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 $\Sigma_1^0$- and $\Sigma_2^0$-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 $\Pi^0_2$-complete. Finally, it is shown that deciding (universal) positive almost-sure termination is $\Sigma_2^0$-complete ($\Pi_3^0$-complete).Comment: MFCS 2015. arXiv admin note: text overlap with arXiv:1410.722

Quantitative and qualitative extensions of event structures

An important application of formal methods is the specification, design, and analysis of functional aspects of (distributed) systems. Recently the study of quantitative aspects of such systems based on formal methods has come into focus. Several extensions of formal methods where the occurrence of actions can be assigned a (fixed) probability and/or the time of occurrence of actions can be constrained are known from the literature

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

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