Randomized Two-Process Wait-Free Test-and-Set

We present the first explicit, and currently simplest, randomized algorithm for 2-process wait-free test-and-set. It is implemented with two 4-valued single writer single reader atomic variables. A test-and-set takes at most 11 expected elementary steps, while a reset takes exactly 1 elementary step. Based on a finite-state analysis, the proofs of correctness and expected length are compressed into one table.Comment: 9 pages, 4 figures, LaTeX source; Submitte

On the Importance of Registers for Computability

All consensus hierarchies in the literature assume that we have, in addition to copies of a given object, an unbounded number of registers. But why do we really need these registers? This paper considers what would happen if one attempts to solve consensus using various objects but without any registers. We show that under a reasonable assumption, objects like queues and stacks cannot emulate the missing registers. We also show that, perhaps surprisingly, initialization, shown to have no computational consequences when registers are readily available, is crucial in determining the synchronization power of objects when no registers are allowed. Finally, we show that without registers, the number of available objects affects the level of consensus that can be solved. Our work thus raises the question of whether consensus hierarchies which assume an unbounded number of registers truly capture synchronization power, and begins a line of research aimed at better understanding the interaction between read-write memory and the powerful synchronization operations available on modern architectures.Comment: 12 pages, 0 figure

Tortoise: Interactive System Configuration Repair

System configuration languages provide powerful abstractions that simplify managing large-scale, networked systems. Thousands of organizations now use configuration languages, such as Puppet. However, specifications written in configuration languages can have bugs and the shell remains the simplest way to debug a misconfigured system. Unfortunately, it is unsafe to use the shell to fix problems when a system configuration language is in use: a fix applied from the shell may cause the system to drift from the state specified by the configuration language. Thus, despite their advantages, configuration languages force system administrators to give up the simplicity and familiarity of the shell. This paper presents a synthesis-based technique that allows administrators to use configuration languages and the shell in harmony. Administrators can fix errors using the shell and the technique automatically repairs the higher-level specification written in the configuration language. The approach (1) produces repairs that are consistent with the fix made using the shell; (2) produces repairs that are maintainable by minimizing edits made to the original specification; (3) ranks and presents multiple repairs when relevant; and (4) supports all shells the administrator may wish to use. We implement our technique for Puppet, a widely used system configuration language, and evaluate it on a suite of benchmarks under 42 repair scenarios. The top-ranked repair is selected by humans 76% of the time and the human-equivalent repair is ranked 1.31 on average.Comment: Published version in proceedings of IEEE/ACM International Conference on Automated Software Engineering (ASE) 201

How to Elect a Leader Faster than a Tournament

The problem of electing a leader from among $n$ contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given $n$ processors, all participants must eventually return a win or lose indication, such that a single contender may win. Despite a considerable amount of work on leader election, the following question is still open: can we elect a leader in an asynchronous fault-prone system faster than just running a $\Theta(\log n)$-time tournament, against a strong adaptive adversary? In this paper, we answer this question in the affirmative, improving on a decades-old upper bound. We introduce two new algorithmic ideas to reduce the time complexity of electing a leader to $O(\log^* n)$, using $O(n^2)$ point-to-point messages. A non-trivial application of our algorithm is a new upper bound for the tight renaming problem, assigning $n$ items to the $n$ participants in expected $O(\log^2 n)$ time and $O(n^2)$ messages. We complement our results with lower bound of $\Omega(n^2)$ messages for solving these two problems, closing the question of their message complexity

Lower Bounds for Shared-Memory Leader Election Under Bounded Write Contention

This paper gives tight logarithmic lower bounds on the solo step complexity of leader election in an asynchronous shared-memory model with single-writer multi-reader (SWMR) registers, for both deterministic and randomized obstruction-free algorithms. The approach extends to lower bounds for deterministic and randomized obstruction-free algorithms using multi-writer registers under bounded write concurrency, showing a trade-off between the solo step complexity of a leader election algorithm, and the worst-case number of stalls incurred by a processor in an execution