From Geometric Semantics to Asynchronous Computability

Goubault, Éric; Mimram, Samuel; Tasson, Christine

doi:10.1007/978-3-662-48653-5_29

Cited by 2 publications

(3 citation statements)

References 30 publications

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“…Let F = G f ull , ∼ A be its N step protocol Kripke frame. As the Lemma below formalizes it, and as observed in a slightly different formal context in [11], the (N step) full information protocol is initial in the wide sub-category of Kripke frames consisting of (N step) protocols (see Figure 1) :…”

Section: Distributed Computability In Terms Of Kripke Framesmentioning

confidence: 99%

Models of fault-tolerant distributed computation via dynamic epistemic logic

Goubault,

Rajsbaum

2017

Preprint

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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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Section: Distributed Computability In Terms Of Kripke Framesmentioning

confidence: 99%

Models of fault-tolerant distributed computation via dynamic epistemic logic

Goubault,

Rajsbaum

2017

Preprint

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“…Fairly recently, an epistemic logic interpreted on simplicial complexes was proposed in [26,20,8], including exact correspondence between simplicial complexes and Kripke models. Also, in those and other works [29,33,9], the action models of [3] are used to model distributed computing tasks and algorithms, with asynchrony treated as in [6].…”

Section: Introductionmentioning

confidence: 99%

“…Also, in those and other works [29,33,9], the action models of [3] are used to model distributed computing tasks and algorithms, with asynchrony treated as in [6]. Action models, which are like Kripke models, also have counterparts that are like simplicial complexes [26,9].…”

Section: Introductionmentioning

confidence: 99%

On Two- and Three-valued Semantics for Impure Simplicial Complexes

van Ditmarsch,

Kuznets,

Randrianomentsoa

2023

Electron. Proc. Theor. Comput. Sci.

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at * Simplicial complexes are a convenient semantic primitive to reason about processes (agents) communicating with each other in synchronous and asynchronous computation. Impure simplicial complexes distinguish active processes from crashed ones, in other words, agents that are alive from agents that are dead. In order to rule out that dead agents reason about themselves and about other agents, three-valued epistemic semantics have been proposed where, in addition to the usual values true and false, the third value stands for undefined: the knowledge of dead agents is undefined and so are the propositional variables describing their local state. Other semantics for impure complexes are two-valued where a dead agent knows everything. Different choices in designing a semantics produce different three-valued semantics, and also different two-valued semantics. In this work, we categorize the available choices by discounting the bad ones, identifying the equivalent ones, and connecting the non-equivalent ones via a translation. The main result of the paper is identifying the main relevant distinction to be the number of truth values and bridging this difference by means of a novel embedding from three-into two-valued semantics. This translation also enables us to highlight quite fundamental modeling differences underpinning various two-and three-valued approaches in this area of combinatorial topology. In particular, pure complexes can be defined as those invariant under the translation.* Funded by the Austrian Science Fund (FWF) ByzDEL project (P33600).

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From Geometric Semantics to Asynchronous Computability

Cited by 2 publications

References 30 publications

Models of fault-tolerant distributed computation via dynamic epistemic logic

Models of fault-tolerant distributed computation via dynamic epistemic logic

On Two- and Three-valued Semantics for Impure Simplicial Complexes

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