2 research outputs found
Probabilistic CTL* : the deductive way
Complex probabilistic temporal behaviours need to be guaranteed in robotics and various other control domains, as well as in the context of families of randomized protocols. At its core, this entails checking infinite-state probabilistic systems with respect to quantitative properties specified in probabilistic temporal logics. Model checking methods are not directly applicable to infinite-state systems, and techniques for infinite-state probabilistic systems are limited in terms of the specifications they can handle.
This paper presents a deductive approach to the verification of countable-state systems against properties specified in probabilistic CTL ∗ , on models featuring both nondeterministic and probabilistic choices. The deductive proof system we propose lifts the classical proof system by Kesten and Pnueli to the probabilistic setting. However, the soundness arguments are completely distinct and go via the theory of martingales. Completeness results for the finite-state case and an infinite-state example illustrate the effectiveness of our approach
Synthesizing Probabilistic Invariants via Doob's Decomposition
When analyzing probabilistic computations, a powerful approach is to first
find a martingale---an expression on the program variables whose expectation
remains invariant---and then apply the optional stopping theorem in order to
infer properties at termination time. One of the main challenges, then, is to
systematically find martingales.
We propose a novel procedure to synthesize martingale expressions from an
arbitrary initial expression. Contrary to state-of-the-art approaches, we do
not rely on constraint solving. Instead, we use a symbolic construction based
on Doob's decomposition. This procedure can produce very complex martingales,
expressed in terms of conditional expectations.
We show how to automatically generate and simplify these martingales, as well
as how to apply the optional stopping theorem to infer properties at
termination time. This last step typically involves some simplification steps,
and is usually done manually in current approaches. We implement our techniques
in a prototype tool and demonstrate our process on several classical examples.
Some of them go beyond the capability of current semi-automatic approaches