Model Checking Temporal Logic Formulas Using Sticker Automata

Abstract

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.

Predicting the results of molecular specific hybridization using boosted tree algorithm

“…It is the gold standard to distinguish bacterial species . In addition, DNA model checking is another example, as shown in Section 5. These facts may help us understand the application prospects of this work in the real world.…”

“…In our previous studies, we presented a series of DNA algorithms to address the DNA model checking problem, which is a famous DNA computing problem proposed by a Turing Award winner Prof Emerson . In one of our previous experiments, we studied the following case on DNA model checking: whether the automaton M 2 in Figure satisfies the temporal logic formula ϕ 2 = (p 1 Uq 1 );(p 2 Uq 2 ) or not.…”