A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2
A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjuncterms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in the functions, which are borrowed fro...
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irk-123456789-1319632018-04-08T03:02:52Z A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 Rytsar, B.Ye. Новые методы в информатике A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjuncterms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in the functions, which are borrowed from the well-known publications. Предложен новый метод минимизации числа переменных в полных и неполных логических функциях, основанный на процедуре расцепления конъюнктермов. Преимущества предложенного метода показаны на примерах определения несущественных переменных в функциях, заимствованных автором из известных публикаций в порядке сравнения. Запропоновано новий метод мінімізації кількості змінних у повних і неповних логікових функціях, що ґрунтується на процедурі розчеплення кон'юнктермів. Переваги пропонованого методу показано на прикладах визначення неістотних змінних у функціях, запозичених автором із відомих публікацій з метою порівняння. 2017 Article A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 / B.Ye. Rytsar // Управляющие системы и машины. — 2017. — № 5. — С. 16-24. — Бібліогр.: 11 назв. — англ. 0130-5395 http://dspace.nbuv.gov.ua/handle/123456789/131963 519.718 en Управляющие системы и машины Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Новые методы в информатике Новые методы в информатике |
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Новые методы в информатике Новые методы в информатике Rytsar, B.Ye. A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 Управляющие системы и машины |
| description |
A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjuncterms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in the functions, which are borrowed from the well-known publications. |
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Article |
| author |
Rytsar, B.Ye. |
| author_facet |
Rytsar, B.Ye. |
| author_sort |
Rytsar, B.Ye. |
| title |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 |
| title_short |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 |
| title_full |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 |
| title_fullStr |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 |
| title_full_unstemmed |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 |
| title_sort |
simple minimization method of the variables number in complete and incomplete logic functions. part 2 |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
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2017 |
| topic_facet |
Новые методы в информатике |
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http://dspace.nbuv.gov.ua/handle/123456789/131963 |
| citation_txt |
A Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 2 / B.Ye. Rytsar // Управляющие системы и машины. — 2017. — № 5. — С. 16-24. — Бібліогр.: 11 назв. — англ. |
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16 ISSN 0130-5395, УСиМ, 2017, № 5
Новые методы в информатике
UDC 519.718
B.Ye. Rytsar
A Simple Minimization Method of the Variables Number in the Complete and Incomplete
Logic System Functions. Part 2
Предложен новый метод минимизации числа переменных в полных и неполных логических функциях, основанный на проце-
дуре расцепления конъюнктермов. Преимущества предложенного метода показаны на примерах определения несущественных
переменных в функциях, заимствованных автором из известных публикаций в порядке сравнения.
Ключевые слова: минимизация числа переменных, логическая функция, несущественная переменная, конъюнктерм, проце-
дура расцепления.
Запропоновано новий метод мінімізації кількості змінних у повних і неповних логікових функціях, що ґрунтується на проце-
дурі розчеплення кон'юнктермів. Переваги пропонованого методу показано на прикладах визначення неістотних змінних у
функціях, запозичених автором із відомих публікацій з метою порівняння.
Ключові слова: мінімізації кількості змінних, логікова функція, неістотна змінна, кон'юнктерм, процедура розчеплення.
A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjunc-
terms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in
the functions, which are borrowed from the well-known publications.
Keywords: minimization of the variables number, logic function, nonessential variable, conjuncterm, splitting procedure.
In the second part we consider the application of the proposed method for the determination of the
nonessential variables in the complete and incomplete logic system functions.
In general case the system of the functions , , in the set-
theoretical format is reflected by the system of perfect STF },{ *1
ii YY , [10]:
, i
n
i kv 2 , (2)
where mij , , , are numeric minterms of the i-th function if of system (2);
the mark * replaces the symbol ~ or 0 depending on the fact which part of n-dimensional boolean space
of the system (2) belongs to indefinite values of the functions if for all , namely: if ~*
ii YY ,
here |||| 10~
iii YYY , then (2) is the system of inpredeterminated (incomplete) functions reflected by the
system of perfect STF },{ ~1
ii YY , if 0*
ii YY , here |||| 10~
iii YYY , then (2) is the system of weakly de-
terminated (incomplete) functions reflected by the system of perfect STF },{ 01
ii YY , if *
iY , then (2) is
the system of complete functions reflected by the system of perfect STF }{ 1
iY .
