# The systems of sequences and the transition formulas, страница 2

## 28.2 The combined method of an algorithm representation

There are some cases algorithms are represented in the combined form. One branch of the algorithm may be represented in a form of the LSA, the others may be represented in a form of transition formulas or sequences.

Using the transformation rules, it is possible to obtain homogeneous representation of the algorithm.

Let it be, the algorithm is determined by the transition formulas and a sequence:

(28.4)

Analysis of the representation shows, there are 4 operators Y1, Y2, Y3, Y4, the initial operator Y0, the finishing operator Yk.

Having used the MSA completed respectively to (28.4), the next system of transition formulas is obtained:

If writing of formulas is performed along the columns of the MSA, the sequence system (28.3) is obtained.

## 28.3 Transforming of the transition formulas into the parenthetic form

The transition formula in the form of (28.5) is called the reduction formula on the variable xl.

,                                             (28.5)

where xlÎ{x1,…,xL}, A an B are the transition formulas inedependent on the xl.

An example of the reduction formula:

(28.6)

If a member of a transition formula doesn’t depend on the xl, it is necessary to multiply this member by the expression  when reducing is performed. In this way, any transition formula may be reduced on any variable. For example, reducing the formula  (28.6) on the variable x2 is following:

(28.7)