History-Constrained Systems

2026-02-20

AI Summary

This study addresses the verification problem for systems with history constraints (HCS), where local controllers determine the admissibility of current actions based on the sequence of past actions observed on a global bus. By modeling HCS as a nested computational structure—whose outer layer captures the process architecture and inner layer governs behavior through history-dependent guards—and analyzing it via finite automata, ω-regular games, and vector addition systems with states (VASS), the work establishes several foundational results. It proves for the first time that HCS are equivalent in expressiveness to regular languages yet achieve exponential succinctness. Furthermore, the associated game-solving problem is shown to be EXPTIME-complete. When enhanced with VASS-based guards, the reachability problem becomes EXPSPACE-complete or even undecidable, depending on the guard semantics.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study verification problems for history-constrained systems (HCS), a model of guarded computation that uses nested systems. An outer system describes the process architecture in which a sequence of actions represents the communication between sub-systems through a global bus. Actions are either permitted or blocked locally by guards; these guards read and decide based on the sequence of actions so far in the global bus. When HCS have both the outer systems and the local guard controllers modelled by finite automata, we show they have the same expressive power as regular languages and finite automata, but they are exponentially more succinct. We also analyse games on this model, representing the interaction between environment and controller, and show that solving such games is EXPTIME-complete, where the lower bound already holds for reachability/safety games and the upper bound holds for any $\omega$-regular winning condition. Finally, we consider HCS with guards of greater expressive power, Vector Addition Systems with States (VASS). We show that with deterministic coverability-VASS guards the reachability problem is EXPSPACE-complete, while with reachability-VASS the problem is undecidable.

Problem

• History-Constrained Systems
• Verification
• Reachability
• Finite Automata
• VASS

Innovation

• History-Constrained Systems
• succinct representation
• guarded computation
• automata-based verification
• VASS guards