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S. V. Sirotinskaya
main algorithms of these combinations are parts of the mathematical logic
methods published before [3]. They are based on the mathematical theory developed for the computer projection [6]. Two of them are intended for the detection and analysis of conjunctive and disjunctive logical dependencies in data
files. The third is the optimization algorithm. It belongs to a class of algorithms
developed in connection with a problem of the Boolean functions minimization
and is employed for the construction of minimum DNF of Boolean functions.
Further more, by a description of data processing, the mentioned algorithms
are grouped into the following three procedures.
Procedure I. This includes the detection of disjunctive logical dependencies,
minimization of Boolean functions expressing them, dependencies analysis;
Procedure II. Besides some additional operations, this includes the Boolean
functions' minimization and dependencies analysis;
Procedure III. This procedure consists of the detection of conjunctive logical
dependencies and Boolean functions' minimization.
A general way of data processing for most variants of the main hypotheses,
investigated by now consists of the following ten steps.
1. Procedure I is applied k+l times to the file T+. By this means, some combinations of variables V s ' s=I,,, .,q, q s k+l, consisting of possible arguments
of function f, are detected within each ofk+l subsequence. Subsequences including only one variable, are also taken into account.
2. Variables which have not entered the combinations V s are removed from the
initial file T.
3. Each combination V s is replaced by a new variable Ps which is the disjunction of all variables from V s .
4. Hypotheses D and E are verified. To do this, the procedure III is applied separately to the part JU of the file T+, which includes only oceanic variables pOj'
j s k, and to the part rc of file T+, which includes only climatic variables pc t>
t s 1. As a result, the following cases are possible: (1) function f cannot be expressed either as a conjunction of variables from JU, or as a conjunction of
variables from rc . Then step 6 for a test of hypothesis A is realized; (2) function f is expressed only as a conjunction of variables from the file JU. This
means that the hypothesis D is true. Then step 8 is carried out; (3) function
f is expressed only as a conjunction of variables from the file rc . This means
that hypothesis E is true. Then step 8 is carried out; (4) function f can be expressed both as a conjunction of variables belonging to both the file JU and
the file rc . Then step 5 is realized.
5. Hypotheses Band C are verified. Here, the following cases are possible: (1)
each variable from the conjunction relating to the file JU is identical to a certain variable from the conjunction relating to the file rc , and vice versa. It
means that the versions I, ILl, IILl of the hypotheses B or C are true, as the
hypotheses Band C are not distinguishable between them. Further, step 8 is
realized; (2) each variable from the conjunction relating to the file JU can be
represented in its turn as a function of variables from the conjunction relating to the file rc, and a function type is also the conjunction. This means that
S. V. Sirotinskaya
main algorithms of these combinations are parts of the mathematical logic
methods published before [3]. They are based on the mathematical theory developed for the computer projection [6]. Two of them are intended for the detection and analysis of conjunctive and disjunctive logical dependencies in data
files. The third is the optimization algorithm. It belongs to a class of algorithms
developed in connection with a problem of the Boolean functions minimization
and is employed for the construction of minimum DNF of Boolean functions.
Further more, by a description of data processing, the mentioned algorithms
are grouped into the following three procedures.
Procedure I. This includes the detection of disjunctive logical dependencies,
minimization of Boolean functions expressing them, dependencies analysis;
Procedure II. Besides some additional operations, this includes the Boolean
functions' minimization and dependencies analysis;
Procedure III. This procedure consists of the detection of conjunctive logical
dependencies and Boolean functions' minimization.
A general way of data processing for most variants of the main hypotheses,
investigated by now consists of the following ten steps.
1. Procedure I is applied k+l times to the file T+. By this means, some combinations of variables V s ' s=I,,, .,q, q s k+l, consisting of possible arguments
of function f, are detected within each ofk+l subsequence. Subsequences including only one variable, are also taken into account.
2. Variables which have not entered the combinations V s are removed from the
initial file T.
3. Each combination V s is replaced by a new variable Ps which is the disjunction of all variables from V s .
4. Hypotheses D and E are verified. To do this, the procedure III is applied separately to the part JU of the file T+, which includes only oceanic variables pOj'
j s k, and to the part rc of file T+, which includes only climatic variables pc t>
t s 1. As a result, the following cases are possible: (1) function f cannot be expressed either as a conjunction of variables from JU, or as a conjunction of
variables from rc . Then step 6 for a test of hypothesis A is realized; (2) function f is expressed only as a conjunction of variables from the file JU. This
means that the hypothesis D is true. Then step 8 is carried out; (3) function
f is expressed only as a conjunction of variables from the file rc . This means
that hypothesis E is true. Then step 8 is carried out; (4) function f can be expressed both as a conjunction of variables belonging to both the file JU and
the file rc . Then step 5 is realized.
5. Hypotheses Band C are verified. Here, the following cases are possible: (1)
each variable from the conjunction relating to the file JU is identical to a certain variable from the conjunction relating to the file rc , and vice versa. It
means that the versions I, ILl, IILl of the hypotheses B or C are true, as the
hypotheses Band C are not distinguishable between them. Further, step 8 is
realized; (2) each variable from the conjunction relating to the file JU can be
represented in its turn as a function of variables from the conjunction relating to the file rc, and a function type is also the conjunction. This means that