825 research outputs found
On the Hardness of Almost-Sure Termination
This paper considers the computational hardness of computing expected
outcomes and deciding (universal) (positive) almost-sure termination of
probabilistic programs. It is shown that computing lower and upper bounds of
expected outcomes is - and -complete, respectively.
Deciding (universal) almost-sure termination as well as deciding whether the
expected outcome of a program equals a given rational value is shown to be
-complete. Finally, it is shown that deciding (universal) positive
almost-sure termination is -complete (-complete).Comment: MFCS 2015. arXiv admin note: text overlap with arXiv:1410.722
Counterexample Generation in Probabilistic Model Checking
Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol
A Weakest Pre-Expectation Semantics for Mixed-Sign Expectations
We present a weakest-precondition-style calculus for reasoning about the
expected values (pre-expectations) of \emph{mixed-sign unbounded} random
variables after execution of a probabilistic program. The semantics of a
while-loop is well-defined as the limit of iteratively applying a functional to
a zero-element just as in the traditional weakest pre-expectation calculus,
even though a standard least fixed point argument is not applicable in this
context. A striking feature of our semantics is that it is always well-defined,
even if the expected values do not exist. We show that the calculus is sound,
allows for compositional reasoning, and present an invariant-based approach for
reasoning about pre-expectations of loops
Advancing Dynamic Fault Tree Analysis
This paper presents a new state space generation approach for dynamic fault
trees (DFTs) together with a technique to synthesise failures rates in DFTs.
Our state space generation technique aggressively exploits the DFT structure
--- detecting symmetries, spurious non-determinism, and don't cares. Benchmarks
show a gain of more than two orders of magnitude in terms of state space
generation and analysis time. Our approach supports DFTs with symbolic failure
rates and is complemented by parameter synthesis. This enables determining the
maximal tolerable failure rate of a system component while ensuring that the
mean time of failure stays below a threshold
Constraint-oriented specification of performance aspects
This note sketches how to extend (distributed) system specifications with
performance constraints. The emphasis is on how to include performance
aspects in a modular way. The key of the approach is to specify random
delays as separated processes that are composed in parallel with an
untimed, functional system specification. The use of parallel processes as
separate constraints is in accordance with the constraint-oriented specification
style as originally proposed by Vissers et al
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
A probabilistic extension of UML statecharts: specification and verification
This paper is the extended technical report that corresponds to a published paper [14]. This paper introduces means to specify system randomness within UML statecharts, and to verify probabilistic temporal properties over such enhanced statecharts which we call probabilistic UML statecharts. To achieve this, we develop a general recipe to extend a statechart semantics with discrete probability distributions, resulting in Markov decision processes as semantic models. We apply this recipe to the requirements-level UML semantics of [8]. Properties of interest for probabilistic statecharts are expressed in PCTL, a probabilistic variant of CTL for processes that exhibit both non-determinism and probabilities. Verification is performed using the model checker Prism. A model checking example shows the feasibility of the suggested approach
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