{"ID":2880576,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13611","arxiv_id":"2508.13611","title":"Bisimilarity and Simulatability of Processes Parameterized by Join Interactions","abstract":"Departing from Larsen's concept of parameterized bisimilarity of processes with respect to interaction with environments, we start an exploration of its natural weakening: bisimilarity of unrestricted join interactions with environments. Parameterized bisimilarity relates processes p and q with respect to an environment e if p and q behave bi-similarly while joining -- respectively the same -- transitions from e. The weakened variant relates processes p and q with respect to environment e if the join-interaction processes p \u0026 e and q \u0026 e of p and q with e are bisimilar. (Hereby join interactions r \u0026 f facilitate a step with label a to r' \u0026 f' if and only if r and f permit a-steps to r' and f' , respectively.) Join-interaction parameterized (ji-parameterized) bisimilarity coincides with parameterized bisimilarity for deterministic environments, but that it is a coarser equivalence in general. We explain how Larsen's concept can be recovered from ji-parameterized bisimilarity by 'determinizing' interactions. We show that by adaptation to simulatability (simulation preorder) the same concept arises: parameterized simulatability coincides with ji-parameterized simulatability. For the discrimination preorder of (ji-)parameterized simulatability on environments we obtain the same result as Larsen did for parameterized bisimilarity. Also, we give a modal-logic characterization of (ji-)parameterized simulatability. Finally we gather open problems, and provide an outlook on our current related work.","short_abstract":"Departing from Larsen's concept of parameterized bisimilarity of processes with respect to interaction with environments, we start an exploration of its natural weakening: bisimilarity of unrestricted join interactions with environments. Parameterized bisimilarity relates processes p and q with respect to an environmen...","url_abs":"https://arxiv.org/abs/2508.13611","url_pdf":"https://arxiv.org/pdf/2508.13611v1","authors":"[\"Clemens Grabmayer\",\"Maurizio Murgia\"]","published":"2025-08-19T08:16:42Z","proceeding":"cs.PL","tasks":"[\"cs.PL\",\"cs.LO\"]","methods":"[\"LoRA\"]","has_code":false}