№5
ПРИКЛАДНАЯ ДИСКРЕТНАЯ МАТЕМАТИКА
ПРИЛОЖЕНИЕ Сентябрь 2012
АННОТАЦИИ ДОКЛАДОВ НА АНГЛИЙСКОМ ЯЗЫКЕ
SECTION 1
Glusko K.L.,Titov S.S.ON THE SOLUTION OF QUADRATIC EQUATIONS
IN BINARY FIELDS.The article presents a fast method to nd the roots of quadratic
equations in nite elds of characteristic two.The generalized formula of semitrace is
obtained based on the construction of normal bases using a symmetric quadratic extension.
Edemskiy V.A.,Antonova O.V.LINEAR COMPLEXITY OF GENERALIZED
CYCLOTOMIC SEQUENCES WITH PERIOD 2
m
p
n
.A method for analyzing
the linear complexity of generalized cyclotomic sequences with period 2
m
p
n
is proposed.
It allows to pick out sequences with the high linear complexity.The linear complexity of
some sequences is computed on the base of classes of quadratic and biquadratic residues.
Zubkov A.M.,Kruglov V.I.ON DISTRIBUTIONS OF WEIGHT SPECTRA FOR
RANDOM LINEAR BINARY CODES.Weight spectra of random binary codes are
considered.Formulas for their means and variances are derived.
Zubkov A.M.,Serov A.A.ESTIMATES FOR THE NUMBER OF BOOLEAN
FUNCTIONS HAVING AFFINE OR QUADRATIC APPROXIMATIONS
WITH A GIVEN ACCURACY.Boolean functions having ane or quadratic ap
proximations with a given accuracy are considered.Twosided inequalities for the number
of such functions are obtained by means of inclusionexclusion formula and estimates of
binomial distribution tails.
Kolomeec N.A.ON NONLINEARITY OF SOME BOOLEAN FUNCTIONS
WITH MAXIMAL ALGEBRAIC IMMUNITY.An estimation for nonlinearity of
Dalai's Boolean functions with maximal possible algebraic immunity in even number of
variables is given.It is proved that the estimation is achieved.
Kolcheva O.L.,Pankratova I.A.STATISTICAL INDEPENDENCE OF THE
BOOLEAN FUNCTION SUPERPOSITION.II.Let x,y,z be sets of dierent
Boolean variables,f(x;y),f
1
(x;y),f
2
(x;y),f
1
(x;y) f
2
(x;y) are Boolean functions being
statistically independent on the variables in x,and h(x
1
;x
2
;z),g(x) are any Boolean func
tions.Then the function h(f
1
(x;y);f
2
(x;y);z) is statistically independent on the variables
in x;and the same is true for the function f(x;y) g(x) i f is balanced or g = const.
Kuznetsova A.S.,Safonov K.V.ON A COMBINATORIAL OPTIMIZATION
PROBLEM.A combinatorial optimization problem reduced to the building a symmetric
group in a format of minimal words is considered.There are solutions for some cases of the
problem.
Kjazhin S.N.,Fomichev V.M.STRUCTURAL PROPERTIES OF PRIMITIVE
SYSTEMS OF NATURAL NUMBERS.The primitive systems of natural numbers
are considered.The structure of their set is described,and the main properties of them
are installed.An algorithm for enumerating primitive systems of natural numbers not
exceeding a given number m is given.
Murin D.M.ABOUT THE NUMBERS OF THE INJECTIVE AND OF THE
SUPERINCREASING VECTORS AND SOME PARTICULARITIES OF
128 Прикладная дискретная математика.Приложение
THE STRONG MODULAR MULTIPLICATION.The numbers of injective and
of superincreasing vectors appeared in knapsack cryptosystems are estimated.Besides,
it is shown that the set of increasing injective vectors is uniformly covered by the vectors
received from the superincreasing vectors through the strong modular multiplication and
the ascending ordering the vector elements.
Pichkur A.B.DESCRIPTION OF THE CLASS OF PERMUTATIONS REP
RESENTED AS A PRODUCT OF TWO PERMUTATIONS WITH FIXED
NUMBER OF MOBILE POINTS.II.The complete description for the structure of
the class of permutations represented as the product of two permutations with q and q +t
mobile points is given in the case 1 6 t < N 2,2 6 q < (N t)=2 +1.
Pogorelov B.A.,Pudovkina M.A.ON COMBINATORIAL PROPERTIES OF THE
GROUP GENERATEDBYXL LAYERS.XSL block ciphers are based on Shannon's
principles of confusion and diusion.Round functions of these ciphers consist of round key
addition,a substitution and a linear transformation.In this paper,the combinatorial
properties of the group generated by the linear transformation and all round keys XOR
addition are described.
