(Relatively) complex computations on private chain?

Question

Is there any way to get rid of gas limitations (or significantly increase them) to be able to do more or less useful stuff in smart contracts (such as RSA signature verification, defining advanced data structures, etc)?

Answer 1

Gas limit is set for the first time in the genesis block and since then it is increased or decreased by miners. From official documentation, Design Rationale - Gas & Fees:

Currently, due to a lack of clear information about how miners will behave in reality, we are going with a fairly simple approach: a voting system. Miners have the right to set the gas limit for the current block to be within ~0.0975% (1/1024) of the gas limit of the last block, and so the resulting gas limit should be the median of miners' preferences. The hope is that in the future we will be able to soft-fork this into a more precise algorithm.

Please note this does not mean you can do complex things on the EVM, but just more things on the EVM in a single transaction or block.

And no, you can't verify an RSA signature inside a smart contract.