FAUST 2 : Formal Abstractions of Uncountable-STate STochastic Processes

@inproceedings{Soudjani2015FAUST2,
  title={FAUST 2 : Formal Abstractions of Uncountable-STate STochastic Processes},
  author={S. Soudjani and C.J.P. Gevaerts and Alessandro Abate},
  booktitle={TACAS},
  year={2015}
}
FAUST $^{\mathsf 2}$ 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… 
Specification-Guided Verification and Abstraction Refinement of Mixed Monotone Stochastic Systems
TLDR
This article presents a procedure to compute a finite-state interval-valued Markov chain (IMC) abstraction of discrete-time, mixed monotone stochastic systems subject to affine disturbances given a rectangular partition of the state space and suggests an algorithm for performing verification against omega-regular properties in IMCs.
Safety Verification of Continuous-Space Pure Jump Markov Processes
TLDR
A formal method to abstract the process as a finite-state discrete-time Markov chain is described, which provides a-priori error bounds on the precision of the abstraction, based on the continuity properties of the stochastic kernel of the process and of its jump rate function.
\mathsf StocHy : Automated Verification and Synthesis of Stochastic Processes
TLDR
Experiments show the StocHy tool’s markedly improved performance when compared to existing abstraction-based approaches, and beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions).
Formal Verification of Stochastic Max-Plus-Linear Systems
TLDR
This work proposes to construct formal, finite abstractions of a given SMPL system first re-formulated as a discrete-time Markov process, then abstracted as a finite-state Markov Chain (MC) to probabilistically model check the obtained MC against bounded-time linear temporal specifications.
Temporal Logic Verification of Stochastic Systems Using Barrier Certificates
TLDR
This paper presents a methodology for temporal logic verification of discrete-time stochastic systems by decomposing the negation of the specification into a union of sequential reachabilities and then using barrier certificates to compute upper bounds for these reachability probabilities.
Temporal logic control of general Markov decision processes by approximate policy refinement
Dynamic Bayesian networks for formal verification of structured stochastic processes
TLDR
A dimension-dependent abstraction of a Markov process satisfying an independence assumption on the driving process noise makes the error bounds more precise than existing approaches to solve the finite-horizon probabilistic invariance problem.
Abstraction-based Synthesis for Stochastic Systems with Omega-Regular Objectives
Interval-valued Markov Chain Abstraction of Stochastic Systems using Barrier Functions
TLDR
This paper shows that bounds on the probability of transition between any two elements of the partition are found by generating stochastic barrier functions via optimization procedures in the form of Sum-of-Squares programs, and presents an algorithm for solving these optimization problems.
Dynamic Bayesian Networks as Formal Abstractions of Structured Stochastic Processes
TLDR
Together, DBN-based representations and algorithms can be significantly more efficient than explicit representations of Markov chains for abstracting and model checking structured Markov processes and makes the error bounds more precise than existing approaches.
...
...

References

SHOWING 1-10 OF 22 REFERENCES
Quantitative automata-based controller synthesis for non-autonomous stochastic hybrid systems
TLDR
The contribution shows that Markov processes that are defined over an uncountable state space and embedding non-determinism in the shape of a control structure can be sufficiently tackled with history-independent Markov policies.
Formula-free finite abstractions for linear temporal verification of stochastic hybrid systems
TLDR
The proposed approach unifies techniques for the approximate abstraction of SHS over different classes of properties by explicitly relating the error introduced by the approximation to the distance between transition kernels of abstract and concrete models, and by propagating the error in time over the horizon of the specification.
Adaptive and Sequential Gridding Procedures for the Abstraction and Verification of Stochastic Processes
TLDR
A novel adaptive and sequential gridding algorithm is presented and is expected to conform to the underlying dynamics of the model and thus to mitigate the curse of dimensionality unavoidably related to the partitioning procedure.
PRISM: A Tool for Automatic Verification of Probabilistic Systems
TLDR
This paper presents an overview of all the main features of PRISM, a probabilistic model checking tool which has already been successfully deployed in a wide range of application domains, from real-time communication protocols to biological signalling pathways.
Probabilistic Reach-Avoid Computation for Partially Degenerate Stochastic Processes
TLDR
This work shows that the probabilistic reach-avoid problem can be characterized-and thus computed-in two sequential steps: the first is a simple deterministic reachability analysis, which is then followed by a probabilism reach- avoidance problem depending on the outcome of the first step.
Finite Abstractions of Stochastic Max-Plus-Linear Systems
TLDR
This work investigates the use of finite abstractions to study the finite-horizon probabilistic invariance problem over Stochastic Max-Plus-Linear (SMPL) systems by tailoring formal abstraction techniques in the literature to generate a finite-state Markov Chain (MC), together with precise guarantees on the level of the introduced approximation.
Quantitative automata model checking of autonomous stochastic hybrid systems
TLDR
This work shows that these quantitative verification problems can be reduced to computing reachability probabilities over the product of an automaton and the DTSHS under study, and quantitatively approximated by procedures over discrete-time Markov chains.
Probabilistic invariance of mixed deterministic-stochastic dynamical systems
TLDR
The contribution shows that the probabilistic invariance problem can be separated into two parts: a deterministic reachability analysis, and a probabilistically invariant problem that depends on the outcome of the first.
A Markov reward model checker
TLDR
MRMC, a model checker for discrete-time and continuous-time Markov reward models, supports reward extensions of PCTL and CSL, and allows for the automated verification of properties concerning long-run and instantaneous rewards as well as cumulative rewards.
...
...