A novel ergodic cellular automaton model of gene-protein network is presented. It shown that the presented can predict occurrences typical nonlinear phenomena a conventional ordinary differential equation model. In addition, theoretical analysis methods are proposed. Using methods, an important advantage revealed: better suited to compared regular (standard) automaton. Furthermore, implemented ...

Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verifica...

• F ⊆ Q is the set of accept or final states. The behavior of a DFA M on an input string x ∈ Σ∗ is as follows. It reads the symbols in x one at a time, from left to right. At each point in time, the automaton has a current state. Initially, the automaton is in state s. If the current state of the automaton is q, and the next symbol in x to be read is a, then the automaton on reading a transitio...

A central result in the theory of ω-automata is McNaughton's Theorem which states that every Buchi automaton is equivalent to a deterministic Muller automaton. The complexity of McNaughton's algorithm is huge. Safra provided an optimal construction. Safra's algorithm converts a Buchi automaton with n states to a deterministic Rabin automaton with n states. Much e orts have been invested to redu...