Symbolic Synthesis for LTLf+ Obligations

TL;DR

This paper introduces a symbolic synthesis method for obligation properties in LTLfp, extending LTLf to infinite traces, and demonstrates its efficiency and practical effectiveness.

Contribution

It presents a novel translation of LTLfp obligation properties into deterministic weak automata, enabling linear-time synthesis and efficient symbolic algorithms.

Findings

Synthesis for LTLfp obligation properties is highly efficient, comparable to LTLf.

Obligation properties can be translated into deterministic weak automata from LTLf automata.

Experimental results show the effectiveness of symbolic algorithms for DWA games.

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.