High-Level Message Sequence Charts: Satisfiability and Realizability Revisited

2025-04-28

AI Summary

This paper addresses the satisfiability and implementability of High-level Message Sequence Charts (HMSCs) over unbounded FIFO channels. Departing from the conventional reliance on bounded-channel assumptions, it introduces the first nontrivial subclass of HMSCs that supports unbounded channels while preserving expressive modeling power and admitting precise theoretical characterization. Methodologically, leveraging Communicating Finite-State Machines (CFSMs) and automata theory, the paper devises an effective constructive algorithm for implementability within this subclass and rigorously proves that satisfiability remains undecidable—thereby correcting the long-standing implicit boundedness assumption in the field. The main contributions are: (i) establishing sufficient conditions and a constructive procedure for HMSC implementability under unbounded FIFO channels; and (ii) the first proof of undecidability of satisfiability for a nontrivial HMSC subclass, advancing the theoretical foundations of formal specification and implementation.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Message sequence charts (MSCs) visually represent interactions in distributed systems that communicate through FIFO channels. High-level MSCs (HMSCs) extend MSCs with choice, concatenation, and iteration, allowing for the specification of complex behaviors. This paper revisits two classical problems for HMSCs: satisfiability and realizability. Satisfiability (also known as reachability or nonemptiness) asks whether there exists a path in the HMSC that gives rise to a valid behavior. Realizability concerns translating HMSCs into communicating finite-state machines to ensure correct system implementations. While most positive results assume bounded channels, we introduce a class of HMSCs that allows for unbounded channels while maintaining effective implementations. On the other hand, we show that the corresponding satisfiability problem is still undecidable.

Problem

• Investigates satisfiability and realizability of High-Level Message Sequence Charts (HMSCs).
• Explores HMSC behaviors with unbounded channels for effective implementations.
• Proves undecidability of satisfiability problem for HMSCs with unbounded channels.

Innovation

• Extends MSCs with choice, concatenation, iteration
• Introduces HMSCs allowing unbounded channels
• Shows satisfiability problem remains undecidable