INFAMY: An Infinite-State Markov Model Checker

Abstract

Abstract. The design of complex concurrent systems often involves intricate performance and dependability considerations. Continuous-time Markov chains (CTMCs) are a widely used modeling formalism, where performance and dependability properties are analyzable by model checking. We present INFAMY, a model checker for arbitrarily structured infinite-state CTMCs. It checks probabilistic timing properties expressible in continuous stochastic logic (CSL). Conventional model checkers explore the given model exhaustively, which is often costly, due to state explosion, and impossible if the model is infinite. INFAMY only explores the model up to a finite depth, with the depth bound being computed on-the-fly. The computation of depth bounds is configurable to adapt to the characteristics of different classes of models. Introducing INFAMYContinuous-time Markov chains (CTMCs) are widely used in performance and dependability analysis and biological modeling. Properties are typically specified in continuous stochastic logic (CSL) [1], a logic inspired by CTL. In CSL, the until operator is equipped with a time interval to express properties such as: "The probability to reach a goal within 2 hours while maintaining a probability of at least 0.5 of communicating periodically (every five minutes) with a base station, is at least 0.9" via P ≥0.9 P ≥0.5 3 ≤5 communicate U ≤120 goal . CSL model checking amounts to analysis of the transient (time-dependent) probability vectors [1], typically carried out by uniformization, where the transient probability is expressed by a weighted infinite sum (weights are given by a Poisson process). The standard methodology in CSL model checking is to truncate the infinite sum up to some pre-specified accuracy [2]. Outside the model checking arena, ideas have been developed [3,4,5] which not only truncate the infinite sum, but also the matrix representing the system, which admits transient analysis of CTMCs with large or even infinite state spaces, provided they are given implicitly in a

Time-Bounded Model Checking of Infinite-State Continuous-Time Markov Chains

“…The experimental evaluation is an extended and revised version of [14]. As in Subsection 3, we consider three different strategies for error-estimation, namely the Uniform chain based, Layered chain based, and the finite state projection (FSP) method.…”

“…We have implemented INFAMY [14], a model checker for infinite Markov (reward) models. INFAMY supports probabilistic programs in a guarded command language with unbounded integers.…”

“…We have implemented the truncation-based CSL model checker INFAMY [14]. Compared to the proof-of-concept implementation of [35], INFAMY features several error estimation methods and a much faster model exploration.…”

Computing Cumulative Rewards Using Fast Adaptive Uniformization

“…On the other hand, not discarding states allows for a simpler representation of state-to-state transitions. It also allows one to handle nested CSL formulas [Hahn et al 2009;Spieler et al 2014], for which FAU does not seem appropriate. The reason is that, when discarding a state, the information about which subformulae of the CSL formula under consideration are fulfilled is lost.…”

Fast Adaptive Uniformization of the Chemical Master Equation

“…10 −5 ). It is, however, also possible to bound the number of iterations by considering the sequence of the transition ratesλ in a similar way as Hahn et al [17].…”