FAUST: Formal Abstractions of Uncountable-STate STochastic Processes

FAUST is a software tool that generates formal abstractions of (possibly non-deterministic) discrete-time Markov processes (dtMP) defined over uncountable (continuous) state spaces. A dtMP model is specified in MATLAB and abstracted as a finite-state Markov chain or a Markov decision process. The abstraction procedure runs in MATLAB and employs parallel computations and fast manipulations based on vector calculus, which allows scaling beyond state-of-the-art alternatives. The abstract model is formally put in relationship with the concrete dtMP via a user-defined maximum threshold on the approximation error introduced by the abstraction procedure. FAUST allows exporting the abstract model to well-known probabilistic model checkers, such as PRISM or MRMC. Alternatively, it can handle internally the computation of PCTL properties (e.g. safety or reach-avoid) over the abstract model. FAUST allows refining the outcomes of the verification procedures over the concrete dtMP in view of the quantified and tunable error, which depends on the dtMP dynamics and on the given formula. The toolbox is available at http://sourceforge.net/projects/faust2/ 1 Models: Discrete-Time Markov Processes We consider a discrete-time Markov process (dtMP) s(k), k ∈ N ∪ {0} defined over a general state space, such as a finite-dimensional Euclidean domain [1] or a hybrid state space [2]. The model is denoted by the pair S = (S, Ts). S is a continuous (uncountable) but bounded state space, e.g. S ⊂ R, n < ∞. We denote by B(S) the associated sigma algebra and refer the reader to [2, 3] for details on measurability and topological considerations. The conditional stochastic kernel Ts : B(S)×S → [0, 1] assigns to each point s ∈ S a probability measure Ts(·|s), so that for any set A ∈ B(S), k ∈ N ∪ {0}, P(s(k + 1) ∈ A|s(k) = s) = ∫