arXiv subjects

Sergio Rajsbaum

Publications and source records attributed to Sergio Rajsbaum.

32 records · Page 2Linked to original sources

arXiv2020

Relaxed Queues and Stacks from Read/Write Operations

Considering asynchronous shared memory systems in which any number of processes may crash, this work identifies and formally defines relaxations of queues and stacks that can be non-blocking or wait-free while being implemented using only read/write operations. Set-linearizability and Interval-linearizability are used to specify the relaxations formally, and precisely identify the subset of executions which preserve the original sequential behavior. The relaxations allow for an item to be returned more than once by different operations, but only in case of concurrency; we call such a property multiplicity. The stack implementation is wait-free, while the queue implementation is non-blocking. Interval-linearizability is used to describe a queue with multiplicity, with the additional relaxation that a dequeue operation can return weak-empty, which means that the queue might be empty. We present a read/write wait-free interval-linearizable algorithm of a concurrent queue. As far as we know, this work is the first that provides formalizations of the notions of multiplicity and weak-emptiness, which can be implemented on top of read/write registers only.

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arXiv2020

A Topological Perspective on Distributed Network Algorithms

More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also be useful for analyzing distributed algorithms in failure-free networks of arbitrary structure. To illustrate this, we analyze consensus, set-agreement, and approximate agreement in networks, and derive lower bounds for these problems under classical computational settings, such as the LOCAL model and dynamic networks.

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arXiv2020

$t$-Resilient $k$-Immediate Snapshot and its Relation with Agreement Problems

An immediate snapshot object is a high level communication object, built on top of a read/write distributed system in which all except one processes may crash. It allows a process to write a value and obtain a set of values that represent a snapshot of the values written to the object, occurring immediately after the write step. Considering an $n$-process model in which up to $t$ processes may crash, this paper introduces first the $k$-resilient immediate snapshot object, which is a natural generalization of the basic immediate snapshot (which corresponds to the case $k=t=n-1$). In addition to the set containment properties of the basic immediate snapshot, a $k$-resilient immediate snapshot object requires that each set returned to a process contains at least $(n-k)$ pairs. The paper first shows that, for $k,t<n-1$, $k$-resilient immediate snapshot is impossible in asynchronous read/write systems. %Then the paper investigates the space of objects that %are impossible to solve in $n$-process $t$-crash read/write systems. Then the paper investigates a model of computation where the processes communicate with each other by accessing $k$-immediate snapshot objects, and shows that this model is stronger than the $t$-crash model. Considering the space of $x$-set agreement problems (which are impossible to solve in systems such that $x\leq t$), the paper shows then that $x$-set agreement can be solved in read/write systems enriched with $k$-immediate snapshot objects for $x=\max(1,t+k-(n-2))$. It also shows that, in these systems, $k$-resilient immediate snapshot and consensus are equivalent when $1\leq t<n/2$ and $t\leq k\leq (n-1)-t$. Hence, %thanks to the problem map it provides, the paper establishes strong relations linking fundamental distributed computing objects (one related to communication, the other to agreement), which are impossible to solve in pure read/write systems.

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arXiv2020

A Distributed Computing Perspective of Unconditionally Secure Information Transmission in Russian Cards Problems

The problem of $A$ privately transmitting information to $B$ by a public announcement overheard by an eavesdropper $C$ is considered. To do so by a deterministic protocol, their inputs must be correlated. Dependent inputs are represented using a deck of cards. There is a publicly known signature $(a,b,c)$, where $n = a + b + c + r$, and $A$ gets $a$ cards, $B$ gets $b$ cards, and $C$ gets $c$ cards, out of the deck of $n$ cards. Using a deterministic protocol, $A$ decides its announcement based on her hand. Using techniques from coding theory, Johnson graphs, and additive number theory, a novel perspective inspired by distributed computing theory is provided, to analyze the amount of information that $A$ needs to send, while preventing $C$ from learning a single card of her hand. In one extreme, the generalized Russian cards problem, $B$ wants to learn all of $A$'s cards, and in the other, $B$ wishes to learn something about $A$'s hand.

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arXiv2020

Knowledge and simplicial complexes

Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and also dynamics in the shape of simplicial action models. We give a survey on how to interpret all such notions on simplicial complexes, building upon the foundations laid in prior work by Goubault and others.

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arXiv2019

A dynamic epistemic logic analysis of the equality negation task

In this paper we study the solvability of the equality negation task in a simple wait-free model where processes communicate by reading and writing shared variables or exchanging messages. In this task, two processes start with a private input value in the set {0,1,2}, and after communicating, each one must decide a binary output value, so that the outputs of the processes are the same if and only if the input values of the processes are different. This task is already known to be unsolvable; our goal here is to prove this result using the dynamic epistemic logic (DEL) approach introduced by Goubault, Ledent and Rajsbaum in GandALF 2018. We show that in fact, there is no epistemic logic formula that explains why the task is unsolvable. We fix this issue by extending the language of our DEL framework, which allows us to construct such a formula, and discuss its utility.

