On Synthesis of Timed Regular Expressions

2025-09-07

AI Summary

This paper addresses the synthesis of Timed Regular Expressions (TREs) for cyber-physical systems: given positive (accept) and negative (reject) behavioral traces, it generates the shortest TRE semantically consistent with the specification. We first establish that TRE synthesis is decidable. Our method proceeds in two stages: (1) parameterized TRE enumeration augmented with prefix/suffix equivalence-based pruning to efficiently generate candidate expressions; and (2) encoding consistency checking as an SMT formula over real-valued timing constraints, followed by SMT solving for both validation and time-parameter synthesis. Evaluation on randomized benchmarks and real-world case studies demonstrates the approach’s effectiveness and scalability, significantly outperforming existing heuristic methods. Key contributions include the decidability proof for TRE synthesis, a sound and complete two-stage minimization framework, and an efficient implementation leveraging modern SMT solvers for timed automata–like reasoning.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Timed regular expressions serve as a formalism for specifying real-time behaviors of Cyber-Physical Systems. In this paper, we consider the synthesis of timed regular expressions, focusing on generating a timed regular expression consistent with a given set of system behaviors including positive and negative examples, i.e., accepting all positive examples and rejecting all negative examples. We first prove the decidability of the synthesis problem through an exploration of simple timed regular expressions. Subsequently, we propose our method of generating a consistent timed regular expression with minimal length, which unfolds in two steps. The first step is to enumerate and prune candidate parametric timed regular expressions. In the second step, we encode the requirement that a candidate generated by the first step is consistent with the given set into a Satisfiability Modulo Theories (SMT) formula, which is consequently solved to determine a solution to parametric time constraints. Finally, we evaluate our approach on benchmarks, including randomly generated behaviors from target timed models and a case study.

Problem

• Synthesizing timed regular expressions from system behaviors
• Generating minimal expressions accepting positive and rejecting negative examples
• Solving SMT formulas for consistent parametric time constraints

Innovation

• Synthesis of timed regular expressions
• Minimal length expression generation
• SMT-based constraint solving method