AI summaryⓘ
The authors study how to automatically create systems that satisfy certain time-based rules called obligation properties, which are a mix of safety (nothing bad happens) and guarantee (something good eventually happens) rules over infinite sequences. They show these properties can be translated into a special kind of mathematical machine called deterministic weak automata, which are easy to work with because they build on simpler automata for finite sequences. This makes the problem of synthesizing such systems very efficient, solvable in linear time after building the automaton. They also test several algorithms for this synthesis and find it performs almost as well as synthesis for finite-sequence rules.
LTLfpobligation propertiessafety propertiesguarantee propertiesdeterministic weak automatadeterministic finite automatatemporal logicsynthesisautomata theorytemporal hierarchy
Authors
Giuseppe De Giacomo, Christian Hagemeier, Daniel Hausmann, Nir Piterman
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.