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arXiv2018

Mastering Concurrent Computing Through Sequential Thinking: A Half-century Evolution

Concurrency, the art of doing many things at the same time is slowly becoming a science. It is very difficult to master, yet it arises all over modern computing systems, both when the communication medium is shared memory and when it is by message passing. Concurrent programming is hard because it requires to cope with many possible, unpredictable behaviors of communicating processes interacting with each other. Right from the start in the 1960s, the main way of dealing with concurrency has been by reduction to sequential reasoning. We trace this history, and illustrate it through several examples, from early ideas based on mutual exclusion, passing through consensus and concurrent objects, until today ledgers and blockchains. We conclude with a discussion on the limits that this approach encounters, related to fault-tolerance, performance, and inherently concurrent problems.

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arXiv2018

A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

The usual epistemic model S5n for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.

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arXiv2017

A characterization of colorless anonymous $t$-resilient task computability

A task is a distributed problem for $n$ processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input or output value of another process. Colorless tasks are well studied in the non-anonymous shared-memory model where each process has a distinct identifier that can be used to access a single-writer/multi-reader shared register. In the anonymous case, where processes have no identifiers and communicate through multi-writer/multi-reader registers, there is a recent topological characterization of the colorless tasks that are solvable when any number of asynchronous processes may crash. In this paper we study the case where at most $t$ processes may crash, where $1 \le t < n$. We prove that a colorless task is $t$-resilient solvable non-anonymously if and only if it is $t$-resilient solvable anonymously. This implies a complete characterization of colorless anonymous t-resilient asynchronous task computability.

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arXiv2017

Models of fault-tolerant distributed computation via dynamic epistemic logic

The computability power of a distributed computing model is determined by the communication media available to the processes, the timing assumptions about processes and communication, and the nature of failures that processes can suffer. In a companion paper we showed how dynamic epistemic logic can be used to give a formal semantics to a given distributed computing model, to capture precisely the knowledge needed to solve a distributed task, such as consensus. Furthermore, by moving to a dual model of epistemic logic defined by simplicial complexes, topological invariants are exposed, which determine task solvability. In this paper we show how to extend the setting above to include in the knowledge of the processes, knowledge about the model of computation itself. The extension describes the knowledge processes gain about the current execution, in problems where processes have no input values at all.

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arXiv2017

A simplicial complex model of dynamic epistemic logic for fault-tolerant distributed computing

The usual epistemic S5 model for multi-agent systems is a Kripke graph, whose edges are labeled with the agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in the Kripke graph, by using as a model its dual, a chromatic simplicial complex. For each state of the Kripke model there is a facet in the complex, with one vertex per agent. If an edge (u,v) is labeled with a set of agents S, the facets corresponding to u and v intersect in a simplex consisting of one vertex for each agent of S. Then we use dynamic epistemic logic to study how the simplicial complex epistemic model changes after the agents communicate with each other. We show that there are topological invariants preserved from the initial epistemic complex to the epistemic complex after an action model is applied, that depend on how reliable the communication is. In turn these topological properties determine the knowledge that the agents may gain after the communication happens.

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arXiv2015

The read/write protocol complex is collapsible

The celebrated \emph{asynchronous computability theorem} provides a characterization of the class of decision tasks that can be solved in a wait-free manner by asynchronous processes that communicate by writing and taking atomic snapshots of a shared memory. Several variations of the model have been proposed (immediate snapshots and iterated immediate snapshots), all equivalent for wait-free solution of decision tasks, in spite of the fact that the protocol complexes that arise from the different models are structurally distinct. The topological and combinatorial properties of these snapshot protocol complexes have been studied in detail, providing explanations for why the asynchronous computability theorem holds in all the models. In reality concurrent systems do not provide processes with snapshot operations. Instead, snapshots are implemented (by a wait-free protocol) using operations that write and read individual shared memory locations. Thus, read/write protocols are also computationally equivalent to snapshot protocols. However, the structure of the read/write protocol complex has not been studied. In this paper we show that the read/write iterated protocol complex is collapsible (and hence contractible). Furthermore, we show that a distributed protocol that wait-free implements atomic snapshots in effect is performing the collapses.

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arXiv2015

Specifying Concurrent Problems: Beyond Linearizability

Tasks and objects are two predominant ways of specifying distributed problems. A task is specified by an input/output relation, defining for each set of processes that may run concurrently, and each assignment of inputs to the processes in the set, the valid outputs of the processes. An object is specified by an automaton describing the outputs the object may produce when it is accessed sequentially. Thus, tasks explicitly state what may happen only when sets of processes run concurrently, while objects only specify what happens when processes access the object sequentially. Each one requires its own implementation notion, to tell when an execution satisfies the specification. For objects linearizability is commonly used, a very elegant and useful consistency condition. For tasks implementation notions are less explored. The paper introduces the notion of interval-sequential object. The corresponding implementation notion of interval-linearizability generalizes linearizability, and allows to associate states along the interval of execution of an operation. Interval-linearizability allows to specify any task, however, there are sequential one-shot objects that cannot be expressed as tasks, under the simplest interpretation of a task. It also shows that a natural extension of the notion of a task is expressive enough to specify any interval-sequential object.

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arXiv2011

An Equivariance Theorem with Applications to Renaming (Preliminary Version)

In the renaming problem, each process in a distributed system is issued a unique name from a large name space, and the processes must coordinate with one another to choose unique names from a much smaller name space. We show that lower bounds on the solvability of renaming in an asynchronous distributed system can be formulated as a purely topological question about the existence of an equivariant chain map from a topological disk to a topological annulus. Proving the non-existence of such a map implies the non-existence of a distributed renaming algorithm in several related models of computation.

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