Multi-Property Synthesis

2026-01-15

AI Summary

This work addresses the challenge of efficiently synthesizing a strategy that realizes the largest satisfiable subset of specifications in LTLf synthesis when multiple specifications cannot be simultaneously satisfied. The authors propose a fully symbolic algorithm that, through a single fixed-point computation, directly associates realizable sets of objectives with states in the product game, thereby avoiding the enumeration of exponentially many subsets. By introducing Boolean objective variables and exploiting objective monotonicity, the method compactly encodes all possible objective combinations, significantly improving computational efficiency. Experimental results demonstrate that the approach achieves up to two orders of magnitude speedup compared to baseline enumeration-based methods.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study LTLf synthesis with multiple properties, where satisfying all properties may be impossible. Instead of enumerating subsets of properties, we compute in one fixed-point computation the relation between product-game states and the goal sets that are realizable from them, and we synthesize strategies achieving maximal realizable sets. We develop a fully symbolic algorithm that introduces Boolean goal variables and exploits monotonicity to represent exponentially many goal combinations compactly. Our approach substantially outperforms enumeration-based baselines, with speedups of up to two orders of magnitude.

Problem

• LTLf synthesis
• multi-property
• realizability
• goal maximization
• symbolic algorithm

Innovation

• LTLf synthesis
• multi-property synthesis
• symbolic algorithm
• goal monotonicity
• fixed-point computation