Potapov V.N.ON ALMOST BALANCED BOOLEAN FUNCTIONS.A Boolean
function is called correlationimmune of degree n m if it takes the value 1 the same
number of times for each mdimensional face of the hypercube.Balanced correlation
immune function is called resilient.The almost balanced (or almost resilient) Boolean
function is dened as a function taking values 1 in a half or in a half plus or minus one of
vertices in each face.Here,some constructions of almost balanced functions are proposed,
some properties and a low bound for the number of these functions are established.
Pudovkina M.A.PROPERTIES OF X;SLAYERS.Round functions of XSL block
ciphers consist of round key addition,a substitution and a linear transformation.In this
paper,the properties of the group generated by the substitution and all round keys XOR
addition are described.
Smyshlyaev S.V.PERFECT BALANCEDNESS OF kVALUED FUNCTIONS
AND GOLI
C CONDITION.Problems of kvalued logic generalizations of Golic Con
jecture are considered.In the case of prime k,a number of results on correctness of kvalued
analogue of Golic Conjecture are obtained in certain subcases.Here,the full proof of in
correctness of Golic Conjecture kvalued analogue in the case of composite k is presented.
Tokareva N.N.ON DECOMPOSITION OF A BOOLEAN FUNCTION INTO
SUM OF BENT FUNCTIONS.In the paper,some new results on bent sum decom
position problem are discussed.It is proved that any Boolean function in n variables of
degree d 6 n=2 can be represented as the sum of not more than 2
2b
b
bent functions,
where b > d and b is the least integer such that 2bjn.
Tuzhilin M.E.LATIN SQUARES AND THEIR APPLICATIONS IN CRYP
TOGRAPHY.This survey contains examples of applications of Latin squares in crypto
graphy.
Frolova A.A.PROPERTY OF KASAMI BENT FUNCTIONS MULTIPLE
DERIVATIVES.It is proved that every bent function Kasami of degree t > 4 has (t 3)
multiple nonzero derivative in the direction of any linearly independent vectors.
Аннотации докладов на английском языке 129
Sholomov L.A.DECOMPOSITION AND APPROXIMATION OF UNDERDE
TERMINED DATA.For any underdetermined source,we consider its decomposition as
product of sources generating symbols 0,1,and the indenite symbol .Also,we learn best
approximate (in a prescribed sense) decomposition if correct decomposition is impossible.
We prove that the best approximate decomposition always exists (for the decomposable
source,it coincides with its decomposition),and it may be constructed by a polynomial
algorithm.For some problems relating to simplications and equivalent transformations of
decompositions,polynomial algorithms are oered.In closing,we state that any underde
termined source has a decomposition in some more general form.
SECTION 2
Borisenko B.B.ON SIMILAR IMAGES SEARCH FOR DIGITAL WATER
MARK DETECTION.An approach to similar images search is discussed.These images
have to satisfy some conditions and should be involved into education sample for the digital
watermark detection method based on the modied Hotelling's control chart.For searching
similar images,the author suggests to dene an image I to be more similar to an image I
1
than to an image I
2
if the hash of I is being nearer to the hash of I
1
than to the hash of I
2
according to a special metric.
Volgin A.V.,Ivanov A.V.A METHOD FOR SEED RECOVERINGIN THE LIN
EAR GENERATOR OVER THE FINITE FIELD COMPLICATED BY MASK
ADDING.In the paper,a method for recovering the initial state of a linear generator com
plicated by mask adding over the nite eld is oered.It is supposed that the additive
constant is unknown.
Glukhov M.M.jr.ABOUT McEliece CRYPTOSYSTEM WITH ALGEBRAIC
GEOMETRIC CODES.A new idea for designing the generator matrix of algebraic
geometric codes in McEliece publickey cryptosystem is described.
Kamaeva A.A.TRUNCATED DIFFERENTIAL CHARACTERISTICS WITH
MINIMUMNUMBEROF ACTIVE BYTES FORSIMPLIFIEDWHIRLPOOL.
In this paper,a truncated dierential characteristics with minimum number of active bytes
is built to produce a collision for two reduced variants of the hash function Whirlpool:
with 1 and 2 rounds in the underlying blockcypher instead of 14.For the rst variant this
number equals 23,for the second one  45.The probabilities of these characteristics are
maximal and equal 2
115
and 2
225
respectively.
Karpunin G.A.,Ermolaeva E.Z.ESTIMATES OF COLLISION RESISTANCE
COMPLEXITY FOR THE HASH FUNCTION RIPEMD.In 2005,Wang et al.
developed practical collision attacks on MD4 and RIPEMD hash functions.For RIPEMD
however,description of the attack has been presented only at ideological level,raising con
cerns about the attack complexity claimed by the authors.X.Wang et al.stated that the
attack complexity is about 2
18
calls of compression function.In this paper,the omitted
details of the Wang attack on RIPEMD hash function are recovered and the singlestep
message modication being the rst stage of this attack is implemented.The experiments
showed that the lower bound of the average complexity of the Wang's attack is greater
than 2
32;49
compression function calls.This estimation is signicantly higher than the one
stated in the Wang's paper.
