Parameterized Infinite-State Reactive Synthesis

2025-08-01

AI Summary

This work addresses the automated synthesis of correct programs for parametric infinite-state systems—programs guaranteed to satisfy specifications under arbitrary parameter instantiations. We propose a counterexample-guided cyclic synthesis framework that integrates anti-unification with syntax-guided synthesis (SyGuS) to generalize concrete program instances into parametric programs, while simultaneously synthesizing parametric invariants and ranking functions as formal verification evidence. Unlike conventional CEGIS, which assumes fixed parameters, our approach explicitly models data and environment parameters within specifications, enabling joint derivation of parametric programs and their correctness proofs. We evaluate the method on extended literature benchmarks and novel case studies, successfully synthesizing several parametric reactive systems and providing formal correctness guarantees across all parameter configurations.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• 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
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We propose a method to synthesize a parameterized infinite-state systems that can be instantiated for different parameter values. The specification is given in a parameterized temporal logic that allows for data variables as well as parameter variables that encode properties of the environment. Our synthesis method runs in a counterexample-guided loop consisting of four main steps: First, we use existing techniques to synthesize concrete systems for some small parameter instantiations. Second, we generalize the concrete systems into a parameterized program. Third, we create a proof candidate consisting of an invariant and a ranking function. Fourth, we check the proof candidate for consistency with the program. If the proof succeeds, the parameterized program is valid. Otherwise, we identify a parameter value for which the proof fails and add a new concrete instance to step one. To generalize programs and create proof candidates, we use a combination of anti-unification and syntax-guided synthesis to express syntactic differences between programs as functions of the parameters. We evaluate our approach on examples from the literature that have been extended with parameters as well as new problems.

Problem

• Synthesize parameterized infinite-state systems for varying parameters
• Verify systems using parameterized temporal logic specifications
• Generalize concrete systems into parameterized programs via anti-unification

Innovation

• Parameterized infinite-state system synthesis method
• Counterexample-guided loop with four steps
• Anti-unification and syntax-guided synthesis combination