Progressive transactional memory in time and space

Transactional memory (TM) allows concurrent processes to organize sequences of operations on shared data items into atomic transactions. A transaction may commit, in which case it appears to have executed sequentially or it may abort, in which case no data item is updated. The TM programming paradigm emerged as an alternative to conventional fine-grained locking techniques, offering ease of programming and compositionality. Though typically themselves implemented using locks, TMs hide the inherent issues of lock-based synchronization behind a nice transactional programming interface. In this paper, we explore inherent time and space complexity of lockbased TMs, with a focus of the most popular class of progressive lockbased TMs. We derive that a progressive TM might enforce a read-only transaction to perform a quadratic (in the number of the data items it reads) number of steps and access a linear number of distinct memory locations, closing the question of inherent cost of read validation in TMs. We then show that the total number of remote memory references (RMRs) that take place in an execution of a progressive TM in which n concurrent processes perform transactions on a single data item might reach Ω(n log n), which appears to be the first RMR complexity lower bound for transactional memory.