Succinctness issues for LTL and safety and cosafety fragments of LTL
Year: 2024
Type: article
Abstract: Linear Temporal Logic over finite traces ( LTL f ) has proved itself to be an important and effective formalism in formal verification as well as in artificial intelligence. Pure past LTL f ( pLTL ) is the variant of LTL f featuring only past temporal modalities, and is naturally interpreted at the end of a finite trace. It is known that each property definable in LTL f is also definable in pLTL , and vice versa (they are expressively equivalent). The same goes for the safety and cosafety fragments of Linear Temporal Logic over infinite traces ( LTL ), when compared to G ( pLTL ) and F ( pLTL ) formulas, respectively, that is, pLTL formulas prefixed by a globally and an eventually modality. However, despite being extensively used in practice, to the best of our knowledge, there is no systematic study of their succinctness. Moreover, when considering (co)safety fragments of LTL devoid of binary temporal modalities, there are no known characterizations based on pLTL . In this paper, we investigate succinctness issues for LTL f and (co)safety fragments of LTL when compared with their pure past counterparts. First, we provide a pure past characterization of the (co)safety fragments of LTL devoid of binary temporal modalities. Then, we prove that the (co)safety fragments of LTL have pure past counterparts that can be exponentially more succinct. Finally, we show that the same holds for LTL f with respect to pLTL , and viceversa: LTL f and pLTL are incomparable when succinctness is concerned.
Source: Information and Computation
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,630
OpenAlex ID: W4405515709