Nonessential variables in the complete and/or incomplete system (2) can be common to all functions
of the system, we call them systemic nonessential variables, and if nonessential variables are only some
of the functions of the system (2), we call them own nonessential variables of these functions. Obvi-
ously, the system of complete functions (2) does not have the systemic nonessential variables, if at least
ISSN 0130-5395, УСиМ, 2017, № 5 17
one of its function has an odd number of minterms. Then, search for nonessential variables is executed
for the subsystem of the system functions (2) having an even number of minterms.
For the definition of certain nonessential variables by the method of splitting minterms mij of the sys-
tem (2) a set YS
1
of the systemic minterms (m)s is formed, where is the set of indices s of
the system functions (2) [10]. In this case we implement the compatible method of splitting conjunc-
terms, similarly as in the case of system functions minimization [9,10].
Over the systemic minterms (m)s, as in the case of a single function (see p. 2 and p. 3), the splitting
procedure is performed using the matrix . Elements of this matrix are systemic splitted conjunc-
terms of -rank and formed by imposition of the masks of literals of -rank on the sys-
temic mintems (m)s. Among pairs of equal by value and having the same indexes are distin-
guished by underlining. Conseguently, if the matrix is covered by such elements of i-th row, then
according to the Theorem (see Section 2), the given system F(X) has a systemic nonessential variable
xp, and if the matrix is covered by two or more rows, then (see corollary Theorem) the given sys-
tem F(X) has two or more systemic nonessential variables. It is clear, that the certain functions of a
given system can have their own nonessential variables. These variables are defined on the next step of
splitting procedure in a similar way (see Section 2). After the determining of the systemic nonessential
variables and/or own nonessential variables of functions, the given final form of the system F(X) is ob-
tained with procedure of distribution of the functions by their indices [10], and, if necessary, by further
minimization procedure.
5. Definition of nonessential variables in the complete system functions. Definition of the nones-
sential variables in the complete system functions is based on the splitting conjuncterms method for the
single function (described in Section 2) and by procedural features of the system functions described
above. Let us illustrate it with a following example.
Example 8. Determining the nonessential variables using the splitting conjuncterms method in the
complete system functions , , given in the perfect STF
.
Solution. Define the STF Y1,2,3
1 of the system minterms (m)1,2,3 of the given system F(X) and execute
the splitting procedure using a matrix M4
3, where the systemic conjuncterms-copies with the same indi-
ces of function (the indices of system functions are shown about the matrix column) are underlined:
.
Thus, according to the Theorem, the given system F(X) has the nonessential variable system x2 .
After the procedure of the functions distribution by their indices we get the simplified system
18 ISSN 0130-5395, УСиМ, 2017, № 5
,
where the fuction f2 after the minimization procedure has also its own nonessential variable x3 .
Answer. The given system F(X) has the nonessential variable system x2 and its function f2 has also
its own nonessential variable x3 .
6. Definition of nonessential variables in the incomplete system functions. In the case of the in-
complete system functions (2) the detection of the nonessential variables gets much more complicated
because of the multivariants of the possible solutions. On the one hand, this is due to the predetermining
of the individual functions, on the other hand, this is due to the need to ensure the compatible system
solution. The peculiarity of the proposed method of determining nonessential variables in the incomplete
system functions is that the splitting of the systemic minterms procedure implements a compatible solu-
tion of the system, providing simultaneous predetermination of its functions. If the given system has at
least one systemic nonessential variable, then according to the Theorem (Section 2), in the splitting ma-
trix of the systemic minerms (m)s one row of systemic conjuncterms-copies of -rank ap-
pears and they cover it.
