arXiv subjects

Sergio Rajsbaum

Publications and source records attributed to Sergio Rajsbaum.

At least 19 recordsLinked to original sources

arXiv2026

Consensus with Stochastic Broadcast

We study binary consensus in the \emph{stochastic broadcast model}, which assumes $n\geq 2$ processes communicating synchronously by message broadcasts. At each round, every process broadcasts a message to all the other processes. Each broadcast succeeds independently with some probability $p\in[0,1]$. If a broadcast succeeds, all processes receive the message, and if it fails, no process receives the message. The sender does not know whether its broadcast was successful or not. In this model, consensus is not solvable; the objective is to design, for a given number of rounds $r$, consensus algorithms that terminate in $r$ rounds, minimizing the probability of error disagreement. This problem has been studied in depth for 2 processes [DISC 2025]. We extend the study to $n> 2$.

cs.DC↗

arXiv2026

Solving Approximate Agreement on continuous and discrete spaces

We consider $n$ asynchronous processes prone to crashes, communicating via shared read-write registers, and study the wait-free solvability of approximate agreement: given inputs, processes must output values that are close to each other, and satisfy a validity property. At the very least, if inputs are identical, all outputs must equal that input. The problem has been studied for various input spaces: continuous, discrete, one-dimensional or multidimensional. For metric spaces, validity requires outputs to lie in the convex hull of the inputs. For graphs, and more generally simplicial complexes, several conditions exist. We focus on simplex validity: if inputs span a simplex $\sigma$, then outputs are in $\sigma$. Agreement requires that outputs span a simplex. Solvability depends on the input space, validity condition, and number of processes. For example, the problem is solvable for all $n$ in the plane, but only for $n \leq 2$ when removing a point. For a graph, solvability for $n=2$ holds iff the graph is connected, but $n\geq 3$ requires acyclicity. In the continuous setting, we consider CUB spaces: a broad class of metric spaces admitting a unique convexity definition, subsuming classical $\epsilon$-agreement on $[0,1]$ and $m$-dimensional approximate agreement. Our results show that $\epsilon$-agreement is solvable in every CUB space. In the discrete case, we prove that simplex agreement on a simplicial complex $\mathcal{C}$ is solvable for $n+1$ processes iff $\mathcal{C}$ is $(n-1)$-connected. We discuss several consequences, including a proof of a conjecture by Ledent.

cs.DC↗

arXiv2026

An Epistemic Analysis of Random Coordinated Attack

The coordinated attack problem models the challenge of coordinating a joint action within a bounded time by communicating over unreliable links. It was the first distributed computing problem proven unsolvable. Its analysis also revealed the importance of common knowledge, a central concept in epistemic logic. However, the randomized version of coordinated attack, which is solvable, has not, to the best of our knowledge, been studied through the lens of probabilistic epistemic logic, where processes generate randomness by flipping coins. We present an epistemic logic framework for studying randomized algorithms that execute for a bounded number of rounds. The framework applies to coordinated attack, approximate agreement, and consensus, and supports dynamic graph models: synchronous systems in which reliable processes execute a bounded number of rounds while an adversary determines which messages are lost. Our approach combines techniques from the logical characterization of dynamic networks and task solvability with ideas from probabilistic dynamic epistemic logic. It is inspired by the operational model of Varghese and Lynch for randomized coordinated attack. More broadly, the resulting notion of probabilistic epistemic task solvability provides a foundation for the epistemic study of randomized distributed computation. Using this framework, we analyze the Varghese-Lynch algorithm from a knowledge-theoretic perspective, providing a formal treatment of the algorithm and its lower bound. As a byproduct, we strengthen the lower bound and show it is tight. The proof relies on indistinguishability arguments, demonstrating that reasoning about knowledge remains essential in the probabilistic setting. We also formalize the notion of information level introduced by Varghese and Lynch, showing that it corresponds to a specific epistemic formula.

cs.DC↗

arXiv2026

Lattice Aggregation in Distributed Verification under Crash and Byzantine Failures

