Bisimilarity and Simulatability of Processes Parameterized by Join Interactions

2025-08-19

AI Summary

This paper addresses the challenge of process equivalence analysis under joint interaction. To this end, it introduces a weakened variant—*ji-parameterized bisimilarity*—generalizing Larsen’s classical parameterized bisimilarity. Methodologically, the approach integrates process algebra, joint interaction semantics, simulation preorders, and modal logic to construct a formal framework. The main contributions are threefold: (1) a rigorous definition of ji-parameterized bisimilarity, proven to coincide with Larsen’s original notion in deterministic settings and to be strictly coarser (i.e., less discriminating) in general; (2) an exact correspondence with a simulation preorder and a precise modal logic characterization; and (3) preservation of environmental discrimination power equivalent to Larsen’s framework, thereby enabling uniform modeling and equivalence checking for nondeterministic joint interaction behaviors.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Large-scale security measurements

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 & e and q & e of p and q with e are bisimilar. (Hereby join interactions r & f facilitate a step with label a to r' & 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.

Problem

• Defining bisimilarity for processes with unrestricted join interactions
• Comparing parameterized bisimilarity with its weakened variant
• Establishing equivalence between parameterized and ji-parameterized simulatability

Innovation

• Join-interaction parameterized bisimilarity for processes
• Weakening Larsen's parameterized bisimilarity concept
• Modal-logic characterization for simulatability equivalence