Between quantum logic and concurrency

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842

Orthomodular Lattices Induced by the Concurrency Relation

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Soundness-preserving composition of synchronously and asynchronously interacting workflow net components

In this paper, we propose a compositional approach to construct formal models of complex distributed systems with several synchronously and asynchronously interacting components. A system model is obtained from a composition of individual component models according to requirements on their interaction. We represent component behavior using workflow nets - a class of Petri nets. We propose a general approach to model and compose synchronously and asynchronously interacting workflow nets. Through the use of Petri net morphisms and their properties, we prove that this composition of workflow nets preserves component correctness.Comment: Preprint of the paper submitted to "Fundamenta Informaticae

Reverse Bisimulations on Stable Configuration Structures

The relationships between various equivalences on configuration structures, including interleaving bisimulation (IB), step bisimulation (SB) and hereditary history-preserving (HH) bisimulation, have been investigated by van Glabbeek and Goltz (and later Fecher). Since HH bisimulation may be characterised by the use of reverse as well as forward transitions, it is of interest to investigate forms of IB and SB where both forward and reverse transitions are allowed. We give various characterisations of reverse SB, showing that forward steps do not add extra power. We strengthen Bednarczyk's result that, in the absence of auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that we need only exclude auto-concurrent events at the same depth in the configuration

A Logic with Reverse Modalities for History-preserving Bisimulations

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natural sublogics of EIL correspond to coarser equivalences. In particular we provide logical characterisations of weak history-preserving (WH) and history-preserving (H) bisimulation. Logics corresponding to HH and H bisimulation have been given previously, but not to WH bisimulation (when autoconcurrency is allowed), as far as we are aware. We also present characteristic formulas which characterise individual structures with respect to history-preserving equivalences.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Application and Theory of Petri Nets33rd International Conference, PETRI NETS 2012, Hamburg, Germany, June 25-29, 2012. Proceedings /

XI, 419p.online resource

Non-Interference Notions Based on Reveals and Excludes Relations for Petri Nets

Abstract. In distributed systems, it is often important that a user is not able to infer if a given action has been performed by another component, while still being able to interact with that component. This kind of problems has been studied with the help of a notion of "interference" in formal models of concurrent systems (e.g. CCS, Petri nets). Here, we propose several new notions of interference for ordinary Petri nets, study some of their properties, and compare them with notions already proposed in the literature. Our new notions rely on the unfolding of Petri nets, and on an adaptation of the "reveals" relation for ordinary Petri nets, previously defined on occurrence nets, and on a new relation, called "excludes", here introduced for detecting negative information flow