A Specification Approach for Distributed Algorithms in Continuous Space-Time

Abstract

Emerging paradigms such as the Internet of Things (IoT), Cyber-Physical Systems, and Wireless Sensor Networks envision distributed computing platforms as dense deployments of interacting devices embedded within physical environments (e.g., agricultural fields, smart cities, traffic systems). To effectively engineer these systems, we must shift our focus from individual devices to the collective behaviour of the ensemble, designing distributed algorithms from a global perspective. Many of these algorithms produce a collective result—a computational field of values distributed across space and time—that converges as device density and execution speed approach infinity. Consequently, the behaviour of such algorithms can be formally captured by computational fields defined over continuous domains: deployment on a discrete network simply leads to an approximation over the ideal continuous behaviour. In this paper, we define a formal framework to capture this idea, and accordingly characterise some fundamental algorithms of collective adaptive behaviour.

Publication
Leveraging Applications of Formal Methods, Verification and Validation (ISoLA 2026)

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Roberto Casadei
Roberto Casadei
Assistant Professor in Computer Science and Engineering @ University of Bologna

My research is at the intersection of artificial collective intelligence and software engineering.