Approximate Verification of Probabilistic Systems

  title={Approximate Verification of Probabilistic Systems},
  author={Richard Lassaigne and Sylvain Peyronnet},
General methods have been proposed [2,4] for the model checking of probabilistic systems, where the verification of a probabilistic statement is reduced to the solution of a linear system over the system’s state space. To overcome the state space explosion problem, some probabilistic model checkers, such as PRISM [3], use MTBDDs. We propose a different solution, in which we use a Monte-Carlo algorithm [6] to approximate Prob[ψ], the probability that a temporal formula is true. We show how to… 
Approximate Probabilistic Model Checking
An approximation method to verify quantitative properties on discrete Markov chains using a randomized algorithm to approximate the probability that a property expressed by some positive LTL formula is satisfied with high confidence by a probabilistic system.
Approximate Probabilistic Model Checking for Programs
This paper verifies a program without constructing the whole transition system using a technique based on Monte-Carlo sampling, also called “approximate model checking”, which avoids the socalled state space explosion phenomenon.
Probabilistic Verification and Approximation
Model Checking Probabilistic Systems
This chapter presents the foundations of Probabilistic model checking, focusing on finite-state Markov decision processes as models and quantitative properties expressed in probabilistic temporal logic, and summarizes the main model-checking algorithms for both PCTL and LTL.
Probabilistic model checking : a comparison of tools
This research studied the efficiency of five probabilistic model checker tools, namely: PRISM (Sparse and Hybrid mode), MRMC, ETMCC, YMER and VESTA, and made a tool by tool comparison, analysing model check times and peak memory usage.
Probabilistic Model Checking
  • C. Baier
  • Computer Science
    Dependable Software Systems Engineering
  • 2016
This chapter presents the foundations of Probabilistic model-checking, focusing on finite-state Markov decision processes as models and quantitative properties expressed in probabilistic temporal logic, and summarises the main model- checking algorithms for both PCTL and LTL.
An Abstraction Framework for Mixed Non-deterministic and Probabilistic Systems
  • M. Huth
  • Computer Science
    Validation of Stochastic Systems
  • 2004
This work sketches how quantitative domain theory may be used to specify the precision of answers obtained from abstract model checks, emphasizing the discrete case.
Model checking for probability and time: from theory to practice
  • M. Kwiatkowska
  • Computer Science
    18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
The experience with implementing PRISM, a probabilistic symbolic model checker, is reported, which demonstrates its usefulness in analyzing real-world probabilism protocols, and outlines future challenges for this research direction.
A Survey of Statistical Model Checking
SMC provides a more widely applicable and scalable alternative to analysis of properties of stochastic systems using numerical and symbolic methods, while emphasizing current limitations and tradeoffs between precision and scalability.


The complexity of probabilistic verification
This work determines the complexity of testing whether a finite state, sequential or concurrent probabilistic program satisfies its specification expressed in linear-time temporal logic and addresses questions for specifications described by ω-automata or formulas in extended temporal logic.
Symbolic Model Checking without BDDs
This paper shows how boolean decision procedures, like Stalmarck's Method or the Davis & Putnam Procedure, can replace BDDs, and introduces a bounded model checking procedure for LTL which reduces model checking to propositional satisfiability.
Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation
An experimental model checker is implemented using the CUDD package and it is demonstrated that model construction and reachability-based model checking is possible in a matter of seconds for certain classes of systems consisting of up to 1030 states.
Monte-Carlo algorithms for enumeration and reliability problems
  • R. Karp, M. Luby
  • Mathematics
    24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
  • 1983
A simple but very general Monte-Carlo technique for the approximate solution of enumeration and reliability problems and several applications are given.
Symmetry breaking in distributed networks
Randomized Algorithms
For many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of
Symbolic modelchecking without BDD ’ s
  • Proc . of 5 th TACAS , LNCS
  • 1999
Symbolic model checking of concurrent probabilistic processes using MTBDDs and the Kronecker representation
  • Proc. of TACAS
  • 1785
Symbolic model checking without BDD's
  • Proc. of 5th TACAS
  • 1573
The complexity of prob abilistic
  • verification.Journal of the ACM,
  • 1995