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

Reducción de orden parcial en model checking probabilista simbólico

Tesis (Lic. en Ciencias de la Computación)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2010.El problema fundamental de los model checkers es la explosión exponencial del espacio de estados que se produce al agregar nuevas componentes o variables. El problema se exacerba en los model checkers probabilistas dado que no sólo requiere una búsqueda exhaustiva del espacio de estado, sino cálculos numéricos cuya cantidad de variables y (des)igualdades depende directamente de la cantidad de estados y transiciones. En este trabajo presentamos la implementación de la técnica de orden parcial en un model checker probabilista simbólico. La noción de orden parcial elegida para implementar en este trabajo es la más moderna. Ésta permite una mayor reducción ya que no tiene en cuenta ejecuciones probabilistas irreales consideradas en técnicas anteriores. La implementación se realizó sobre PRISM, que es un model checker probabilista moderno y potente, cuya distribución es de carácter libre.Luis María Ferrer Fioriti

MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata

Markov automata combine continuous time, probabilistic transitions, and nondeterminism in a single model. They represent an important and powerful way to model a wide range of complex real-life systems. However, such models tend to be large and difficult to handle, making abstraction and abstraction refinement necessary. In this paper we present an abstraction and abstraction refinement technique for Markov automata, based on the game-based and menu-based abstraction of probabilistic automata. First experiments show that a significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156