Least Upper Bounds for Probability Measures and Their Applications to Abstractions [chapter]

Rohit Chadha, Mahesh Viswanathan, Ramesh Viswanathan
2008 Lecture Notes in Computer Science  
Abstraction is a key technique to combat the state space explosion problem in model checking probabilistic systems. In this paper we present new ways to abstract Discrete Time Markov Chains (DTMCs), Markov Decision Processes (MDPs), and Continuous Time Markov Chains (CTMCs). The main advantage of our abstractions is that they result in abstract models that are purely probabilistic, which maybe more amenable to automatic analysis than models with both nondeterministic and probabilistic steps
more » ... typically arise from previously known abstraction techniques. A key technical tool, developed in this paper, is the construction of least upper bounds for any collection of probability measures. This upper bound construction may be of independent interest that could be useful in the abstract interpretation and static analysis of probabilistic programs.
doi:10.1007/978-3-540-85361-9_23 fatcat:lhwghcgjejhejafoxnvrp365hy