36 research outputs found
Assume-guarantee verification for probabilistic systems
We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume- guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible
The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes
We present a spectrum of trace-based, testing, and bisimulation equivalences
for nondeterministic and probabilistic processes whose activities are all
observable. For every equivalence under study, we examine the discriminating
power of three variants stemming from three approaches that differ for the way
probabilities of events are compared when nondeterministic choices are resolved
via deterministic schedulers. We show that the first approach - which compares
two resolutions relatively to the probability distributions of all considered
events - results in a fragment of the spectrum compatible with the spectrum of
behavioral equivalences for fully probabilistic processes. In contrast, the
second approach - which compares the probabilities of the events of a
resolution with the probabilities of the same events in possibly different
resolutions - gives rise to another fragment composed of coarser equivalences
that exhibits several analogies with the spectrum of behavioral equivalences
for fully nondeterministic processes. Finally, the third approach - which only
compares the extremal probabilities of each event stemming from the different
resolutions - yields even coarser equivalences that, however, give rise to a
hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241
Probabilistic Action System Trace Semantics
Action systems are a construct for reasoning about concurrent, reactive systems, in which concurrent behaviour is described by interleaving atomic actions. Sere and Troubitsyna have proposed an extension to action systems in which actions may be expressed and composed using discrete probabilistic choice as well as demonic nondeterministic choice. In this paper we develop a trace-based semantics for probabilistic action systems. This semantics provides a simple theoretical base on which practical refinement rules for probabilistic action systems may be justified
An Event Structure Model for Probabilistic Concurrent Kleene Algebra
We give a new true-concurrent model for probabilistic concurrent Kleene
algebra. The model is based on probabilistic event structures, which combines
ideas from Katoen's work on probabilistic concurrency and Varacca's
probabilistic prime event structures. The event structures are compared with a
true-concurrent version of Segala's probabilistic simulation. Finally, the
algebraic properties of the model are summarised to the extent that they can be
used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013
Separable GPL: Decidable Model Checking with More Non-Determinism
Generalized Probabilistic Logic (GPL) is a temporal logic, based on the modal mu-calculus, for specifying properties of branching probabilistic systems. We consider GPL over branching systems that also exhibit internal non-determinism under linear-time semantics (which is resolved by schedulers), and focus on the problem of finding the capacity (supremum probability over all schedulers) of a fuzzy formula. Model checking GPL is undecidable, in general, over such systems, and existing GPL model checking algorithms are limited to systems without internal non-determinism, or to checking non-recursive formulae. We define a subclass, called separable GPL, which includes recursive formulae and for which model checking is decidable. A large class of interesting and decidable problems, such as termination of 1-exit Recursive MDPs, reachability of Branching MDPs, and LTL model checking of MDPs, whose decidability has been studied independently, can be reduced to model checking separable GPL. Thus, GPL is widely applicable and, with a suitable extension of its semantics, yields a uniform framework for studying problems involving systems with non-deterministic and probabilistic behaviors
Using schedulers to test probabilistic distributed systems
This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-012-0244-5. Copyright Ā© 2012, British Computer Society.Formal methods are one of the most important approaches to increasing the confidence in the correctness of software systems. A formal specification can be used as an oracle in testing since one can determine whether an observed behaviour is allowed by the specification. This is an important feature of formal testing: behaviours of the system observed in testing are compared with the specification and ideally this comparison is automated. In this paper we study a formal testing framework to deal with systems that interact with their environment at physically distributed interfaces, called ports, and where choices between different possibilities are probabilistically quantified. Building on previous work, we introduce two families of schedulers to resolve nondeterministic choices among different actions of the system. The first type of schedulers, which we call global schedulers, resolves nondeterministic choices by representing the environment as a single global scheduler. The second type, which we call localised schedulers, models the environment as a set of schedulers with there being one scheduler for each port. We formally define the application of schedulers to systems and provide and study different implementation relations in this setting
Faithful Simulation of Randomized BFT Protocols on Block DAGs
Byzantine Fault-Tolerant (BFT) protocols that are based on Directed Acyclic Graphs (DAGs) are attractive due to their many advantages in asynchronous blockchain systems. These DAG-based protocols can be viewed as a simulation of some BFT protocol on a DAG. Many DAG-based BFT protocols rely on randomization, since they are used for agreement and ordering of transactions, which cannot be achieved deterministically in asynchronous systems. Randomization is achieved either through local sources of randomness, or by employing shared objects that provide a common source of randomness, e.g., common coins.
A DAG simulation of a randomized protocol should be faithful, in the sense that it precisely preserves the properties of the original BFT protocol, and in particular, their probability distributions. We argue that faithfulness is ensured by a forward simulation. We show how to faithfully simulate any BFT protocol that uses public coins and shared objects, like common coins