Identifiers in Registers - Describing Network Algorithms with Logic

TL;DR

This paper introduces a formal model for distributed network algorithms using register automata, linking it to an extension of first-order logic with a partial fixpoint operator, bridging automata theory and logic.

Contribution

It establishes an expressive equivalence between a class of distributed algorithms modeled by register automata and an extension of first-order logic with a partial fixpoint operator.

Findings

Model captures a broad class of synchronous network algorithms.

Shows equivalence with an extension of first-order logic on graphs.

Connects automata-based models with logical definability.

Abstract

We propose a formal model of distributed computing based on register automata that captures a broad class of synchronous network algorithms. The local memory of each process is represented by a finite-state controller and a fixed number of registers, each of which can store the unique identifier of some process in the network. To underline the naturalness of our model, we show that it has the same expressive power as a certain extension of first-order logic on graphs whose nodes are equipped with a total order. Said extension lets us define new functions on the set of nodes by means of a so-called partial fixpoint operator. In spirit, our result bears close resemblance to a classical theorem of descriptive complexity theory that characterizes the complexity class PSPACE in terms of partial fixpoint logic (a proper superclass of the logic we consider here).