Example 9. The incomplete system functions , , i 1, 2,..., 6 , given
in the Table 2.1, to reduce the system functions of the essential variables (this system is borrowed from
[6, p. 68]).
T a b l e 2.1
0 3 4 6 11 12 14 16 17 19 20 22
5
4
3
2
1
x
x
x
x
x
0 0 0 0 0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 0 0 0 0 0
0 0 1 1 0 1 1 0 0 0 1 1
0 1 0 1 1 0 1 0 0 1 0 1
0 1 0 0 1 0 0 0 1 1 0 0
6
5
4
3
2
1
Y
Y
Y
Y
Y
Y
1 0 1 0 1 0 1 0 0 0 1 1
0 0 1 1 0 1 1 0 1 1 0 0
0 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 1 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0 0 0 0 1
0 0 0 0 0 0 0 1 0 0 0 0
Solution. From the Table 2.1 define the systemic minterms (m)s that form the perfect STF Ys
1 and the
perfect STF Ys
0 of the given system F(X), where :
(10000)6, (10001)2,4, (10011)2, (10100)1,3, (10110)1,5}1
(01110)4,5,6, (10000)1,2,3,4,5, (10001)1,3,5,6, (10011)1,3,4,5,6, (10100)2,4,5,6, (10110)2,3,4,6}1
From Table 2.1 we can also define the perfect STF , where . In
decimal format the perfect STF , whose
minterms (the numbers are absent in Table 2.1) participate in the predetermination procedure.
ISSN 0130-5395, УСиМ, 2017, № 5 19
Let us execute the splitting procedure by using the matrix M6
5 for the systemic minterms of the STF
Ys
1 (the numbers above the columns of the matrix are numbers of the given system F(X)):
In the matrix M6
5 the systemic conjuncterms are highlighted in bold font. We don’t take them into
further consideration because their minterms belong to Ys
0 . For example,
contain the minterm or , where and etc.. In the
matrix M6
5 we underline equal elements with the indices of common functions defined by their intersec-
tion. For example, the conjuncterm has the index 2, because it is defined by intersection
and etc.. The remaining elements of the matrix M6
5 have indices of generating sys-
temic minterms that are not specified here.
As one can see, in the matrix M6
5 there is not any row that would cover it. Thus, according to the
theorem (see Section 2) the given system F(X) does not have systemic nonessential variables.
To determine the nonessential variables in the certain system functions we take only those elements
from each row of the matrix M6
5 which have an index of specific function. This set doesn’t include ele-
ments of the row containing at least one element that was eliminated due to the loss of index of the cor-
responding function. For example, for the function f1 such rows are 3-th and 6-th and for the function f2
are 1-th and 6-th rows.
Consequently, the elements of the matrix M6
5 with index 1 of the function f1 are STF
.
According to the Theorem the function f1 has the nonessential variable x5. The minimal STF Y1
1 is
obtained after the splitting procedure of the obtained conjuncterms of the 4-rank using the matrix M5
4 :
.
To verify the obtained results let us transform the minimal STF Y1
1 into the perfect STF
, where the predetermi-
nated minterms from the set Ys
~ are highlighted in bold.
The elements with the index 2 of the matrix M6
5 form a set with two rows for the function f2 :
20 ISSN 0130-5395, УСиМ, 2017, № 5
.
Hence, we see that the function f2 for the 2nd solution has two nonessential variables x2 and x4 , that
after minimization is reflected by STF Y2 , this way (for verification) we transform into the perfect STF
, where the predeterminated minterms from
the set Ys
~ are highlighted in bold.
For the function f3 we have STF , where the elements
with nonessential variable x5 are highlighted in bold. Minimal STF Y3
1 of the function f3 is obtained af-
ter the splitting procedure of these elements:
.
Thus, the function f3 has the minimal STF ,
where the predeterminated minterms of the perfect STF Y3
1 are highlighted in bold.
