Mei et al.[12] proposed a complex event detection method based on

finite automaton, and some of their improved processing methods, for example, Jin et al.[13] proposed a complex event processing method based on timed petri-net.

It consists in the construction of a minimal

finite automaton (FA) which can traverse the border of any cluster on any 2D binary grid and always stops in the planar site percolation model.

A deterministic

finite automaton ([1.sub.[epsilon]]DFA or 2DFA) can be obtained from 1.sub.[epsilon]NFA or 2NFA by claiming that the transition set H does not allow executing more than one possible transition at a time.

Those models are

Finite Automaton model (Kanchana Rajaram and Chitra Babu, 2014) for deriving transactional properties such as compensable, pivot, Retriable.

A deterministic

finite automaton ([1.sub.[epsilon]]DFA or 2DFA) can be obtained from [1.sub.[epsilon]]NFA or 2NFA by claiming that the transition set H does not allow executing more than one possible transition at a time.

In diagnosability verification, first, it is proven that if a part of observations in the system can be expressed as a regular language, that is, a language accepted by some

finite automaton, then diagnosability is decidable.

A push-down automaton is a

finite automaton (nondeterministic) which has a stack, a kind of simple memory in which it can store information in a last-in-first-out fashion.

A

finite automaton starts in state [q.sub.0] and processes the input symbols sequentially.

* Definition 2.2 A Deterministic

Finite Automaton (DFA) is a 5-tuple A = (Q, [SIGMA], [delta], [q.sub.0], F) where Q is a

Even simple controlling structure (formally represented as a small

finite automaton) can create rare combinations of events when acting on inputs without such rare combinations, which suggests that pure testing-based approach cannot prove reliability.

also introduced a kind off fuzzy

finite automaton in 1999 [10].

An Hidden Markov Model (HMM) is mathematically equal to a stochastic

finite automaton defined by a 5-tuple A = (Q, [summation of], [DELTA], [pi], [OMICRON]) where Q = {[s.sub.0], [s.sub.1], [s.sub.2], [s.sub.3], ..., [s.sub.m]} is finite set of states, [summation of] is an alphabet of output symbols, [DELTA] = {[p.sub.ij]/1 [less than or equal to] i, j [less than or equal to] m} is a state transition probability distribution and [pi] = {[[pi].sub.i]/ 1 [less than or equal to] i [less than or equal to] m} is an initial state distribution, [OMICRON] is the set {[e.sub.j](x)/1 [less than or equal to] j [less than or equal to] n} of output symbol probabilities such that