Is it possible to perform queries on the blockchain, based on transaction properties (other then hash), such as its data/sender/value/etc fields? For example, is it possible to "ask the blockchain" to return all transactions whose data match a certain regular expression (or string)?

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The answer is no.

The standard ethereum clients (geth and parity) maintain only a limited set of indexes for querying the blockchain. For example, you can look up a transaction by its hash (using web3 getTransaction(hash) or RPC eth_getTransactionByHash) but you cannot look up transactions by sender. Services like http://etherscan.io that offer more complete navigation use custom clients that build additional indexes.

Quoted answer: https://ethereum.stackexchange.com/a/10894/36613

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