It is well-known that the simplest and most important type of automata is

finite automata. After the introduction of fuzzy set theory by [47] Zadeh in 1965, the first mathematical formulation of fuzzy automata was proposed by[46] Wee in 1967, considered as a generalization of fuzzy automata theory.

output multipattern detection model of complex event; In the realizing step of constructing multipattern detection model above, the main function of state transfer function is to realize the state transition path of

finite automata. The primary function of failure transfer function is to point to the next state when the mismatch occurs in it.

In order to include time variables [40], the theory of the

finite automata was extended.

After the publication of Shannon's paper in 1951 [1], many scientists considered the behavior of systems of

finite automata (FAs) in labyrinths, for example, in connected sets of cells of a grid or lattice.

About this reply Kripke observes that a realistic comparison of our brains to computers would have to be a comparison to computers like so-called

finite automata, with a bounded storage capacity.

Five electrical engineering papers propose a conversion method between left linear grammar and right linear grammar via

finite automata, measure vacuum levels in MEMS packaging, detect a magnetizing inrush current in single-phase traction transformers, control the angle of DC motor output, and estimate lithium battery state-of-charge.

They showed that a promise version of emptiness problem is undecidable for one-way probabilistic

finite automata. In the literature, some separation results regarding restricted computational models have also been given in the form of promise problems.

Transforming two-way alternating

finite automata to oneway nondeterministic automata.

Using SAX to code every document into events sequence as Xfilter system input, a Yfilter was proposed to combine all FSMs to a Non-deterministic

Finite Automata (NFA) to enhance the time and space using performance of Xfilter (Altinel el al., 2003).

It is concluded that the procedure of double encryption of an image using the

finite automata provides an improved and advanced system for image security.

Deterministic

finite automata (DFA) and nondeterministic

finite automata (NFA) are the typical application of regular expressions.