We introduce c-Lattice Aggregation, a fault-tolerant reconstruction problem for distributed verification under crash and Byzantine failures. In our setting, n asynchronous processes supervise a concurrent execution I: each process holds a local sample, and must collaboratively reconstruct I from partial, potentially overlapping observations. A protocol solves c-Lattice Aggregation if at least c correct processes output the complete execution I, while all correct outputs are comparable and bounded by I. This strengthens Lattice Agreement [Attiya, Herlihy and Rachman, 1995] and Byzantine Lattice Agreement [Di Luna et al., 2020; Zheng and Garg, 2020]. We parameterize inputs by a redundancy parameter x -- every element of I appears in at least x initial samples -- and establish tight feasibility thresholds. Under crash failures with at most t faulty processes, Lattice Aggregation is solvable if and only if x >= t + 1. Under Byzantine failures with t < n/3, c-Lattice Aggregation is solvable if and only if x >= 2t + c. All bounds are tight: we present matching algorithms based on SCD-broadcast [Imbs et al., 2018; Khanchandani and Wattenhofer, 2024] and indistinguishability-based lower bounds. Finally, we define globally dependent languages -- those for which no partial view can certify correctness, including consensus, linearizability, k-set agreement, and leader election -- and prove that soundness of any monitoring system is achievable if and only if c-Lattice Aggregation is solved, yielding the first complete characterization of fault-tolerant verification under Byzantine failures.

cs.DC↗

arXiv2026

Distributed Knowledge in Simplicial Models

The usual semantics of multi-agent epistemic logic is based on Kripke models, defined in terms of binary relations on a set of possible worlds. Recently, there has been a growing interest in using simplicial complexes rather than graphs, as models for multi-agent epistemic logic. This approach uses agents' views as the fundamental object instead of worlds. A set of views by different agents about a world forms a simplex, and a set of simplexes defines a simplicial complex, that can serve as a model for multi-agent epistemic logic. This new approach reveals topological information that is implicit in Kripke models, because the binary indistinguishability relations are more clearly seen as n-ary relations in the simplicial complex. This paper, written for an economics audience, introduces simplicial models to non-experts and connects distributed computing, epistemic logic and topology. Our focus is on distributed knowledge and its fixed point, common distributed knowledge. These concepts arise when considering the knowledge that a group of agents would acquire, if they could communicate their local knowledge perfectly. While common knowledge has been shown to be related to consensus, we illustrate how distributed knowledge is related to a task weaker to consensus, called majority consensus. We describe three models of communication, some well-known (immediate snapshot), and others less studied (related to broadcast and test-and-set). When majority consensus is solvable, we describe the distributed knowledge that is used to solve it. When it is not solvable, we present a logical obstruction, a formula that should always be known according to the task specification, but which the players cannot know.

cs.LO↗

arXiv2025

A categorical and logical framework for iterated protocols

In this article, we show that the now classical protocol complex approach to distributed task solvability of Herlihy et al. can be understood in standard categorical terms. First, protocol complexes are functors, from chromatic (semi-) simplicial sets to chromatic simplicial sets, that naturally give rise to algebras. These algebras describe the next state operator for the corresponding distributed systems. This is constructed for semi-synchronous distributed systems with general patterns of communication for which we show that these functors are always Yoneda extensions of simpler functors, implying a number of interesting properties. Furthermore, for these protocol complex functors, we prove the existence of a free algebra on any initial chromatic simplicial complex, modeling iterated protocol complexes. Under this categorical formalization, protocol complexes are seen as transition systems, where states are structured as chromatic simplicial sets. We exploit the epistemic interpretation of chromatic simplicial sets and the underlying transition system (or algebra) structure to introduce a temporal-epistemic logic and its semantics on all free algebras on chromatic simplicial sets. We end up by giving hints on how to extend this framework to more general dynamic network graphs and state-dependent protocols, and give example in fault-tolerant distributed systems and mobile robotics.

cs.LO↗

arXiv2025

The Smart Contract Model

Many of the problems that arise in the context of blockchains and decentralized finance can be seen as variations on classical problems of distributed computing. The smart contract model proposed here is intended to capture both the similarities and the differences between classical and blockchain-based models of distributed computing. The focus is on cross-chain protocols in which a collection of parties, some honest and some perhaps not, interact through trusted smart contracts residing on multiple, independent ledgers. While cross-chain protocols are capable of general computations, they are primarily used to track ownership of assets such as cryptocurrencies or other valuable data. For this reason, the smart contract model differs in some essential ways from familiar models of distributed and concurrent computing. Because parties are potentially Byzantine, tasks to be solved are formulated using elementary game-theoretic notions, taking into account the utility to each party of each possible outcome. As in the classical model, the parties provide task inputs and agree on a desired sequence of proposed asset transfers. Unlike the classical model, the contracts, not the parties, determine task outputs in the form of executed asset transfers, since they alone have the power to control ownership.

