Using Statistical Model Checking for Measuring Systems

Abstract

Abstract. State spaces represent the way a system evolves through its different possible executions. Automatic verification techniques are used to check whether the system satisfies certain properties, expressed using automata or logic-based formalisms. This provides a Boolean indication of the system's fitness. It is sometimes desirable to obtain other indications, measuring e.g., duration, energy or probability. Certain measurements are inherently harder than others. This can be explained by appealing to the difference in complexity of checking CTL and LTL properties. While the former can be done in time linear in the size of the property, the latter is PSPACE in the size of the property; hence practical algorithms take exponential time. While the CTL-type of properties measure specifications that are based on adjacency of states (up to a fixpoint calculation), LTL properties have the flavor of expecting some multiple complicated requirements from each execution sequence. In order to quickly measure LTL-style properties from a structure, we use a form of statistical model checking; we exploit the fact that LTL-style properties on a path behave like CTL-style properties on a structure. We then use CTL-based measuring on paths, and generalize the measurement results to the full structure using optimal Monte Carlo estimation techniques. To experimentally validate our framework, we present measurements for a flocking model of bird-like agents.

Attacking the V: On the Resiliency of Adaptive-Horizon MPC

“…We assume that the attack lasts for a limited amount of time, after which the controller attempts to bring the system back into the good set of states. When there is no attack, the system behavior is the one given by equation (6). Note that there can be many different criteria for evaluating the success of an attack, but in our experiments, the controller is declared the winner if it can bring the flock to V-formation.…”

“…The particular SMC procedure we use is described in [6] and based on an additive or absolute-error (ε, δ)-Monte-Carloapproximation scheme. This technique requires running N i.i.d.…”

Distributed adaptive-neighborhood control for stochastic reachability in multi-agent systems

“…Since the exact solution to this stochastic reachability problem is intractable (infinite/continuous state and action spaces), we solve it approximately using statistical model checking (SMC). In particular, as the probability estimate of reaching a V-formation under our algorithm is relatively high, we can safely employ the additive error (ε, δ)-Monte-Carlo-approximation scheme from [4]. This requires L i.i.d.…”

“…(t) ← nfy; // Initially no bird has a fixed solution4 while ¬Fixed(a(t)) do // while not all birds have a fixed solution ← {j | 1 j B ∧ ¬Fixed(aj(t))}; ← Neighbors(i, k); // Find k nearest neighbors of i9 ∆i ← J(sN i )/(m−t); sN i ,sN i , a h i N i , Ji) ← LocalAMPC(M, sN i , aN i , ∆i, hmax, β); 11endfor * ← arg min i∈R Ji; // Find the bird with the best solution13 forall b ∈ Neighbors(i * , k) // Fix i * 's neighbors solution14 do b (t) ← a h i N i * [b]; // a h i b (t)is the solution for bird b ) ← first(a(t)); s ← s; // First action and next state19 if t−1 − J( s) > ∆ then20 t ← J( s); t ← t+1; // Proceed to the next level 21 end 22…”

Compositional, Approximate, and Quantitative Reasoning for Medical Cyber-Physical Systems with Application to Patient-Specific Cardiac Dynamics and Devices

“…If a point violates the property, then by how much does it violate it? Quantitative reasoning [2,10,11] can be seen as lifting the model checking problem from a boolean setting to one in which the results are interpreted over a metric space.…”