A multiprocessor system providing transactional memory. A first processor initiates a transaction which includes reading first data into a private cache of the first processor, and performing a write operation on the first data in the private cache of the first processor. In response to detecting that prior to the write operation the first data was last modified by a second processor, the first processor writes the modified first data into a last level cache (LLC) accessible by the multiple processors. The system sets a cache line state index string to indicate that the first data written into the LLC was last modified by the first processor, invalidates the first data in the private cache of the first processor, and commits the transaction to the transactional memory system. This allows more efficient accesses to the data by the multiple processors.