In our scheme, in order the realize to the merging operation for the same prefix, suffix or subpattern in single pattern detection models of complex event, three important functional functions: state

transition function, failure

transition function and output function, are used to merge and generate our multipattern detection model during the traversing process of NFA based models in our scheme.

The diagnoser given by (3) is an automaton where the set of states are represented by [Q.sub.d] [subset or equal to] Q, the set of events are represented by [[summation].sub.o] = [??]([M.sub.0]) [union] [T.sub.o], the notation [[delta].sub.d] : [Q.sub.d] x [[summation].sub.o] [right arrow] [Q.sub.d] represents the partial state

transition function, and the initial state is denoted by [q.sub.0] = ([M.sub.0], N)}.

[2] use street distance parameters depending on the direction of street derived from Manhattan grid geometry, or in [11] the same parameters are used for

transition function between LOS and NLOS regions.

But the output function can be voltage (or current) in any branch of the electrical circuit and then the transition conductivity h(t - [THETA]) should be replaced by the corresponding voltage (or current)

transition function.

Taking into account (2), (3), (5), and (6), one can write defining relation for the

transition function of the model [M.sup.D.sub.j]:

where I is the input events' set; O is the output events' set; S is the sequential states' set; [[delta].sub.int]: S [right arrow] S is the internal

transition function; [[delta].sub.ext]: Q * I [right arrow] S is the external

transition function; Q = {(s, e)|s [member of] S, 0 [less than or equal to] e [less than or equal to] [t.sub.a] (s)} is the total state of M; [rho]: S [right arrow] O is the output function; and [t.sub.a]: S [right arrow] Real is the time advance function.

A

transition function is defined as [mathematical expression not reproducible] for each z [member of] Z.

Table 4 Results of Rate of

Transition Function with Weibull Probability Distribution Model Weibull regression - log relative rate of

transition function No.

The function g([RISK.sub.i,t]; [gamma], [theta]) is a

transition function of the observable variable [RISK.sub.i,t], continuous and bounded between 0 and 1.

Where Z is the tape alphabet, Z is the tape alphabet state space, s be the initial state and 8 is the state

transition function. The proposed blind Turing machine processed over the encrypted text and using a proper encryption of the original

transition function in M is done.

Because we will work with discrete-time Markov processes, it is natural to define a

transition function [a.sub.ij] = P([x.sub.t] = [s.sub.j] | [x.sub.t-1] = [s.sub.i]) and an associated transition matrix A.

The Markov branching process (MBP) is the discrete-state Markov process ([Z.sub.t] : t [greater than or equal to] 0) on the state-space S = {0,1, ...} whose

transition function F(t) = [[f.sub.ij](t)] is standard and satisfies the branching property,