Symbolic Synthesis for LTLf+ Obligations

2026-04-20

AI Summary

This work addresses the synthesis problem for LTLf specifications extended with obligation properties—i.e., positive Boolean combinations of safety and guarantee properties—over infinite traces. To this end, it introduces a novel approach that directly constructs a symbolic deterministic weak automaton (DWA) for infinite traces from the symbolic DFA of an LTLf prefix property. Leveraging the favorable algorithmic properties of DWAs, the method enables efficient synthesis, achieving linear-time synthesis after automaton construction and supporting polynomial-time minimization and game solving. Experimental results demonstrate that the proposed framework attains synthesis performance comparable to classical LTLf approaches, confirming its efficiency and practicality.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• 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

Abstract

We study synthesis for obligation properties expressed in LTLfp, the extension of LTLf to infinite traces. Obligation properties are positive Boolean combinations of safety and guarantee (co-safety) properties and form the second level of the temporal hierarchy of Manna and Pnueli. Although obligation properties are expressed over infinite traces, they retain most of the simplicity of LTLf. In particular, we show that they admit a translation into symbolically represented deterministic weak automata (DWA) obtained directly from the symbolic deterministic finite automata (DFA) for the underlying LTLf properties on trace prefixes. DWA inherit many of the attractive algorithmic features of DFA, including Boolean closure and polynomial-time minimization. Moreover, we show that synthesis for LTLfp obligation properties is theoretically highly efficient - solvable in linear time once the DWA is constructed. We investigate several symbolic algorithms for solving DWA games that arise in the synthesis of obligation properties and evaluate their effectiveness experimentally. Overall, the results indicate that synthesis for LTLfp obligation properties can be performed with virtually the same effectiveness as LTLf synthesis.

Problem

• LTLfp
• obligation properties
• symbolic synthesis
• infinite traces
• temporal hierarchy

Innovation

• LTLfp
• obligation properties
• symbolic synthesis
• deterministic weak automata
• DWA games