First-order store and visibility in name-passing calculi

2025-04-24

AI Summary

This paper addresses the behavioral complexity arising from higher-order value storage in the π-calculus by introducing the first visibility-based type system that enforces first-order value storage, thereby enabling fine-grained control over computational structure. Methodologically, it pioneers the integration of the game-semantic notion of visibility into π-calculus typing, establishing precise characterizations of may-testing equivalence and barbed equivalence under two distinct constraints: sequentiality and well-bracketing. Specifically, may-testing equivalence is characterized by visibility-driven labeled bisimilarity, while barbed equivalence is captured by trace equivalence. The work unifies behavioral equivalence theories across diverse computational paradigms, substantially strengthening the semantic foundations of name-passing calculi under restricted storage conditions. It thus provides novel formal tools for designing secure and verifiable concurrent programs.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

The $pi$-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how $pi$-calculus processes can be controlled so that computations can only involve storage of first-order values. The discipline is enforced by a type system that is based on the notion of visibility, coming from game semantics. We discuss the impact of visibility on the behavioural theory. We propose characterisations of may-testing and barbed equivalence, based on (variants of) trace equivalence and labelled bisimilarity, in the case where computation is sequential, and in the case where computation is well-bracketed.

Problem

• Control π-calculus processes for first-order storage
• Enforce discipline via visibility-based type system
• Characterize may-testing and barbed equivalence variants

Innovation

• Enforce first-order storage via typing
• Use visibility from game semantics
• Characterize equivalences for sequential computation