The Semantics of Progress in Lock-Based Transactional Memory

Transactional memory (TM) is a promising paradigm for concurrent programming. Whereas the number of TM implementations is growing, however, little research has been conducted to precisely define TM semantics, especially their progress guarantees. This paper is the first to formally define the progress semantics of lock-based TMs, which are considered the most effective in practice. We use our semantics to reduce the problems of reasoning about the correctness and computability power of lock-based TMs to those of simple try-lock objects. More specifically, we prove that the verification of any set of transactions accessing an arbitrarily large set of shared variables can be reduced to the verification of a simple property of each individual (logical) try-lock used by those transactions. We use this theorem to determine the correctness of state-of-the-art lock-based TMs and highlight various configuration ambiguities. We also prove that lock-based TMs have consensus number~2. This means that, on the one hand, a lock-based TM cannot be implemented using only read-write memory, but, on the other hand, it does not need very powerful instructions such as the commonly used compare-and-swap. We finally use our semantics to formally capture an inherent trade-off in the performance of lock-based TM implementations. Namely, we show that the space complexity of every lock-based software TM implementation that uses invisible reads is at least exponential in the number of objects accessible to transactions.