An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties
نویسندگان
چکیده
In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT solver. The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula. We provide a prototype and show the efficiency of our approach on a number of benchmarks.
منابع مشابه
Bayesian analysis of continuous time Markov chains with application to phylogenetic modelling
Bayesian analysis of continuous time, discrete state space time series is an important and challenging problem, where incomplete observation and large parameter sets call for user-defined priors based on known properties of the process. Generalized linear models have a largely unexplored potential to construct such prior distributions. We show that an important challenge with Bayesian generaliz...
متن کاملMean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms
Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events that can be non-exponentially distributed. Within parametric ACTMCs, the parameters of alarm-event distributions are not given explicitly and can be subject of parameter synthesis. An algorithm solving the ε-optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives is presente...
متن کاملParametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for the parameters. Among the tasks typically addressed in the analysis of parametric Markov chains are (1) the computation of closed-form solutions for reachabil...
متن کاملEfficient estimators for functionals of Markov chains with parametric marginals
Suppose we observe a geometrically ergodic Markov chain with a parametric model for the marginal, but no (further) information about the transition distribution. Then the empirical estimator for a linear functional of the joint law of two successive observations is no longer efficient. We construct an improved estimator and show that it is efficient. The construction is similar to a recent one ...
متن کاملAdvances in Probabilistic Model Checking
Random phenomena occur in many applications: security, communication protocols, distributed algorithms, and performance and dependability analysis, to mention a few. In the last two decades, efficient model-checking algorithms and tools have been developed to support the automated verification of models that incorporate randomness. Popular models are Markov decision processes and (continuous-ti...
متن کامل