# Bounded Model Checking for GSMP Models of Stochastic Real-Time Systems

@inproceedings{Alur2006BoundedMC, title={Bounded Model Checking for GSMP Models of Stochastic Real-Time Systems}, author={Rajeev Alur and Mikhail Bernadsky}, booktitle={HSCC}, year={2006} }

Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMP). While GSMPs is a rich model for stochastic systems widely used in performance evaluation, existing model checking algorithms are applicable only to subclasses such as discrete-time or continuous…

## 21 Citations

### Symbolic Analysis for GSMP Models with One Stateful Clock

- Mathematics, Computer ScienceHSCC
- 2007

A symbolic solution for the case where firing times are random variables over a rich class of distributions, but only one event is allowed to retain its firing time when a discrete change occurs is presented.

### Probabilistic Model Checking of Regenerative Concurrent Systems

- Computer ScienceIEEE Transactions on Software Engineering
- 2016

The proposed solution is based on the analysis of regeneration points in model executions: a regeneration is encountered after a discrete event if the future evolution depends only on the current marking and not on its previous history, thus satisfying the Markov property.

### Probabilistic Model Checking of Non-Markovian Models with Concurrent Generally Distributed Timers

- Computer Science2011 Eighth International Conference on Quantitative Evaluation of SysTems
- 2011

Transient stochastic state classes can be used to perform bounded probabilistic model checking also for models with underlying GSMPs, and the conditions for termination of the resulting algorithm are characterized, both in exact and approximate evaluation.

### Model Checking Probabilistic Timed Automata with One or Two Clocks

- Computer ScienceLog. Methods Comput. Sci.
- 2007

This work shows that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one clock Probabilistic timed automata, and are EXPTIME- complete for probabilism timed automATA with two clocks.

### Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects

- Computer ScienceArXiv
- 2019

This work introduces a logical formalism for reasoning about upper and lower bounds on time, and studies the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied, and considers the question of when a system is faster than another system.

### Analysing Decisive Stochastic Processes

- Mathematics, Computer ScienceICALP
- 2016

This paper extends the concept of decisiveness to more general stochastic processes and obtains decidability results for both qualitative and quantitative verification problems on some classes of real-time stoChastic processes, including generalized semi-Markov processes and Stochastic timed automata.

### On Zone-Based Analysis of Duration Probabilistic Automata

- Computer ScienceINFINITY
- 2010

An extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic Dpa).

### When are Stochastic Transition Systems Tameable?

- Computer Science, MathematicsJ. Log. Algebraic Methods Program.
- 2018

### Transient Analysis of Networks of Stochastic Timed Automata Using Stochastic State Classes

- Computer ScienceQEST
- 2013

This paper introduces Networks of Stochastic Timed Automata (NSTA), where the components interact with each other by message broadcasts, and characterize this general state space Markov process through transient stochastic state classes that sample the state and the absolute age after each event.

### Hybrid Automata for Formal Modeling and Verification of Cyber-Physical Systems

- Computer Science, MathematicsArXiv
- 2015

A review of Hybrid automata as modeling and verification framework for cyber-physical systems, and some of the key results related to practical verification questions related to hybrid automata are surveyed.

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