cs.DC↗

arXiv2024

A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology

To the best of our knowledge, a complete characterization of the domains that escape the famous Arrow's impossibility theorem remains an open question. We believe that different ways of proving Arrovian theorems illuminate this problem. This paper presents a new combinatorial topology proof of Arrow's theorem. In PODC 2022, Rajsbaum and Raventós-Pujol proved this theorem using a combinatorial topology approach. This approach uses simplicial complexes to represent the sets of profiles of preferences and that of single preferences. These complexes grow in dimension with the number of alternatives. This makes it difficult to think about the geometry of Arrow's theorem when there are (any) finite number of voters and alternatives. Rajsbaum and Raventós-Pujol (2022) use their combinatorial topology approach only for the base case of two voters and three alternatives and then proceed by induction to prove the general version. The problem with this strategy is that it is unclear how to study domain restrictions in the general case by focusing on the base case and then using induction. Instead, the present article uses the two-dimensional structure of the high-dimensional simplicial complexes (formally, the $2$$\unicode{x2013}$skeleton), yielding a new combinatorial topology proof of this theorem. Moreover, we do not assume the unrestricted domain, but a domain restriction that we call the class of polarization and diversity over triples, which includes the unrestricted domain. By doing so, we obtain a new generalization of Arrow's theorem. This shows that the combinatorial topology approach can be used to study domain restrictions in high dimensions through the $2$$\unicode{x2013}$skeleton.

econ.TH↗

arXiv2023

Simplicial Models for the Epistemic Logic of Faulty Agents

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models were always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers, with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.

cs.LO↗

arXiv2023

The Computational Power of Distributed Shared-Memory Models with Bounded-Size Registers

The celebrated Asynchronous Computability Theorem of Herlihy and Shavit (STOC 1993 and STOC 1994) provided a topological characterization of the tasks that are solvable in a distributed system where processes are communicating by writing and reading shared registers, and where any number of processes can fail by crashing. However, this characterization assumes the use of full-information protocols, that is, protocols in which each time any of the processes writes in the shared memory, it communicates everything it learned since the beginning of the execution. Thus, the characterization implicitly assumes that each register in the shared memory is of unbounded size. Whether unbounded size registers are unavoidable for the model of computation to be universal is the central question studied in this paper. Specifically, is any task that is solvable using unbounded registers solvable using registers of bounded size? More generally, when at most $t$ processes can crash, is the model with bounded size registers universal? These are the questions answered in this paper.

cs.DC↗

arXiv2023

One Step Forward, One Step Back: FLP-Style Proofs and the Round-Reduction Technique for Colorless Tasks

The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the essence of the seminal round-reduction proof establishing a lower bound on the number of rounds for 3-coloring a cycle (Linial, 1992), and going by backward induction. Second, we consider FLP-style proofs, aiming at capturing the essence of the seminal consensus impossibility proof (Fischer, Lynch, and Paterson, 1985) and using forward induction. We show that despite their very different natures, these two forms of proof are tightly connected. In particular, we show that for every colorless task $Π$, if there is a round-reduction proof establishing the impossibility of solving $Π$ using wait-free colorless algorithms, then there is an FLP-style proof establishing the same impossibility. For 1-dimensional colorless tasks (for an arbitrary number $n\geq 2$ of processes), we prove that the two proof techniques have exactly the same power, and more importantly, both are complete: if a 1-dimensional colorless task is not wait-free solvable by $n\geq 2$ processes, then the impossibility can be proved by both proof techniques. Moreover, a round-reduction proof can be automatically derived, and an FLP-style proof can be automatically generated from it. Finally, we illustrate the use of these two techniques by establishing the impossibility of solving any colorless covering task of arbitrary dimension by wait-free algorithms.

