Models of fault-tolerant distributed computation via dynamic epistemic logic

TL;DR

This paper extends dynamic epistemic logic models of distributed computation to include knowledge about the computation model itself, especially in scenarios where processes lack input values, enhancing understanding of task solvability.

Contribution

It introduces an extension to existing logic models to incorporate knowledge about the computation environment, addressing scenarios with no process inputs.

Findings

Extended logical framework captures knowledge about the computation model.

Analyzed scenarios where processes have no input values.

Provides a formal semantics linking knowledge and task solvability.

Abstract

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.