On the robustness of Herlihy's hierarchy

A wait-free hierarchy maps object types to levels in Z(+) U (infinity) and has the following property: if a type T is at level N, and T' is an arbitrary type, then there is a wait-free implementation of an object of type T', for N processes, using only registers and objects of type T. The infinite hierarchy defined by Herlihy is an example of a wait-free hierarchy. A wait-free hierarchy is robust if it has the following property: if T is at level N, and S is a finite set of types belonging to levels N - 1 or lower, then there is no wait-free implementation of an object of type T, for N processes, using any number and any combination of objects belonging to the types in S. Robustness implies that there are no clever ways of combining weak shared objects to obtain stronger ones. Contrary to what many researchers believe, we prove that Herlihy's hierarchy is not robust. We then define some natural variants of Herlihy's hierarchy, which are also infinite wait-free hierarchies. With the exception of one, which is still open, these are not robust either. We conclude with the open question of whether non-trivial robust wait-free hierarchies exist

Extranatural Inflation Redux

The success of a given inflationary model crucially depends upon two features: its predictions for observables such as those of the Cosmic Microwave background (CMB) and its insensitivity to the unknown ultraviolet (UV) physics such as quantum gravitational effects. Extranatural inflation is a well motivated scenario which is insensitive to UV physics by construction. In this five dimensional model, the fifth dimension is compactified on a circle and the zero mode of the fifth component of a bulk $U(1)$ gauge field acts as the inflaton. In this work, we study simple variations of the minimal extranatural inflation model in order to improve its CMB predictions while retaining its numerous merits. We find that it is possible to obtain CMB predictions identical to those of e.g. ${\cal R} + {\cal R}^2$ Starobinsky model of inflation and show that this can be done in the most minimal way by having two additional extra light fermionic species in the bulk, with the same $U(1)$ charges. We then find the constraints that CMB observations impose on the parameters of the model.Comment: Journal version (to appear in Phy. Rev. D

Compositional Reasoning is not possible in Determining the Solvability of Consensus

Consensus, which requires processes with different input values to eventually agree on one of these values, is a fundamental problem in fault-tolerant computing. We study this problem in the context of asynchronous shared-memory systems. In our model, shared-memory consists of a sequence of cells and supports a specific set of operations. Prior research on consensus focussed on its solvability in shared-memories supporting specific operations. In this paper, we investigate the following general question: Let OP1 and OP2 be any two sets of operations such that each set includes read and write operations. Suppose there is no consensus protocol for N processes in a shared-memory that supports only operations in OP1 and in a shared-memory that supports only operations in OP2. Does it follow that there is no consensus protocol for N processes in a shared-memory that supports all operations in OP1 and all operations in OP_2? This question is in the same spirit as the robustness question, but there are significant differences, both conceptually and in the models of shared-memory for which the two questions are studied. For deterministic types, the robustness question has been known to have a positive answer, In contrast, we prove that the answer to the question posed above is negative even if operations are deterministic

Efficiently Implementing a Large Number of LL/SC Objects

Over the past decade, a pair of instructions called load-linked (LL) and store-conditional (SC) have emerged as the most suitable synchronization instructions for the design of lock-free algorithms. However, current architectures do not support these instructions; instead, they support either CAS (e.g., UltraSPARC, Itanium) or restricted versions of LL/SC (e.g., POWER4, MIPS, Alpha). Thus, there is a gap between what algorithm designers want (namely, LL/SC) and what multiprocessors actually support (namely, CAS or RLL/RSC). To bridge this gap, a flurry of algorithms that implement LL/SC from CAS have appeared in the literature. The two most recent algorithms are due to Doherty, Herlihy, Luchangco, and Moir (2004) and Michael (2004). To implement M LL/SC objects shared by N processes, Doherty et al.\u27s algorithm uses only O(N + M) space, but is only non-blocking and not wait-free. Michael\u27s algorithm, on the other hand, is wait-free, but uses O(N^2 + M) space. The main drawback of his algorithm is the time complexity of the SC operation: although the expected amortized running time of SC is only O(1), the worst-case running time of SC is O(N^2). The algorithm in this paper overcomes this drawback. Specifically, we design a wait-free algorithm that achieves a space complexity of O(N^2 + M), while still maintaining the O(1) worst-case running time for LL and SC operations

Recoverable FCFS Mutual Exclusion with Wait-Free Recovery

Traditional mutual exclusion locks are not resilient to failures: if there is a power outage, the memory is wiped out. Thus, when the system comes back on, the lock will have to be restored to the initial state, i.e., all processes are rolled back to the Remainder section and all variables are reset to their initial values. Recently, Golab and Ramaraju showed that we can improve this state of the art by exploiting the Non-Volatile RAM (NVRAM). They designed algorithms that, by maintaining shared variables in NVRAM, allow processes to recover from crashes on their own without a need for a global reset, even though a crash can wipe out the local memory of a process. We present a Recoverable Mutual Exclusion algorithm using the commonly supported CAS primitive. The main features of our algorithm are that it satisfies FCFS, it ensures that each process recovers in a wait-free manner, and in the absence of failures, it guarantees a worst-case Remote Memory Reference (RMR) complexity of O(lg n) on both Cache Coherent (CC) and Distributed Shared Memory (DSM) machines, where n is the number of processes for which the algorithm is designed. This bound matches the Omega(lg n) RMR lower bound by Attiya, Hendler, and Woelfel for Mutual Exclusion algorithms that use comparison primitives

Constant RMR Solutions to Reader Writer Synchronization

We study Reader-Writer Exclusion, a well-known variant of the Mutual Exclusion problem where processes are divided into two classes--readers and writers--and multiple readers can be in the Critical Section (CS) at the same time, although no process may be in the CS at the same time as a writer. Since readers don\u27t conflict with each other, they should not obstruct each other. Specifically, the concurrent entering property must be satisfied: if all writers are in the remainder section, each reader should be able to enter the CS in a bounded number of its own steps. Three versions of the Reader-Writer Exclusion problem are commonly studied--one where writers have priority over readers, another where readers have priority, and the last where neither class has priority over the other and no process may starve. To ensure high performance on Cache-Coherent (CC) and Distributed Shared Memory (DSM) multiprocessors, algorithms should be designed to generate as few remote memory references (RMRs) as possible. The ideal would be to achieve constant RMR complexity, i.e., the worst case number of RMRs that a process generates in order to enter and exit the CS once is a constant, independent of the number of processes. Constant RMR complexity algorithms have existed for Mutual Exclusion for two decades, but none exists for Reader-Writer Exclusion. Danek and Hadzilacos\u27 lower bound proof implies that it is impossible to achieve sublinear RMR complexity for DSM machines. For CC machines, the best existing bound, also due to Danek and Hadzilacos , is O(log n), where n is the number of processes. In this work, we present the first constant RMR complexity algorithms for all three versions of the Reader-Writer Exclusion problem (for CC machines)