Wait-Free Solvability of Equality Negation Tasks

We introduce a family of tasks for n processes, as a generalization of the two process equality negation task of Lo and Hadzilacos (SICOMP 2000). Each process starts the computation with a private input value taken from a finite set of possible inputs. After communicating with the other processes using immediate snapshots, the process must decide on a binary output value, 0 or 1. The specification of the task is the following: in an execution, if the set of input values is large enough, the processes should agree on the same output; if the set of inputs is small enough, the processes should disagree; and in-between these two cases, any output is allowed. Formally, this specification depends on two threshold parameters k and l, with k<l, indicating when the cardinality of the set of inputs becomes "small" or "large", respectively. We study the solvability of this task depending on those two parameters. First, we show that the task is solvable whenever k+2 <= l. For the remaining cases (l = k+1), we use various combinatorial topology techniques to obtain two impossibility results: the task is unsolvable if either k <= n/2 or n-k is odd. The remaining cases are still open

The solvability of consensus in iterated models extended with safe-consensus

The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC'09) as a weakening of the classic consensus. When there is concurrency, the consensus output can be arbitrary, not even the input of any process. They showed that safe-consensus is equivalent to consensus, in a wait-free system. We study the solvability of consensus in three shared memory iterated models extended with the power of safe-consensus black boxes. In the first model, for the $i$-th iteration, processes write to the memory, invoke safe-consensus boxes and finally they snapshot the memory. We show that in this model, any wait-free implementation of consensus requires $\binom{n}{2}$ safe-consensus black-boxes and this bound is tight. In a second iterated model, the processes write to memory, then they snapshot it and finally they invoke safe-consensus boxes. We prove that in this model, consensus cannot be implemented. In the last iterated model, processes first invoke safe-consensus, then they write to memory and finally they snapshot it. We show that this model is equivalent to the previous model and thus consensus cannot be implemented.Comment: 49 pages, A preliminar version of the main results appeared in the SIROCCO 2014 proceeding

Locality and Checkability in Wait-free Computing

22 pagesThis paper studies several notions of locality that are inherent to the specification of distributed tasks and independent of the computing environment, and investigates the ability of a shared memory wait-free system to solve tasks satisfying various forms of locality. First, we define a task to be projection-closed if every partial output π(t) for a full input s is also a valid output for the partial input π(s) and prove that projection-closed tasks are precisely those tasks that are wait-free checkable. Our second main contribution is dealing with a stronger notion of lo- cality of topological nature. A task T = (I, O, ∆) is said to be locality- preserving if and only if O is a covering complex of I, that is, each simplex s of I is mapped by ∆ to a set of simplexes of O each isomorphic to s. This topological property yields obstacles for wait-free solvability different in nature from the classical agreement impossibility results. On the other hand, locality-preserving tasks are projection-closed and therefore always wait-free checkable. We provide a classification of locality-preserving tasks in term of their computational power, by establishing a correspondence between locality-preserving tasks and subgroups of the edgepath group of a complex. Using this correspondence, we prove the existence of hierarchies of locality-preserving tasks, each one containing a universal task (induced by the universal covering complex), and at the bottom the trivial identity task

A single amino acid substitution in the novel H7N9 influenza A virus NS1 protein increases CPSF30 binding and virulence

Although an effective interferon antagonist in human and avian cells, the novel H7N9 influenza virus NS1 protein is defective at inhibiting CPSF30. An I106M substitution in H7N9 NS1 can restore CPSF30 binding together with the ability to block host gene expression. Furthermore, a recombinant virus expressing H7N9 NS1-I106M replicates to higher titers in vivo, and is subtly more virulent, than parental. Natural polymorphisms in H7N9 NS1 that enhance CPSF30 binding may be cause for concern

Strong Equivalence Relations for Iterated Models

The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS). It is known that AS and IIS are equivalent with respect to \emph{wait-free task} computability: a distributed task is solvable in AS if and only if it solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in \emph{sub-models} of AS (i.e. proper subsets of its runs) or computability of \emph{long-lived} objects, and a stronger equivalence relation is needed. In this paper, we consider \emph{adversarial} sub-models of AS and IIS specified by the sets of processes that can be \emph{correct} in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly long-lived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. %This holds whether the object is one-shot or long-lived. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS