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Global Protocols under Rendezvous Synchrony: From Realizability to Type Checking

Elaine Li, Felix Stutz

TL;DR

The paper investigates synchronous realizability of global protocols under rendezvous synchronization, establishing decidability and complexity results for transitive concurrency alphabets and identifying EXPTIME bounds for unambiguous trace languages. It advances trace-theoretic methods by connecting global protocols to canonical SCSMs and providing reductions that yield 2-EXPTIME and 3-EXPTIME (respectively) upper bounds, while also proving undecidability in general. A novel type system for pi-calculus processes against local SCSMs is introduced, capable of handling mixed choice, session interleaving, and delegation. The work integrates with MST and HMSCs literature, clarifying the frontiers of realizability and verification and outlining future work on infinite-state and symbolic protocols.

Abstract

Global protocol specifications are the starting point of top-down verification methodologies, and serve as a blueprint for synthesizing local specifications that guarantee the correctness of distributed implementations. In this work, we study global protocol specifications targeting distributed processes that communicate via rendezvous synchrony. We obtain the following positive results for the synchronous realizability problem: (a) realizability is decidable for global protocols over a transitive concurrency alphabet in 2-EXPTIME in the size of the protocol, and in 3-EXPTIME in the size of the alphabet, and (b) realizability is decidable in EXPTIME for global protocols that unambiguously represent their trace language. Unambiguous global protocols encompass fragments of directed and sender-driven choice protocols studied in prior work. Further, our reductions admit the corollary that the synchronous verification problem is solvable with the same complexity, where a candidate realization is included as part of the input. We then prove a negative result stating that synchronous realizability is undecidable in general. Finally, we propose a type system to check pi-calculus processes against local specifications in the form of synchronous communicating state machines. Our type system is the first to support processes with local mixed choice in the presence of session interleaving and~delegation.

Global Protocols under Rendezvous Synchrony: From Realizability to Type Checking

TL;DR

The paper investigates synchronous realizability of global protocols under rendezvous synchronization, establishing decidability and complexity results for transitive concurrency alphabets and identifying EXPTIME bounds for unambiguous trace languages. It advances trace-theoretic methods by connecting global protocols to canonical SCSMs and providing reductions that yield 2-EXPTIME and 3-EXPTIME (respectively) upper bounds, while also proving undecidability in general. A novel type system for pi-calculus processes against local SCSMs is introduced, capable of handling mixed choice, session interleaving, and delegation. The work integrates with MST and HMSCs literature, clarifying the frontiers of realizability and verification and outlining future work on infinite-state and symbolic protocols.

Abstract

Global protocol specifications are the starting point of top-down verification methodologies, and serve as a blueprint for synthesizing local specifications that guarantee the correctness of distributed implementations. In this work, we study global protocol specifications targeting distributed processes that communicate via rendezvous synchrony. We obtain the following positive results for the synchronous realizability problem: (a) realizability is decidable for global protocols over a transitive concurrency alphabet in 2-EXPTIME in the size of the protocol, and in 3-EXPTIME in the size of the alphabet, and (b) realizability is decidable in EXPTIME for global protocols that unambiguously represent their trace language. Unambiguous global protocols encompass fragments of directed and sender-driven choice protocols studied in prior work. Further, our reductions admit the corollary that the synchronous verification problem is solvable with the same complexity, where a candidate realization is included as part of the input. We then prove a negative result stating that synchronous realizability is undecidable in general. Finally, we propose a type system to check pi-calculus processes against local specifications in the form of synchronous communicating state machines. Our type system is the first to support processes with local mixed choice in the presence of session interleaving and~delegation.
Paper Structure (42 sections, 54 theorems, 15 equations, 4 figures)

This paper contains 42 sections, 54 theorems, 15 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Words.
  4. Message Alphabets.
  5. Finite Automata.
  6. Global Protocols.
  7. Restricting Protocols to Participants.
  8. Synchronous Communicating State Machines.
  9. Synchronous Product of an SCSM
  10. Synchronous Protocol Semantics.
  11. Realizability
  12. Trace theory preliminaries
  13. Traces and Trace Languages.
  14. Rational, Recognizable, and Unambiguous Trace Languages.
  15. Equivalence, Inclusion and Multiplicity Equivalence
  16. ...and 27 more sections

Key Result

proposition 1

Let $\mathcal{G}$ be a global protocol. Then, it holds that $\mathcal{L}_{\mathit{sync}}(\mathcal{G}) = [\mathcal{L}(\mathcal{G})]_\equiv$ and $\mathcal{L}_{\mathit{sync}}(\mathcal{G})$ is a rational trace language over the concurrent alphabet $(\Gamma, \equiv)$, existentially defined by $\mathcal{L

Figures (4)

  • Figure 1: A global protocol (\ref{['fig:receiver-power-sync-protocol']}), local specifications as finite automata (\ref{['fig:receiver-power-sync-p']}, \ref{['fig:receiver-power-sync-q']}, and \ref{['fig:receiver-power-sync-r']}), and implementations as $\pi$-calculus processes (\ref{['fig:receiver-power-sync-procs']}).
  • Figure 2: Contextualization of our positive results. Known results DBLP:conf/ppdp/GiustoLU25 are depicted in gray. Sets denote trace languages (existentially) represented by regular string languages. For every set without a complexity annotation, its complexity is the smallest of all supersets.
  • Figure 3: Reduction rules for processes.
  • Figure 4: Typing rules for processes.

Theorems & Definitions (77)

  • definition 1: Synchronous Realizability Problem
  • definition 2: Synchronous Verification Problem
  • Remark 3.1
  • definition 3
  • proposition 1
  • proposition 2
  • definition 4: Canonical SCSM
  • lemma 1
  • lemma 2
  • lemma 3
  • ...and 67 more