.
Besides the potential double-spending, I see another potential problem in this scenario: if an Armenian miner keeps mining and spends immediately their earned coins before the reconnection, most probably those transactions will be deemed invalid when the network gets reunified. And, just like @user622, I wonder what would happen if the disruption takes longer than a week - if I understood correctly, transactions can't be live for more than 2 days, so all the isolated Armenian transactions would get reverted, right? – Joe Pineda – 2013-06-13T21:53:42.863
And I believe bitcoin's protocol should probably change to make these type of events less traumatic. I can very well imagin such situations being used against island-nations by either terrorists or governments. Should bitcoin become enormously popular in Cuba, for instance, I can easily imagine the USA cutting off the cables on purpose and doing an enormous damage to their economy... – Joe Pineda – 2013-06-13T21:55:54.530
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Related: http://bitcointalk.org/index.php?topic=106302.0
– Stephen Gornick – 2013-09-26T05:30:46.760Would it be possible to physically transfer files to mitigate the consequences? – barrymac – 2011-10-26T12:50:31.427
1Thilo seems to answer in short, but what if the connection is severed for say a month and there is lively transactions in Armenia for that period. Would that cause merging issues upon reconnection? – None – 2011-10-26T13:37:59.537
2@evanh: Assuming nobody actually attempted any double-spend attacks, there would be no problem -- all the 'lost' transactions in the reorganization would eventually be mined into new blocks. What this means is that in order to trust a transaction, you need not just confirmations but also to make sure you're talking to a large enough network. – David Schwartz – 2011-10-26T14:09:41.027