Computation Tree Logic Formula Model Checking Using DNA Computing

Computation tree logic model checking is a formal verification technology that can ensure the correctness of systems. The vast storage density of deoxyribonucleic acid (DNA) molecules and the massive parallelism of DNA computing offer new methods for computation tree logic model checking. In this study, we propose a computation tree logic model checking method based on DNA computing. First, a system to-be-checked and a computation tree logic formula are encoded by single-stranded DNA molecules. Second, these singlestranded DNA molecules are mixed to spontaneously hybridize and form partial or complete double-stranded molecules. Finally, a series of molecular manipulations are applied to detect the double-stranded molecules so that the result whether the system satisfies the computation tree logic formula is obtained. Biological simulations confirm the validity of the new method.

An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

We describe a set of simple features that are sufficient in order to make the satisfiability problem of logics interpreted on trees Tower-hard. We exhibit these features through an Auxiliary Logic on Trees (), a modal logic that essentially deals with reachability of a fixed node inside a forest and features modalities from sabotage modal logic to reason on submodels. After showing that admits a Tower-complete satisfiability problem, we prove that this logic is captured by four other logics that were independently found to be Tower-complete: two-variables separation logic, quantified computation tree logic, modal logic of heaps and modal separation logic. As a by-product of establishing these connections, we discover strict fragments of these logics that are still non-elementary.