Realisability and Complementability of Multiparty Session Types

2025-07-23

AI Summary

This paper investigates realizability and complementability of global types in multiparty session types (MPST): realizability asks whether the projection of a global type yields precisely its intended local behaviors; complementability asks whether a global type exists whose projection describes complementary local behaviors. We first establish that realizability implies complementability and construct a global-type complement with linear blowup. For point-to-point communication, we devise a PSPACE algorithm to decide whether a complementary global type is realizable. In the synchronous model, we prove that all realizable global types are necessarily complementable. Our work integrates formal type theory, projection semantics, constructive complementation, and complexity analysis to unify the relationship between these two fundamental properties. The results provide both theoretical foundations and algorithmic support for completeness verification and protocol synthesis in MPST.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Multiparty session types (MPST) are a type-based approach for specifying message-passing distributed systems. They rely on the notion of global type specifying the global behaviour and local types, which are the projections of the global behaviour onto each local participant. An essential property of global types is realisability, i.e., whether the composition of the local behaviours conforms to those specified by the global type. We explore how realisability of MPST relates to their complementability, i.e., whether there exists a global type that describes the complementary behaviour of the original global type. First, we show that if a global type is realisable with p2p communications, then it is realisable with synchronous communications. Second, we show that if a global type is realisable in the synchronous model, then it is complementable, in the sense that there exists a global type that describes the complementary behaviour of the original global type. Third, we give an algorithm to decide whether a complementable global type, given with an explicit complement, is realisable in p2p. The algorithm is PSPACE in the size of the global type and its complement. As a side contribution, we propose a complementation construction for global types with sender-driven choice with a linear blowup in the size of the global type.

Problem

• Investigates realisability of multiparty session types in distributed systems
• Explores complementability of global types in synchronous communication models
• Provides algorithm for checking realisability in p2p with explicit complements

Innovation

• Realisability with p2p implies synchronous realisability
• Synchronous realisability ensures complementability existence
• PSPACE algorithm decides p2p realisability with complement