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4.2 Satisfiability, validity, and model checking We have seen that logic provides many examples of problems which are studied in complexity theory.

By utilizing automatic and exhaustive verification of model checking, we found that previous models cannot properly capture essential checkpoint conditions in the presence of timing variations.

Then, after we know that the event potassium outside the cell ends happens, through model checking, we can focus the other approaches to identify and understand it better.

In the synchronous model checking, we assume that all the events occur synchronously, i.e., the state of each node is updated at the same time.

Furthermore, using model checking we have shown that these events happen infinitely often.

We prefix these specifications so as to express the possibility (EX) to reach the appropriate attractor from at least one initial state, and the necessity (AX) to leave the switch-off steady state for all initial states in switch-on conditions: Using symbolic model checking, we test the feasibility of ϕ3.

To further improve model checking performance, we show how to embed our approach into an extension of counterexample guided abstraction refinement with Craig interpolants.

Besides well-known LTL and CTL model checking algorithms, we adapt a previously unexplored form of the liveness-to-safety approach to the problem.

Following the logical model checking step, we then incorporated currently available information on biochemical reactions in order to derive a more detailed reaction-rate model of curli regulation.

Using the synchronous and asynchronous model checking methods, we can test this type of dynamic behaviors in the ER-Golgi network through verifying the following CTL formulas.

Using the model checking method, we verified several Alzheimer's disease and cancer-related properties, and also identified important proteins (NFκB, ATF4, ASK1 and TRAF2) in the ER-Golgi network, which might be responsible for the pathogenesis of cancer and AD.