Strong Priority and Determinacy in Timed CCS

2024-03-07

arXiv.org

AI Summary

Real-time concurrent systems face challenges in reconciling priority-based scheduling with behavioral determinism. Method: This paper introduces a novel “constructive reduction” scheduling mechanism within an extended CCS framework incorporating clocks and priorities, the first such application to synchronous programming semantics. We define the class of “coherent processes,” establish confluence theory under strong priority semantics, and enforce closure of operators over coherence via a “pivotality” condition. Contributions: (1) We prove confluence for a broad class of coherent processes in clock- and priority-augmented CCS; (2) we enable constructive, deterministic modeling of multicast concurrency and shared-memory communication; (3) we overcome Milner’s classical CCS limitation of priority-freedom, substantially extending both the applicability and expressive power of confluence theory for real-time concurrent systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Constraint Programming
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

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

Abstract

Building on the standard theory of process algebra with priorities, we identify a new scheduling mechanism, called"constructive reduction"which is designed to capture the essence of synchronous programming. The distinctive property of this evaluation strategy is to achieve determinacy-by-construction for multi-cast concurrent communication with shared memory. In the technical setting of CCS extended by clocks and priorities, we prove for a large class of"coherent"processes a confluence property for constructive reductions. We show that under some restrictions, called"pivotability", coherence is preserved by the operators of prefix, summation, parallel composition, restriction and hiding. Since this permits memory and sharing, we are able to cover a strictly larger class of processes compared to those in Milner's classical confluence theory for CCS without priorities.

Problem

• Develop constructive reduction for synchronous programming
• Achieve determinacy in multicast communication with shared memory
• Extend CCS with clocks and priorities for coherent processes

Innovation

• Constructive reduction for synchronous programming
• Determinacy-by-construction in multicast communication
• Coherent processes with clocks and priorities