# Linear-Time Model Checking Branching Processes

@inproceedings{Kiefer2021LinearTimeMC, title={Linear-Time Model Checking Branching Processes}, author={Stefan Kiefer and Pavel Semukhin and Cas Widdershoven}, booktitle={CONCUR}, year={2021} }

Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov chains (but not generally Markov decision processes). We study the complexity of model checking branching processes against linear-time omega-regular specifications: is it the case almost surely that every branch of a tree randomly generated by the branching… Expand

#### References

SHOWING 1-10 OF 32 REFERENCES

Model Checking Stochastic Branching Processes

- Physics, Computer Science
- MFCS
- 2012

This paper considers the problem of model checking stochastic branching process, and develops a PSPACE algorithm for model checking a branching process against a formula of this logic, and suggests a tree extension of the logic PCTL, and shows that the qualitative fragment of this Logic can be model checked in polynomial time. Expand

Model Checking of Recursive Probabilistic Systems

- Mathematics, Computer Science
- TOCL
- 2012

This article studies the problem of model checking an RMC against an ω-regular specification, given in terms of a Büchi automaton or a Linear Temporal Logic (LTL) formula, and establishes a number of strong upper bounds, as well as lower bounds, both for qualitative and quantitative problems. Expand

Separable GPL: Decidable Model Checking with More Non-Determinism

- Computer Science
- CONCUR
- 2018

This work considers GPL over branching systems that also exhibit internal non-determinism under linear-time semantics, and defines a subclass, called separable GPL, which includes recursive formulae and for which model checking is decidable. Expand

Verifying omega-Regular Properties of Markov Chains

- Computer Science
- CAV
- 2004

This work solves the general problem of linear-time probabilistic model checking with respect to ω-regular specifications and uses alternating Buchi infinite-word automata, which have emerged recently as a generic specification formalism for developing model checking algorithms. Expand

An Optimal Automata Approach to LTL Model Checking of Probabilistic Systems

- Computer Science
- LPAR
- 2003

This study shows that checking whether a probabilistic system satisfies an ω-automaton with positive probability can be solved in linear time for this kind of automata, and extends the study to the evaluation of this probability. Expand

Verifying temporal properties of finite-state probabilistic programs

- Mathematics, Computer Science
- [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
- 1988

The complexity of testing whether a finite-state (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an… Expand

Markov Chains and Unambiguous Büchi Automata

- Computer Science
- CAV
- 2016

A polynomially time-bounded algorithm for probabilistic model checking of discrete-time Markov chains against unambiguous Buchi automata specifications is provided and an implementation and experiments are reported on. Expand

Automata on Infinite Objects

- Computer Science, Mathematics
- Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
- 1990

This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. Expand

Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations

- Mathematics, Computer Science
- JACM
- 2009

It is shown that the PSPACE upper bounds cannot be substantially improved without a breakthrough on long standing open problems: the square-root sum problem and an arithmetic circuit decision problem that captures P-time on the unit-cost rational arithmetic RAM model. Expand

Automatic verification of probabilistic concurrent finite state programs

- Computer Science
- 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985

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. Expand