Decision Problems for Interval Markov Chains
نویسندگان
چکیده
Interval Markov Chains (IMC) are the base of a classic probabilistic specification theory by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study complexity of several problems for this abstraction, that stem from compositional modeling methodologies. In particular we close the complexity gap for thorough refinement of two IMCs and for deciding the existence of a common implementation for an unbounded number of IMCs, showing that these problems are EXPTIME-complete. We also prove that deciding consistency of an IMC is polynomial and discuss suitable notions of determinism for such specifications.
منابع مشابه
Model-Checking Markov Chains in the Presence of Uncertainties
We investigate the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie. We consider two semantic interpretations for the uncertainty in the transi...
متن کاملModel-Checking ω-Regular Properties of Interval Markov Chains
We study the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie. We consider two semantic interpretations for the uncertainty in the transition p...
متن کاملComputing 2-Step Predictions for Interval-Valued Finite Stationary Markov Chains
Markov chains are a useful tool for solving practical problems. In many real-life situations, we do not know the exact values of initial and transition probabilities; instead, we only know the intervals of possible values of these probabilities. Such interval-valued Markov chains were considered and analyzed by I. O. Kozine and L. V. Utkin in their Reliable Computing paper. In their paper, they...
متن کاملReachability in Parametric Interval Markov Chains Using Constraints
Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigat...
متن کاملA new machine replacement policy based on number of defective items and Markov chains
A novel optimal single machine replacement policy using a single as well as a two-stage decision making process is proposed based on the quality of items produced. In a stage of this policy, if the number of defective items in a sample of produced items is more than an upper threshold, the machine is replaced. However, the machine is not replaced if the number of defective items is less than ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011