A computing system processes memory transactions for parallel processing of multiple threads of execution by support of which an application need not be aware. The computing system transactional memory support provides a Transaction Table in memory and performs fast detection of potential conflicts between multiple transactions. Special instructions may mark the boundaries of a transaction and identify memory locations applicable to a transaction. A ‘private to transaction’ (PTRAN) tag, enables a quick detection of potential conflicts with other transactions that are concurrently executing on another thread of said computing system. The tag indicates whether (or not) a data entry in memory is part of a speculative memory state of an uncommitted transaction that is currently active in the system. A transaction program employs a plurality of Set Associative Transaction Tables, one for each microprocessor, and Load and Store Summary Tables in memory for fast processing of common conflict.