Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

`Electronic Publishing' -- Practice and Experience

Electronic Publishing -- Origination, Dissemination and Design (EP-odd) is an academic journal which publishes refereed papers in the subject area of electronic publishing. The authors of the present paper are, respectively, editor-in-chief, system software consultant and senior production manager for the journal. EP-odd's policy is that editors, authors, referees and production staff will work closely together using electronic mail. Authors are also encouraged to originate their papers using one of the approved text-processing packages together with the appropriate set of macros which enforce the layout style for the journal. This same software will then be used by the publisher in the production phase. Our experiences with these strategies are presented, and two recently developed suites of software are described: one of these makes the macro sets available over electronic mail and the other automates the flow of papers through the refereeing process. The decision to produce EP-odd in this way means that the publisher has to adopt production procedures which differ markedly from those employed for a conventional journal

Comparing BDD and SAT based techniques for model checking Chaum's Dining Cryptographers Protocol

We analyse different versions of the Dining Cryptographers protocol by means of automatic verification via model checking. Specifically we model the protocol in terms of a network of communicating automata and verify that the protocol meets the anonymity requirements specified. Two different model checking techniques (ordered binary decision diagrams and SAT-based bounded model checking) are evaluated and compared to verify the protocols

Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud \ud An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud \ud To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud \ud To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies