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The emergence of systems with non-volatile main memory (NVM) increases the interest in the design of emph{recoverable concurrent objects} that are robust to crash-failures, since their operations are able to recover from such failures by using state retained in NVM. Of particular interest are recoverable algorithms that, in addition to ensuring object consistency, also provide emph{detectability}, a correctness condition requiring that the recovery code can infer if the failed operation was linearized or not and, in the former case, obtain its response. In this work, we investigate the space complexity of detectable algorithms and the external support they require. We make the following three contributions. First, we present the first wait-free bounded-space detectable read/write and CAS object implementations. Second, we prove that the bit complexity of every $N$-process obstruction-free detectable CAS implementation, assuming values from a domain of size at least $N$, is $Omega(N)$. Finally, we prove that the following holds for obstruction-free detectable implementations of a large class of objects: their recoverable operations must be provided with emph{auxiliary state} -- state that is not required by the non-recoverable counterpart implementation -- whose value must be provided from outside the operation, either by the system or by the caller of the operation. In contrast, this external support is, in general, not required if the recoverable algorithm is not detectable.
Relaxing the sequential specification of shared objects has been proposed as a promising approach to obtain implementations with better complexity. In this paper, we study the step complexity of relaxed variants of two common shared objects: max regi
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. This is
We present a tight RMR complexity lower bound for the recoverable mutual exclusion (RME) problem, defined by Golab and Ramaraju cite{GR2019a}. In particular, we show that any $n$-process RME algorithm using only atomic read, write, fetch-and-store, f
We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in a
Shors and Grovers famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_ do, and spec