It is known from the above properties that for any set of maximum-length IDOSs the states involved in the rural symmetric augmentation are the same such that a random concatenation will do.

As mentioned above, transitions in a test sequence are of three kinds and the cost of a test sequence comes from the UIO sequences which have been appended for the purpose of transition verification and the transitions which have been appended for the purpose of concatenation of test subsequences to generate a minimum-length rural postman tour.

The minimum-length rural postman tour is generated by the rural symmetric augmentation and thus the cost of [beta] for concatenation comes from the replicated transitions during the rural symmetric augmentation.

And concatenation of parameters often modulates the individual actions of the components, thus altering their local functionality by relaying global context.

Concatenation of inter-parametric variables of complex system, causes an integration considering their time and space characteristic into an organized whole.

For two nodes, we can construct the concatenation, say, PQ, in the same way as the FLMS construction, except that we construct P and Q at the same time.

In our formal development, we will use a different construction (that essentially constructs the send sequence for all links of an execution at the same time) for concatenation.

The first thing we need to do is define a

concatenation operation o on physical objects, which works in the obvious additive way; thus, if b and c are foot-long rulers, then [Mathematical Expression Omitted] is two feet long.

We define the operation of concatenation on a true list and an arbitrary list by the following equality:

The value of the third term is never defined, since the concatenation of numbers is not possible.

for arbitrary t and for every disjoint x and y in c by definition of concatenation, [b.sub.t], when t is taken as arbitrary, is an order- and addition-preserving function from c onto c.

It is worth observing that autoconcatenation is the repeated concatenation of a magnitude z in c with itself.