Compositional Verification of Stigmergic Collective Systems

Abstract

Collective adaptive systems may be broadly defined as ensembles of autonomous agents, whose interaction may lead to the emergence of global features and patterns. Formal verification may provide strong guarantees about the emergence of these features, but may suffer from scalability issues caused by state space explosion. Compositional verification techniques, whereby the state space of a system is generated by combining (an abstraction of) those of its components, have shown to be a promising countermeasure to the state space explosion problem. Therefore, in this work we apply these techniques to the problem of verifying collective adaptive systems with stigmergic interaction. Specifically, we automatically encode these systems into networks of LNT processes, apply a static value analysis to prune the state space of individual agents, and then reuse compositional verification procedures provided by the CADP toolbox. We demonstrate the effectiveness of our approach by verifying a collection of representative systems. ⋆ Work partially funded by ERC consolidator grant no. 772459 D-SynMA (Distributed Synthesis: from Single to Multiple Agents).

Compositional verification of priority systems using sharp bisimulation

“…The server handles this request by calling a helper function refreshVar(M, x, i): this, in turn, updates M so that M x i,j = GREATER for every j ̸ = i. Gate request, instead, allows an agent to retrieve the value of M x i,j (lines [10][11][12][13][14][15][16][17]. What actually happens, here, is that the server simultaneously offers all the contents of M over this gate.…”

“…. one in Listing 1, lines [12][13][14], some of these actions may be further guarded by additional conditions. Thus, before getting to choose the next action to perform, we evaluate a function canProceed that tells us whether at least one of these guards can be satisfied (line 7).…”

“…First, we applied divsharp minimization to the 180 CTL problems 12 of the RERS 2019 challenge 13 . We compared the obtained LTS sizes to those obtained initially using the partial reduction algorithm presented in [32], which was applied compositionally.…”

“…We assume identifiers of agents to be in the range [0, n − 1], and that ℓ is initially set to n for every agent. As the system evolves, each agent repeatedly assigns its own id to ℓ, but only as long as ℓ > id (lines [12][13]. The repetitiveness of the agents' behaviour is implemented by the recursive call to Behavior at line 14.…”

“…A system of autonomous agents such as this one may be seen as a network of LTSs, namely one per agent plus an additional one that stores information about the timestamps. For the scope of this work, we developed a workflow [13] in the SLiVER tool 16 [14, 12] that turns a LAbS specification into an LNT program with this network structure, shown in Listing 2. Intuitively, agents in this LNT program may perform refresh actions to obtain a fresh timestamp for the stigmergy variable ℓ; stig actions to signal that they have set some stigmergic variable to a new value; 17 and request actions to compare timestamps with the sender of a stigmergy message.…”