Probabilistic Timed Automata with Clock-Dependent Probabilities

Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition probabilities can depend linearly on clock values. Clock-dependent probabilistic timed automata allow the modelling of a continuous relationship between time passage and the likelihood of system events. We show that the problem of deciding whether the maximum probability of reaching a certain location is above a threshold is undecidable for clock-dependent probabilistic timed automata. On the other hand, we show that the maximum and minimum probability of reaching a certain location in clock-dependent probabilistic timed automata can be approximated using a region-graph-based approach.Comment: Full version of a paper published at RP 201

Unary probabilistic and quantum automata on promise problems

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.Comment: Minor correction

Quantum walks can find a marked element on any graph

We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically smaller than the classical hitting time $HT(P,M)$ of any reversible random walk $P$ on the graph. In the case of multiple marked elements, the number of steps is given in terms of a related quantity $HT^+(\mathit{P,M})$ which we call extended hitting time. Our approach is new, simpler and more general than previous ones. We introduce a notion of interpolation between the random walk $P$ and the absorbing walk $P'$, whose marked states are absorbing. Then our quantum walk is simply the quantum analogue of this interpolation. Contrary to previous approaches, our results remain valid when the random walk $P$ is not state-transitive. We also provide algorithms in the cases when only approximations or bounds on parameters $p_M$ (the probability of picking a marked vertex from the stationary distribution) and $HT^+(\mathit{P,M})$ are known.Comment: 50 page

Distribution-based bisimulation for labelled Markov processes

In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based bisimulations, our distribution bisimulation is weaker, but corresponds more closely to linear properties. We construct a logic and a metric to describe our distribution bisimulation and discuss linearity, continuity and compositional properties.Comment: Accepted by FORMATS 201

Limit behaviour of upper and lower expected time averages in discrete-time imprecise Markov chains

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of ‘plausible’ transition probabilities. Our main result is a necessary and sufficient condition under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process’ initial state. Remarkably, our condition is considerably weaker than those needed to establish similar results for so-called limit—or steady state—upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages

The stubborn non-probabilist : "negation incoherence" and a new way to block the Dutch Book argument

We rigorously specify the class of nonprobabilistic agents which are, we argue, immune to the classical Dutch Book argument. We also discuss the notion of expected value used in the argument as well as sketch future research connecting our results to those concerning incoherence measures

Using Simulation Models to Evaluate Ape Nest Survey Techniques

BACKGROUND: Conservationists frequently use nest count surveys to estimate great ape population densities, yet the accuracy and precision of the resulting estimates are difficult to assess. METHODOLOGY/PRINCIPAL FINDINGS: We used mathematical simulations to model nest building behavior in an orangutan population to compare the quality of the population size estimates produced by two of the commonly used nest count methods, the 'marked recount method' and the 'matrix method.' We found that when observers missed even small proportions of nests in the first survey, the marked recount method produced large overestimates of the population size. Regardless of observer reliability, the matrix method produced substantial overestimates of the population size when surveying effort was low. With high observer reliability, both methods required surveying approximately 0.26% of the study area (0.26 km(2) out of 100 km(2) in this simulation) to achieve an accurate estimate of population size; at or above this sampling effort both methods produced estimates within 33% of the true population size 50% of the time. Both methods showed diminishing returns at survey efforts above 0.26% of the study area. The use of published nest decay estimates derived from other sites resulted in widely varying population size estimates that spanned nearly an entire order of magnitude. The marked recount method proved much better at detecting population declines, detecting 5% declines nearly 80% of the time even in the first year of decline. CONCLUSIONS/SIGNIFICANCE: These results highlight the fact that neither nest surveying method produces highly reliable population size estimates with any reasonable surveying effort, though either method could be used to obtain a gross population size estimate in an area. Conservation managers should determine if the quality of these estimates are worth the money and effort required to produce them, and should generally limit surveying effort to 0.26% of the study area, unless specific management goals require more intensive sampling. Using site- and time- specific nest decay rates (or the marked recount method) are essential for accurate population size estimation. Marked recount survey methods with sufficient sampling effort hold promise for detecting population declines

Incremental Verification of Parametric and Reconfigurable Markov Chains

The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for non-stochastic systems that allow to focus only on small instances, there is little hope that such approaches extend to the quantitative analysis of probabilistic systems, as the probabilities depend on the size of a system. The unicorn would be an automatic transformation of a parametrised system into a formula, which allows to plot, say, the likelihood to reach a goal or the expected costs to do so, against the parameters of a system. While such analysis exists for narrow classes of systems, such as waiting queues, we aim both lower---stepwise exploring the parameter space---and higher---considering general systems. The novelty is to heavily exploit the similarity between instances of parametrised systems. When the parameter grows, the system for the smaller parameter is, broadly speaking, present in the larger system. We use this observation to guide the elegant state-elimination method for parametric Markov chains in such a way, that the model transformations will start with those parts of the system that are stable under increasing the parameter. We argue that this can lead to a very cheap iterative way to analyse parametric systems, show how this approach extends to reconfigurable systems, and demonstrate on two benchmarks that this approach scales