# Statistical model checking

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.

Simulation of stochastic hybrid systems previously handled only discrete nondeterministic choices, while an action allowed to fire anywhere in a time interval gives a single state infinitely many options. The new method discretizes each action's time interval separately, learns a scheduler with Q-learning over the finite abstraction, and uses precomputed symbolic reachable states to steer simulation and prune unreachable regions in a correct-by-construction way. On the water tank benchmark the simulation reproduces the maximum reachability probabilities reported by an existing method; on a water tank variant with a low-probability underflow objective, guidance makes learning clearly faster than unguided simulation and yields a reachability probability of at least 45%.

In a Mesa implementation of the Schelling segregation model, one agent's symbolic rule for classifying neighbors is replaced by a locally served Qwen3.5 model that classifies through tool calls, while the rest of the dynamics stays fixed. Statistical model checking with MultiVeStA shows the expected ratio of happy agents rising from about 0.65 to about 1.0 within 60 steps in both variants, with point-wise t-tests finding no difference, yet the LLM version takes 8,917 seconds against about 2 seconds. The 0.8b and 2b models show semantic errors, wrong tool-call counts or stuck generation in unit-style checks, while 4b and 9b pass all of them.

In a Mesa implementation of the Schelling segregation model, one agent's symbolic rule for classifying neighbors is replaced by a locally served Qwen3.5 model that classifies through tool calls, while the rest of the dynamics stays fixed. Statistical model checking with MultiVeStA shows the expected ratio of happy agents rising from about 0.65 to about 1.0 within 60 steps in both variants, with point-wise t-tests finding no difference, yet the LLM version takes 8,917 seconds against about 2 seconds. The 0.8b and 2b models show semantic errors, wrong tool-call counts or stuck generation in unit-style checks, while 4b and 9b pass all of them.