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Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov…
Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation…
Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
We present a control framework for robot-assisted dressing that augments low-level hazard response with runtime monitoring and formal verification. A parametric discrete-time Markov chain (pDTMC) models the dressing process, while Bayesian…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
The importance of preventing microarchitectural timing side channels in security-critical applications has surged in recent years. Constant-time programming has emerged as a best-practice technique for preventing the leakage of secret…
Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
Model checking is a powerful technique for software verification. However, the approach notably suffers from the infamous state space explosion problem. To tackle this, in this paper, we introduce a novel symbolic method for encoding Petri…
Propositional Projection Temporal Logic (PPTL) is a useful formalism for reasoning about period of time in hardware and software systems and can handle both sequential and parallel compositions. In this paper, based on discrete time Markov…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
We present a compositional model checking algorithm for Markov decision processes, in which they are composed in the categorical graphical language of string diagrams. The algorithm computes optimal expected rewards. Our theoretical…
In this paper, we study the problem of model-checking quantum pushdown systems from a computational complexity point of view. We arrive at the following equally important, interesting new results: We first extend the notions of the {\it…
The IC3 algorithm represents the state-of-the-art (SOTA) hardware model checking technique, owing to its robust performance and scalability. A significant body of research has focused on enhancing the solving efficiency of the IC3…
Probabilistic model checkers like PRISM only check probabilistic systems of a fixed size. To guarantee the desired properties for an arbitrary size, mathematical analysis is necessary. We show for two case studies how this can be done in…
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
Verifying the behaviors of autonomous systems with learned perception components is a challenging problem due to the complexity of the perception and the uncertainty of operating environments. Probabilistic model checking is a powerful tool…
A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo…