user33528: Does it cost more storage?
For the transaction verification, to which extent bigger blocks make it more computational intensive?
In terms of computational complexity, is the verification process a O(n) computation or anything else?

user33898: Short answer: For big players the cost is mostly negligible.
Longer answer (independent of the current block size debate):
Hard Drive Cost:
A bigger block will take up more disk space. Right now the block size is limited to 1 MB. If the block size is increased to 2 MB and assuming all blocks are always being filled to the max size then you will need about twice the hard drive space to store the same amount of 2 MB blocks as you needed for 1MB blocks.
Network Bandwidth Cost:
If block size is increased, a full node has to relay a bigger size block. Sending and receiving more data will have an impact on cost as well.
Real Time Computational Cost:
A full node has to hash a block and verify that the hash has n amount of leading zeros. Increasing the block size will result in hashing a larger amount of data which increases verification time.
Big O Complexity:
Big O would depend on whatever the Big O is for sha256.

33528: <p>Does it cost more storage?
For the transaction verification, to which extent bigger blocks make it more computational intensive?
In terms of computational complexity, is the verification process a O(n) computation or anything else?</p>
 33898: <p>Short answer: For big players the cost is mostly negligible.</p>

<p>Longer answer (independent of the current block size debate):</p>

<p>Hard Drive Cost:
A bigger block will take up more disk space. Right now the block size is limited to 1 MB. If the block size is increased to 2 MB and assuming all blocks are always being filled to the max size then you will need about twice the hard drive space to store the same amount of 2 MB blocks as you needed for 1MB blocks.</p>

<p>Network Bandwidth Cost:
If block size is increased, a full node has to relay a bigger size block. Sending and receiving more data will have an impact on cost as well.</p>

<p>Real Time Computational Cost:
A full node has to hash a block and verify that the hash has n amount of leading zeros. Increasing the block size will result in hashing a larger amount of data which increases verification time.</p>

<p>Big O Complexity:
Big O would depend on whatever the Big O is for sha256.</p>
