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We investigate the time and space complexity of detecting and preventing ABAsin shared memory algorithms for systems with n processes and bounded baseobjects. To that end, we define ABA-detecting registers, which are similar tonormal read/write registers, except that they allow a process q to detect witha read operation, whether some process wrote the register since q's last read.ABA-detecting registers can be implemented trivially from a single unboundedregister, but we show that they have a high complexity if base objects arebounded: An obstruction-free implementation of an ABA-detecting single bitregister cannot be implemented from fewer than n-1 bounded registers. Moreover,bounded CAS objects (or more generally, conditional read-modify-writeprimitives) offer little help to implement ABA-detecting single bit registers:We prove a linear time-space tradeoff for such implementations. We show thatthe same time-space tradeoff holds for implementations of single bit LL/SCprimitives from bounded writable CAS objects. This proves that theimplementations of LL/SC/VL by Anderson and Moir (1995) as well as Jayanti andPetrovic (2003) are optimal. We complement our lower bounds with tight upperbounds: We give an implementation of ABA-detecting registers from n+1 boundedregisters, which has step complexity O(1). We also show that (bounded) LL/SC/VLcan be implemented from a single bounded CAS object and with O(n) stepcomplexity. Both upper bounds are asymptotically optimal with respect to theirtime-space product. These results give formal evidence that the ABA problem isinherently difficult, that even writable CAS objects do not provide significantbenefits over registers for dealing with the ABA problem itself, and that thereis no hope of finding a more efficient implementation of LL/SC/VL from boundedCAS objects and registers than the ones mentioned.

On the Time and Space Complexity of ABA Prevention and Detection