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Monitoring Spatially Distributed Cyber-Physical Systems with Alternating Finite Automata

Anand Balakrishnan, Sheryl Paul, Simone Silvetti, Laura Nenzi, Jyotirmoy V. Deshmukh

TL;DR

This paper proposes a novel construction of (weighted) alternating finite automata from STREL specifications that efficiently encodes these semantics and demonstrates how this automaton semantics can be used to perform both, offline and online monitoring for STREL specifications using a simulated drone swarm environment.

Abstract

Modern cyber-physical systems (CPS) can consist of various networked components and agents interacting and communicating with each other. In the context of spatially distributed CPS, these connections can be dynamically dependent on the spatial configuration of the various components and agents. In these settings, robust monitoring of the distributed components is vital to ensuring complex behaviors are achieved, and safety properties are maintained. To this end, we look at defining the automaton semantics for the Spatio-Temporal Reach and Escape Logic (STREL), a formal logic designed to express and monitor spatio-temporal requirements over mobile, spatially distributed CPS. Specifically, STREL reasons about spatio-temporal behavior over dynamic weighted graphs. While STREL is endowed with well defined qualitative and quantitative semantics, in this paper, we propose a novel construction of (weighted) alternating finite automata from STREL specifications that efficiently encodes these semantics. Moreover, we demonstrate how this automaton semantics can be used to perform both, offline and online monitoring for STREL specifications using a simulated drone swarm environment.

Monitoring Spatially Distributed Cyber-Physical Systems with Alternating Finite Automata

TL;DR

This paper proposes a novel construction of (weighted) alternating finite automata from STREL specifications that efficiently encodes these semantics and demonstrates how this automaton semantics can be used to perform both, offline and online monitoring for STREL specifications using a simulated drone swarm environment.

Abstract

Modern cyber-physical systems (CPS) can consist of various networked components and agents interacting and communicating with each other. In the context of spatially distributed CPS, these connections can be dynamically dependent on the spatial configuration of the various components and agents. In these settings, robust monitoring of the distributed components is vital to ensuring complex behaviors are achieved, and safety properties are maintained. To this end, we look at defining the automaton semantics for the Spatio-Temporal Reach and Escape Logic (STREL), a formal logic designed to express and monitor spatio-temporal requirements over mobile, spatially distributed CPS. Specifically, STREL reasons about spatio-temporal behavior over dynamic weighted graphs. While STREL is endowed with well defined qualitative and quantitative semantics, in this paper, we propose a novel construction of (weighted) alternating finite automata from STREL specifications that efficiently encodes these semantics. Moreover, we demonstrate how this automaton semantics can be used to perform both, offline and online monitoring for STREL specifications using a simulated drone swarm environment.

Paper Structure

This paper contains 22 sections, 6 theorems, 15 equations, 2 figures, 1 table.

Key Result

lemma 1

For any discrete-time STREL specification, $\varphi$, there exists a corresponding SpLTL specification $\varphi'$ such that

Figures (2)

  • Figure 1: A spatially distributed system of drones coordinating with each other to "flock" towards a common goal. The drones can have requirements to maintain communications with ground stations (blue circles) either directly or through a flock member.
  • Figure 2: Experimental setup indicating different maps with varying number of obstacles, obstacle densities and number of agents. Communication radii of ground stations are indicated by the blue circles.

Theorems & Definitions (17)

  • definition 1: Semiring kuich1986semiringsgolan1999semirings
  • definition 2: De Morgan Algebras cignoli1983dualities
  • definition 3: Distance Domain
  • definition 4: Spatial Model nenzi2022logic
  • definition 5: Paths in $\mathcal{S}$
  • definition 6: Distance functions and Distance over paths
  • definition 7: $K$-Labeled Trace
  • definition 8: Alternating Automata vardi1996automatatheoretic
  • lemma 1
  • theorem 1: Linear-sized SpLTL automata
  • ...and 7 more