1. A non-transitory computer-accessible storage medium storing program instructions that when executed on one or more processors: receive, at a log-based transaction manager, a transaction descriptor of a requested transaction from a client, wherein the transaction descriptor comprises at least (a) a first committed state identifier (CSI) of a source data store from which data is read during the requested transaction, (b) respective read signatures indicative of one or more objects from which data is read during the requested transaction and (c) respective write signatures indicative of one or more objects to which data is to be written in response to a commit of the requested transaction; identify, by the log-based transaction manager using the first CSI, a subset of transaction records stored in a particular persistent log to be examined for conflicts prior to committing the requested transaction, wherein the particular persistent log comprises transaction records corresponding to previously-committed transactions associated with one or more data stores including the source data store, in response to a determination, by the log-based transaction manager, that none of the objects indicated by the read signatures of the requested transaction have been modified by a write operation indicated in the subset of transaction records, accept the requested transaction for commit.