Concurrency, Causality and Conflict via Independence in Reversible Calculi

Computer Science > Logic in Computer Science [Submitted on 16 Sep 2026] Title:Concurrency, Causality and Conflict via Independence in Reversible Calculi View PDF HTML (experimental)Abstract:Among the different ways of approaching the semantics of process calculi, true-concurrency models stand out for their ability to highlight subtle interplays between events. At their heart lie three crucial relations: concurrency, causality and conflict. This paper shows that reversibility, when endowed with a notion of independence, provides a rich tooling to study and characterise these true-concurrency relations. First, we prove that systems admitting pre-reversibility (i.e., that can be extended with an independence relation satisfying some basic axioms) have a unique notion of independence, events, concurrency, causality and conflict. We then analyse the relationship between independence and the true-concurrency relations, establishing novel independence-based characterisations of causality and conflict. Our second series of contributions revolves around two concrete process calculi and two syntactic notions defined on their transition labels, namely independence and dependence; we prove that they partition connected transitions and characterise elegantly concurrency on adjacent transitions. This part of our development was machine-checked using the proof assistant Beluga. Last, we study how the key mechanism commonly used in reversible process algebra can be used as a proxy to retrieve causality and core independence on past events. We conclude by discussing how our results extend beyond reversible systems. Ancillary-file links: Ancillary files (details): - LICENSE - README.md - beluga_cloc_config.txt - code/bijection/bijection.bel - code/bijection/definitions.bel - code/bijection/functionality.bel - code/bijection/lemmas-lifting.bel - code/bijection/totality.bel - code/ccsk/axioms/bti.bel - code/ccsk/axioms/cire.bel - code/ccsk/axioms/defs-and-properties.bel - code/ccsk/axioms/ed.bel - code/ccsk/axioms/events.bel - code/ccsk/axioms/id.bel - code/ccsk/axioms/ire.bel - code/ccsk/axioms/pci.bel - code/ccsk/axioms/rpi.bel - code/ccsk/axioms/sp.bel - code/ccsk/axioms/wf.bel - code/ccsk/basic-properties.bel - code/ccsk/complementarity.bel - code/ccsk/definitions.bel - code/ccsk/unique-step.bel - code/ccskp/axioms/bti.bel - code/ccskp/axioms/cire.bel - code/ccskp/axioms/defs-and-properties.bel - code/ccskp/axioms/ed.bel - code/ccskp/axioms/events.bel - code/ccskp/axioms/fld.bel - code/ccskp/axioms/id.bel - code/ccskp/axioms/ire.bel - code/ccskp/axioms/pci.bel - code/ccskp/axioms/rpi.bel - code/ccskp/axioms/sp.bel - code/ccskp/axioms/wf.bel - code/ccskp/basic-properties.bel - code/ccskp/complementarity.bel - code/ccskp/connectedness-relationship-one.bel - code/ccskp/connectedness-relationship-two.bel - code/ccskp/definitions.bel - code/ccskp/lemmas-bijection.bel - code/ccskp/lemmas-connectedness-one.bel - code/ccskp/lemmas-connectedness-two.bel - code/ccskp/unique-step.bel - code/ccskp/unique.bel - code/shared/basic-properties.bel - code/shared/definitions.bel - code/shared/unique.bel - examples/causality-relations/connectedness.bel - examples/causality-relations/dependence.bel - examples/causality-relations/independence.bel - examples/examples-paper.bel - examples/processes/keyed.bel - examples/processes/standard.bel - examples/processes/stuck-keyed.bel - examples/processes/stuck-std.bel - examples/proof-labels/not-valid.bel - examples/proof-labels/valid.bel - examples/transitions/backward-transitions-ccsk.bel - examples/transitions/backward-transitions-ccskp.bel - examples/transitions/events.bel - examples/transitions/forward-transitions-ccsk.bel - examples/transitions/forward-transitions-ccskp.bel - examples/transitions/stuck-keyed-ccsk.bel - examples/transitions/stuck-keyed-ccskp.bel - examples/transitions/stuck-std-ccsk.bel - examples/transitions/stuck-std-ccskp.bel - makefile - overview.md - run/code.cfg - run/examples/ex-causality-relations.cfg - run/examples/ex-paper.cfg - run/examples/ex-processes.cfg - run/examples/ex-proof-labels.cfg - run/examples/ex-transitions.cfg - run_all.cfg References & Citations Loading... 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