Characterizing Implementability of Global Protocols with Infinite States and Data

2024-11-08

arXiv.org

AI Summary

This paper investigates the distributed asynchronous realizability of symbolic multiparty communication protocols—featuring infinite states and data values—i.e., whether a global protocol can be decomposed into deadlock-free, behaviorally equivalent local implementations. Methodologically, it introduces the first unified semantic characterization of realizability based on (co-)reachability, systematically classifying all sources of unrealizability; develops the first sound and relatively complete realizability decision algorithm for symbolic protocols; and integrates dependency-refining predicates, protocol projection, and (co-)reachability analysis with complexity-theoretic reductions. Contributions include: (i) establishing co-NP-completeness for realizability under explicit finite representations, and PSPACE-completeness under symbolic representations; and (ii) tightening the complexity upper bound for classic session type fragments from PSPACE to co-NP—thereby achieving a precise, optimal characterization.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

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: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We study the implementability problem for an expressive class of symbolic communication protocols involving multiple participants. Our symbolic protocols describe infinite states and data values using dependent refinement predicates. Implementability asks whether a global protocol specification admits a distributed, asynchronous implementation, namely one for each participant, that is deadlock-free and exhibits the same behavior as the specification. We provide a unified explanation of seemingly disparate sources of non-implementability through a precise semantic characterization of implementability for infinite protocols. Our characterization reduces the problem of implementability to (co)reachability in the global protocol restricted to each participant. This compositional reduction yields the first sound and relatively complete algorithm for checking implementability of symbolic protocols. We use our characterization to show that for finite protocols, implementability is co-NP-complete for explicit representations and PSPACE-complete for symbolic representations. The finite, explicit fragment subsumes a previously studied fragment of multiparty session types for which our characterization yields a co-NP decision procedure, tightening a prior PSPACE upper bound.

Problem

• Characterize implementability of infinite symbolic protocols
• Reduce implementability to (co)reachability in global protocols
• Provide sound and complete algorithm for implementability checking

Innovation

• Dependent refinement predicates used
• Reduction to (co)reachability achieved
• Sound completeness algorithm developed