Executing the similar procedure for the function f4 , we get its nonessential variable x2 :
.
From here STF , i.e. the perfect STF .
For the function f5 we have STF . From
here we obtain two solutions: 1) with the nonessential variable x5 that corresponds to STF
, i.e. , and 2) with the nonessential variable x3 that corresponds
to STF , i.e. .
For f6 we get , i.e. .
Thus, the given system F(X) after "screening" its nonessential variables becomes the following:
ISSN 0130-5395, УСиМ, 2017, № 5 21
Comparing with [6], the obtained result is better due to the compatible solution of the given system
by conjuncterms splitting method, since the two more nonessential variables are found. In particular, in
the functions f2 and f6 one more nonessential variable x4 is found in addition to x2 and the function f5
has two solutions from which it is worth keeping , since the functions f1 and f3 have
the nonessential variable x5 too.
Example 10. The system of incomplete weakly determinated functions , ,
given in Table 2.2, must be reduced to the system functions from essential vari-
ables (this system is borrowed from [1, p. 275]).
T a b l e 2.2
x1 x2 x3 x4 x5 x6
1 0 1 1 0 0
1 1 0 0 0 0
0 0 1 0 1 1
1 1 1 0 1 0
0 1 0 0 1 0
f1 f2 f3 f4 f5
0 0 1 0 1
0 1 0 1 1
1 1 1 0 1
1 0 1 0 0
1 0 1 0 0
Solution. From Table 2.2 we get such STF of the given system F(X):
, где We execute the splitting procedure using the matrix M6
5 with the systemic minterms of the STF Ys
1:
.
Here none of the systemic conjuncterm of the 5-rank ( i
5 )s' , predeterminated by minterms of the
set Ys'
~ , does not intersect with any systemic minterm (mi )s' of the set Ys'
0 , i.e. , where
is a set of numbers of the functions, which includes ( i
5 )s' . For example, the intersection
, where (here minterm (101101)3,5 belongs
Ys
~ ) and , and therefore
. Since all the elements of the matrix M6
5
within the minimal pre-
22 ISSN 0130-5395, УСиМ, 2017, № 5
determination (one of minterm from Ys
~ ) do not intersect with the elements of the set Ys'
0 , and according
to the Theorem (see Section 2) all the variables of the given incomplete system functions are illusive
nonessential variables. However, the number of nonessential variables decreases if to increase the power
of predetermination set by reducing the rank of systemic splitted conjuncterms. This can be seen at the
following levels of the splitting procedure for the given systemic minterms using the matrices M6
4 , M6
3
and M6
2 (the matrix M6
1
can not be considered because all its rows have predeterminated conjuncterms
of the 1-rank, containing the elements of the set Ys'
0 ).
Consider the matrix M6
2 , where the elements containing the set Ys'
0
are highlighted in bold (for exam-
ple, ). Rows with elements are not taken into consideration to simplify the ma-
trix M6
2 up to four rows:
Hence, we have four possible solutions of this problem, where the positions of the dashes in the
systemic conjuncterms of the 2-rank indicate the nonessential variables of the given incomplete (weakly
determinated) system functions F(X). The validity of the obtained result can be easily checked by
writing the STF Ys
1 for each of these solutions to ensure that the resulting conjuncterm ( i
2 )s' of a
function contains the systemic minterm (m)s' , i.e. , and the rest of minterms belong to Ys
~ .
We illustrate this with an example of the 4-th solution, where the given system reflects the STF
:
, ,
ISSN 0130-5395, УСиМ, 2017, № 5 23
, ,
.
The validity result confirms the correctness of 4-th solution. Similar conclusion should be made for
the remaining solutions for this problem.