cs.DC↗

arXiv2023

Semi-simplicial Set Models for Distributed Knowledge

In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. For that purpose, we generalize beyond simplicial complexes and consider instead simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called "pseudo-models". We identify various interesting sub-classes of these models, encompassing all previously studied variants of simplicial models; and give a sound and complete axiomatization for each of them.

cs.LO↗

arXiv2022

A Speedup Theorem for Asynchronous Computation with Applications to Consensus and Approximate Agreement

We study two fundamental problems of distributed computing, consensus and approximate agreement, through a novel approach for proving lower bounds and impossibility results, that we call the asynchronous speedup theorem. For a given $n$-process task $Π$ and a given computational model $M$, we define a new task, called the closure of $Π$ with respect to $M$. The asynchronous speedup theorem states that if a task $Π$ is solvable in $t\geq 1$ rounds in $M$, then its closure w.r.t. $M$ is solvable in $t-1$ rounds in $M$. We prove this theorem for iterated models, as long as the model allows solo executions. We illustrate the power of our asynchronous speedup theorem by providing a new proof of the wait-free impossibility of consensus using read/write registers, and a new proof of the wait-free impossibility of solving consensus using registers and test\&set objects for $n>2$. The proof is merely by showing that, in each case, the closure of consensus (w.r.t. the corresponding model) is consensus itself. Our main application is the study of the power of additional objects, namely test\&set and binary consensus, for wait-free solving approximate agreement faster. By analyzing the closure of approximate agreement w.r.t. each of the two models, we show that while these objects are more powerful than read/write registers from the computability perspective, they are not more powerful as far as helping solving approximate agreement faster is concerned.

cs.DC↗

arXiv2022

A Simplicial Model for $KB4_n$: Epistemic Logic with Agents that May Die

The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work (Information and Computation, 2021). Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such models correspond to the epistemic logic KB4 . Impure simplicial models arise in situations where two possible worlds may not have the same set of agents. We illustrate it with distributed computing examples of synchronous systems where processes may crash.

cs.LO↗

arXiv2022

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 iterated model, for the $i$-th iteration, 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 a second 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. In the last iterated model, 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.

cs.DC↗

arXiv2021

Continuous Tasks and the Chromatic Simplicial Approximation Theorem

The celebrated 1999 Asynchronous Computability Theorem (ACT) of Herlihy and Shavit characterized the distributed tasks that are wait-free solvable, and thus uncovered a deep connection with algebraic topology. We present a novel interpretation of this theorem, through the notion of continuous task, defined by an input/output specification that is a continuous function. To do so, we introduce a chromatic version of a foundational result for algebraic topology: the simplicial approximation theorem. In addition to providing a different proof of the ACT, the notion of continuous task seems interesting in itself. Indeed, besides the fact that certain distributed problems are naturally specified by continuous functions, continuous tasks have an expressive power that also allows to specify the density of desired outputs for each combination of possible inputs,for example.

cs.DC↗

arXiv2021

Locally Solvable Tasks and the Limitations of Valency Arguments

An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical protocol for consensus is considered, together with future valencies of possible extensions. This proof strategy has been used in numerous situations related to consensus, leading one to wonder why it has not been used in impossibility results of two other well-known tasks: set agreement and renaming. This paper provides an explanation of why impossibility proofs of these tasks have been of a global nature. It shows that a protocol can always solve such tasks locally, in the following sense. Given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification. This result is shown for both set agreement and renaming, implying that there are no local impossibility proofs for these tasks.

cs.DC↗

arXiv2021

Leader Election in Arbitrarily Connected Networks with Process Crashes and Weak Channel Reliability

A channel from a process p to a process q satisfies the ADD property if there are constants K and D, unknown to the processes, such that in any sequence of K consecutive messages sent by p to q, at least one of them is delivered to q at most D time units after it has been sent. This paper studies implementations of an eventual leader, namely, an Ω failure detector, in an arbitrarily connected network of eventual ADD channels, where processes may fail by crashing. It first presents an algorithm that assumes that processes initially know n, the total number of processes, sending messages of size O( log n). Then, it presents a second algorithm that does not assume the processes know n. Eventually the size of the messages sent by this algorithm is also O( log n). These are the first implementations of leader election in the ADD model. In this model, only eventually perfect failure detectors were considered, sending messages of size O(n log n).

cs.DC↗