617 research outputs found
Distributed Branching Bisimulation Reduction of State Spaces
AbstractEnumerative model checking tools are limited by the size of the state space to which they can be applied. Reduction modulo branching bisimulation usually results in a much smaller state space and therefore enables model checking of much larger state spaces. We present an algorithm for reducing state spaces modulo branching bisimulation which is suitable for distributed implementation. The target architecture is a cluster with a high bandwidth interconnect. The algorithm is based on partition refinement and it works on transition systems which contain cycles of invisible steps, without eliminating strongly connected components first. To avoid fine grained parallelism, the algorithm refines the whole partition instead of just a single block in the partition. We prove correctness and also present some experimental results obtained with single threaded and distributed prototypes
Distributed Branching Bisimulation Minimization by Inductive Signatures
We present a new distributed algorithm for state space minimization modulo
branching bisimulation. Like its predecessor it uses signatures for refinement,
but the refinement process and the signatures have been optimized to exploit
the fact that the input graph contains no tau-loops.
The optimization in the refinement process is meant to reduce both the number
of iterations needed and the memory requirements. In the former case we cannot
prove that there is an improvement, but our experiments show that in many cases
the number of iterations is smaller. In the latter case, we can prove that the
worst case memory use of the new algorithm is linear in the size of the state
space, whereas the old algorithm has a quadratic upper bound.
The paper includes a proof of correctness of the new algorithm and the
results of a number of experiments that compare the performance of the old and
the new algorithms
Sigref – A Symbolic Bisimulation Tool Box
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.
We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information
Confluence Reduction for Probabilistic Systems (extended version)
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic bisimulation and can be applied on-the-fly. To support the technique, we introduce a method for detecting confluent transitions in the context of a probabilistic process algebra with data, facilitated by an earlier defined linear format. A case study demonstrates that significant reductions can be obtained
Measurable Stochastics for Brane Calculus
We give a stochastic extension of the Brane Calculus, along the lines of
recent work by Cardelli and Mardare. In this presentation, the semantics of a
Brane process is a measure of the stochastic distribution of possible
derivations. To this end, we first introduce a labelled transition system for
Brane Calculus, proving its adequacy w.r.t. the usual reduction semantics.
Then, brane systems are presented as Markov processes over the measurable space
generated by terms up-to syntactic congruence, and where the measures are
indexed by the actions of this new LTS. Finally, we provide a SOS presentation
of this stochastic semantics, which is compositional and syntax-driven.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
Process algebra for performance evaluation
This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions
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
State space reduction using partial -confluence
We present an efficient algorithm to determine the maximal class of confluent -transitions in a labelled transition system. Confluent -transitions are inert with respect to branching bisimulation. This allows to use -priorisation, which means that in a state with a confluent outgoing -transition all other transitions can be removed, maintaining branching bisimulation. In combination with the removal of -loops, and the compression of-sequences this yields an efficient algorithm to reduce the size of large state spaces
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