Modeling with history-dependent Petri nets

Most information systems that are driven by process models (e.g., workflow management systems) record events in event logs, also known as transaction logs or audit trails. We consider processes that not only keep track of their history in a log, but also make decisions based on this log. Extending our previous work on history-dependent Petri nets we propose and evaluate a methodology for modelling processes by such nets and show how history-dependent nets can combine modelling comfort with analysability

Synchronous counting and computational algorithm design

Consider a complete communication network on n nodes, each of which is a state machine with s states. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are “odd” and which are “even”. We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states s. We use computational techniques to construct very compact deterministic algorithms for the first non-trivial case of f = 1. While no algorithm exists for n < 4, we show that as few as 3 states are sufficient for all values n ≥ 4. We prove that the problem cannot be solved with only 2 states for n = 4, but there is a 2-state solution for all values n ≥ 6.Peer reviewe

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

Tableau calculi for answer set programming

We introduce a formal proof system based on tableau methods for analyzing computations made in Answer Set Programming (ASP). Our approach furnishes declarative and fine-grained instruments for characterizing operations as well as strategies of ASP-solvers. First, the granulation is detailed enough to capture the variety of propagation and choice operations of algorithms used for ASP; this also includes SAT-based approaches. Second, it is general enough to encompass the various strategies pursued by existing ASP-solvers. This provides us with a uniform framework for identifying and comparing fundamental properties of algorithms. Third, the approach allows us to investigate the proof complexity of algorithms for ASP, depending on choice operations. We show that exponentially different best-case computations can be obtained for different ASP-solvers. Finally, our approach is flexible enough to integrate new inference patterns, so to study their relation to existing ones. As a result, we obtain a novel approach to unfounded set handling based on loops, being applicable to non-SAT-based solvers. Furthermore, we identify backward propagation operations for unfounded sets