Analysis of Probabilistic Basic Parallel Processes

@inproceedings{Bonnet2014AnalysisOP,
  title={Analysis of Probabilistic Basic Parallel Processes},
  author={R{\'e}mi Bonnet and Stefan Kiefer and Anthony Widjaja Lin},
  booktitle={FoSSaCS},
  year={2014}
}
Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs — in particular reachability with probability 1 of different classes of target sets (e.g. upward-closed… 

Figures from this paper

Reachability for Branching Concurrent Stochastic Games
We give polynomial time algorithms for deciding almost-sure and limit-sure reachability in Branching Concurrent Stochastic Games (BCSGs). These are a class of infinite-state imperfectinformation
Fair Termination for Parameterized Probabilistic Concurrent Systems
TLDR
The encoding reduces termination with finitary fairness to verifying parameterized termination without fairness over probabilistic systems in regular model checking (for which a verification framework already exists), and shows that the algorithm is the first fully-automatic method that can prove termination for many interesting examples from distributed algorithms and evolutionary biology.
Reachability for Branching Concurrent Stochastic Games
We give polynomial time algorithms for deciding almost-sure and limit-sure reachability in Branching Concurrent Stochastic Games (BCSGs). These are a class of infinite-state imperfect-information
Fair Termination for Parameterized Probabilistic Concurrent Systems (Technical Report)
TLDR
The encoding reduces termination with finitary fairness to verifying parameterized termination without fairness over probabilistic systems in regular model checking (for which a verification framework already exists), and shows that the algorithm is the first fully-automatic method that can prove termination for many interesting examples from distributed algorithms and evolutionary biology.
Greatest Fixed Points of Probabilistic Min/Max Polynomial Equations, and Reachability for Branching Markov Decision Processes
TLDR
This paper gives polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs) and studies more general branching simple stochastic games (BSSGs) with (non-)reachability objectives.
Explorer Greatest Fixed Points of Probabilistic Min / Max Polynomial Equations , and Reachability for Branching Markov Decision Processes ?
TLDR
This paper gives polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs) and shows how to compute the GFP of max/min PPSs to desired precision in P-time.
Probabilistic Analysis of Binary Sessions
TLDR
A type system is developed for a simple session calculus featuring probabilistic choices and it is shown that the success probability of well-typed processes agrees with that of the sessions they use.

References

SHOWING 1-10 OF 21 REFERENCES
Undecidable Equivalences for Basic Parallel Processes
TLDR
All other equivalences in the linear/branching time hierarchy are examined and it is shown that none of them are decidable for BPP.
Strong bisimilarity on basic parallel processes in PSPACE-complete
  • P. Jančar
  • Computer Science
    18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
TLDR
The paper shows an algorithm which, given a basic parallel processes (BPP) system, constructs a set of linear mappings which characterize the (strong) bisimulation equivalence on the system, and shows that PSPACE-completeness is established.
Petri Nets, Commutative Context-Free Grammars, and Basic Parallel Processes
The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class
Termination of Probabilistic Concurrent Program
TLDR
In this model synchronization protocols that use randomization are in certain cases no more powerful than deterministic protocols and no fully symmetric randomized protocol can ensure mutual exclusion and freedom from lockout.
Automatic verification of probabilistic concurrent finite state programs
  • Moshe Y. Vardi
  • Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
TLDR
An automata-theoretic approach is described, whereby probabilistic quantification over sets of computations is reduced to standard quantificationover individual computations, and a new determinization construction for ω-automata is used to improve the time complexity of the algorithm by two exponentials.
On the Model Checking Problem for Branching Time Logics and Basic Parallel Processes
TLDR
It is shown that the model checking problem for branching time logics and Basic Parallel Processes is undecidable for the logic ∀L(O, F, U) (equivalent to CTL*) in the usual interleaving semantics, but decidable in a standard partial order interpretation.
Non-interleaving bisimulation equivalences on Basic Parallel Processes
Space-efficient scheduling of stochastically generated tasks
From Fairness to Chance
  • L. D. Alfaro
  • Computer Science
    Electron. Notes Theor. Comput. Sci.
  • 1999
Games for Counting Abstractions
...
1
2
3
...