The given system F(X) based on the minimization of its functions with the essential variables are
presented as follows reflecting four solutions of STF {Yi
1} , :
1. = ,
where x2, x4, x5, x6 are the systemic nonessential variables;
2. = ,
where x1, x3, x4, x6 are the systemic nonessential variables and the function f1 has also the nonessential
variable x2 ;
3. = ,
where x1, x2, x4, x6 are the systemic nonessential variables and the function f1 has also the nonessential
variable x3 ;
4. = ,
24 ISSN 0130-5395, УСиМ, 2017, № 5
where x1, x3, x3, x6 are the systemic nonessential variables and the function f2 has also the nonessential
variable x5.
Note that in [1, p. 276] there is only the 2-nd solution of definition of the nonessential variables
without minimization of the system functions.
Conclusion
An application of conjuncterms splitting method for the reduction of a number of the nonessential
variables in complete and incomplete system functions is described. The peculiarities and advantages of
the proposed method are analyzed in the first part of the article. They are also inherent to the mentioned
system functions that are illustrated by the examples borrowed from the well-known publications.
1. Zakrevskij A.D., Pottosin Ju.V., Cheremisinova L.D. Logicheskie osnovy proektirovanija diskretnyh ustrojstv – М.:
Fizmatlit, 2007. – P. 269–277. (In Russian).
2. Kambayashi Y. Logic design of programmable logic arrays // IEEE Trans. on Computers, C-28, Sept. 1979. – N 9. – P. 609–617.
3. Sasao T. Memory-Based Logic Synthesis. – Springer Science+Business Media, LLC 2011. – P. 119–135. – www.
springer.com/us/book/9781441981035
4. Implicit algorithm for multi-valued input support manipulation / A. Mishchenko, C. Files, M. Perkowski et al. // Proc.
4thIntl. Workshop on Boolean Problems, Sept. 2000, Freiberg, Germany.
5. Sasao T. On the number of dependent variables for incompletely specified multiple-valued functions // 30th Int. Symp.
Multiple-Valued Logic, Portland, Oregon, U.S.A., May 23–25, 2000. – P. 91–97. – http://dblp.uni-trier.de/db/conf/
ismvl/ismvl2000.html#Sasao00
6. Majewski W. Uklady logiczne. Wybrane zagadnienia. – Warszawa, WPW. – 1997. – 180 s.
7. Sasao T. On the number of variables to represent sparse logic functions, ICCAD-2008, San Jose, CA, USA, Nov. 10–13,
2008. – P. 45–51. – http://alcom.ee.ntu.edu.tw/system/privatezone/meetingfile/200903100035361.pdf
8. Sasao T. On the number of LUTs to realize sparse logic functions, Int. Workshop on Logic and Synthesis (IWLS-2009),
Berkeley, CA, U.S.A., July 31 – Aug. 2, 2009. – P. 64–71. – http://www.lsi-cad.com/sasao/Papers/files/ IWLS2009_ sasao.pdf
9. Rytsar B. Reduktsiya nesuttyevykh zminnykh systemy bul'ovykh funktsiy // Visn. NU Radioelektronika i telekomu-
nikatsiyi. – 2001. – N 428. – P. 184–189. (In Ukrainian).
10. Rytsar B.Ye. Teoretyko-mnozhynni optymizatsiyni metody lohichnoho syntezu kombinatsiynykh merezh: Dys. … d.t.n.
– L'viv, 2004. – 348 p. (In Ukrainian).
11. Rytsar B., Romanowski P., Shvay A. Set-theoretical Constructions of Boolean Functions and theirs Applications in
Logic Synthesis // Fundamenta Informaticae. – 2010. – 99, N 3. – P. 339–354.
Поступила 21.05.2017
E-mail: bohdanrytsar@gmail.com
© Б.Е. Рыцар, 2017
B.Ye. Rytsar – Doctor Sc., Professor, Department of Radioelectronic Devices Systems, Institute of Telecommunications, Radioelectronics
and Electronic Engineering, L’viv polytechnic National University, Ad.: Bandera srt., 12, L’viv, Ukraine, e-mail: bohdanrytsar@gmail.com
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|