177 research outputs found
On the axiomatizability of impossible futures
A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves omega-completeness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, ground- and omega-complete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a finite, sound, ground-complete axiomatization for the concrete impossible futures preorder, which implies a finite, sound, ground-complete axiomatization for the weak impossible futures preorder. In contrast, we prove that no finite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is ground-complete. If the alphabet of actions is infinite, then the aforementioned ground-complete axiomatizations are shown to be omega-complete. If the alphabet is finite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a finite basis
Limit Synchronization in Markov Decision Processes
Markov decision processes (MDP) are finite-state systems with both strategic
and probabilistic choices. After fixing a strategy, an MDP produces a sequence
of probability distributions over states. The sequence is eventually
synchronizing if the probability mass accumulates in a single state, possibly
in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a
probability distribution in the sequence assigns probability at least p to some
state, and we distinguish three synchronization modes: (i) sure winning if
there exists a strategy that produces a 1-synchronizing sequence; (ii)
almost-sure winning if there exists a strategy that produces a sequence that
is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure
winning if for all epsilon > 0, there exists a strategy that produces a
(1-epsilon)-synchronizing sequence.
We consider the problem of deciding whether an MDP is sure, almost-sure,
limit-sure winning, and we establish the decidability and optimal complexity
for all modes, as well as the memory requirements for winning strategies. Our
main contributions are as follows: (a) for each winning modes we present
characterizations that give a PSPACE complexity for the decision problems, and
we establish matching PSPACE lower bounds; (b) we show that for sure winning
strategies, exponential memory is sufficient and may be necessary, and that in
general infinite memory is necessary for almost-sure winning, and unbounded
memory is necessary for limit-sure winning; (c) along with our results, we
establish new complexity results for alternating finite automata over a
one-letter alphabet
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
Is timed branching bisimilarity a congruence indeed?
We show that timed branching bisimilarity as defined by Van der Zwaag [17] and Baeten and Middelburg [2] is not an equivalence relation, in case of a dense time domain. We propose an adaptation based on Van der Zwaag's definition, and prove that the resulting timed branching bisimilarity is an equivalence indeed. Furthermore, we prove that in case of a discrete time domain, Van der Zwaag's definition and our adaptation coincide. Finally, we prove that a rooted version of timed branching bisimilarity is a congruence over a basic timed process algebra containing parallelism, successful termination and deadlock
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
Neonatal Fc receptor promoter gene polymorphism does not predict pharmacokinetics of IVIg or the clinical course of GBS
Treatment of Guillain-Barré syndrome with a standard course of high-dose intravenous immunoglobulin (IVIg) results in a variable clinical recovery which is associated with changes in serum IgG levels after treatment. The neonatal Fc-receptor protects IgG from degradation, and a genetic polymorphism in its promoter region that influences the expression of Fc-receptor, may in part explain the variation in IgG levels and outcome. This polymorphism was determined by polymerase chain reaction in a cohort of 257 patients with Guillain-Barré syndrome treated with IVIg. We could not demonstrate a relation between this polymorphism, the pharmacokinetics of IVIg, or the clinical course and outcome
Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory
There are two fundamentally different approaches to specifying and verifying
properties of systems. The logical approach makes use of specifications given
as formulae of temporal or modal logics and relies on efficient model checking
algorithms; the behavioural approach exploits various equivalence or refinement
checking methods, provided the specifications are given in the same formalism
as implementations.
In this paper we provide translations between the logical formalism of
Hennessy-Milner logic with greatest fixed points and the behavioural formalism
of disjunctive modal transition systems. We also introduce a new operation of
quotient for the above equivalent formalisms, which is adjoint to structural
composition and allows synthesis of missing specifications from partial
implementations. This is a substantial generalisation of the quotient for
deterministic modal transition systems defined in earlier papers
On Process-Algebraic Proof Methods for Fault Tolerant Distributed Systems
Abstract. Distributed Algorithms are hard to prove correct. In settings with process failures, things get worse. Among the proof methods proposed in this context, we focus on process calculi, which offer a tight connection of proof concepts to the actual code representing the algorithm. We use Distributed Consensus as a case study to evaluate recent developments in this field. Along the way, we find that the classical assertional style for proofs on distributed algorithms can be used to structure bisimulation relations. For this, we propose the definition of uniform syntactic descriptions of reachable states, on which state-based assertions can be conveniently formulated. As a result, we get the best of both worlds: on the one hand invariant-style representation of proof knowledge; on the other hand the bisimulation-based formal connection to the code
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