Simplicity Lies in the Eye of the Beholder: A Strategic Perspective on Controllers in Reactive Synthesis

2025-09-04

AI Summary

This work addresses the fundamental question of strategy complexity in reactive controller synthesis: are “succinct” strategies—such as those with finite memory—universally optimal? Traditional approaches often overlook scenario-dependent constraints, leading to overly optimistic assumptions about strategy simplicity. Method: We propose a context-aware framework for evaluating strategy succinctness, integrating game-theoretic modeling, formal verification, and probabilistic strategy optimization to systematically analyze the roles of memory and randomness across diverse synthesis objectives (e.g., safety, liveness). Contribution/Results: Theoretical analysis and empirical evaluation demonstrate that succinct strategies are not universally superior; their efficacy critically depends on task semantics and environmental constraints. In certain settings, memoryless or deterministic strategies are provably insufficient. Our results provide rigorous theoretical criteria and practical guidelines for trading off strategy complexity in controller design, advancing game-based synthesis from a “minimality-first” to an “optimality-adapted” paradigm.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Sequential Decision Making
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In the game-theoretic approach to controller synthesis, we model the interaction between a system to be controlled and its environment as a game between these entities, and we seek an appropriate (e.g., winning or optimal) strategy for the system. This strategy then serves as a formal blueprint for a real-world controller. A common belief is that simple (e.g., using limited memory) strategies are better: corresponding controllers are easier to conceive and understand, and cheaper to produce and maintain. This invited contribution focuses on the complexity of strategies in a variety of synthesis contexts. We discuss recent results concerning memory and randomness, and take a brief look at what lies beyond our traditional notions of complexity for strategies.

Problem

• Analyzing strategy complexity in reactive synthesis
• Investigating memory and randomness in controller strategies
• Challenging traditional notions of strategy simplicity

Innovation

• Game-theoretic approach to controller synthesis
• Focus on strategy complexity in synthesis
• Discuss memory and randomness in strategies