Kovalev D.S.FPGA IMPLEMENTATION OF FAPKC4.The paper presents
FPGA implementation of the latest version of Finite Automata Public Key Cryptosystem
130 Прикладная дискретная математика.Приложение
(FAPKC4).The change of the throughput/hardware resources in comparison with the
basic cryptosystem (FAPKC) is investigated.These parameters for encryption/decryption
and digital signature is compared.A comparison of software and hardware implementations
of FAPKC4 is given too.
Kogos K.G.,Fomichev V.M.CRYPTOGRAPHIC PROPERTIES OF BRANCH
ING OF FUNCTIONS OF VECTOR SPACES.The report is devoted to branchings
of vector functions by the transformations having a given sign.Two approaches for using
them for the solution of systems of the nonlinear equations are discussed.
Koreneva A.M.,Fomichev V.M.CRYPTOGRAPHIC PROPERTIES OF BLOCK
CIPHERS BASED ON SHIFT REGISTERS.Cryptographic properties of register
type block ciphers are studied.A way for designing a block encryption algorithm which
is based on shift register with length 4 over the set of binary 16dimensional vectors is
investigated.
Loshkaryov S.D.DIFFERENTIAL EQUATIONS FOR HASH FUNCTIONS
FROM MDxFAMILY.Creating a hash function cryptographers almost never prove
the selection of algorithmic blocks,the order of blocks.The hashfunction HAVAL pro
posed in 1992 is probably the only exception from this rule.This hashfunction is con
structed of blocks with specic properties such as strong independence of output bits,strong
avalanche eect,01 balance and others for Boolean functions,and the result hash func
tion was proposed to be cryptographically strong.But time had shown that it is not true.
The papers,proposing other popular hashfunctions such as MD4,MD5,SHA0,SHA1,
SHA2,RIPEMD,GOST 34.1194 and others,do not contain any proof for choice of ele
ments.The algorithms used in construction of the hashfamily of MDx contain constant
values,addition modulo 2
32
,rotations and primitive Boolean functions,chosen by the au
thor.The cryptanalytics almost had not undertaken yet any attempts to prove the choice
of elements and if it is possible to change them to improve the cryptographic properties
of the algorithm.The main target of this paper is an analysis of how primitive Boolean
functions and rotations in uence the resistance of MD5 to dierential attacks.
Medvedev N.V.,Titov S.S.PROBLEMS OF ALMOST THRESHOLD SECRET
SHARING SCHEMES.The article deals with questions of information security,secret
sharing schemes.The problem of structure access realization by elliptic curves is discussed.
It is shown that one can realize secret sharing schemes with innite set of participants,
and the everywhere density of rational points is an analogue of perfectness.The problem
of unreplacible participants is considered.It is proved that the binary almost threshold
matroids without unreplacible participants are only matroids on Reed  Muller codes of
rst order.
Stolov E.L.MATHEMATICAL MODEL OF RANDOMGENERATOR BASED
ON TERNARY LOGIC.A mathematical model of physical generator that is based on
ternary logic is suggested.A few combinational units form a ring circuit.Each unit realizes
the same ternary logical function,and the circuit works as a chaotic generator.It is proved
that signal on output of any unit has uniform distribution.
Chikishev G.O.ONETIME RINGSIGNATURE INECASH.Ring signature allows
to specify a set of potential message signers instead of the actual signer.In this paper,a
new signature type is introduced  the onetime ring signature which allows to sign only
Аннотации докладов на английском языке 131
one message.The use of the same secret key twice reveals signer's identity.A protocol for
untraceable payments in Bitcoin ecash system is also oered.
Shushuev G.I.OPTIMAL LINEAR APPROXIMATIONS FOR FEISTEL NET
WORKS.ESTIMATION FOR THE RESISTANCE OF THE CIPHER SMS4
TO LINEAR CRYPTANALYSIS.An approach to obtain the best linear approxi
mations for Feistel networks is proposed.The resistance of the cipher SMS4 to linear
cryptanalysis is investigated.
SECTION 3
Bernstein A.Yu.,Shilov N.V.\ROBOTS INSPACE"MULTIAGENT PROBLEM:
INFORMATION AND CRYPTOGRAPHIC ASPECTS.The multiagent problem
RinS (Robot in Space) considered here is formulated as follows:there are n > 2 autonomous
robots that need to agree without outside on distribution of shelters so that the straight
paths to the shelters will not intersect.The problemis closely related to geometry problems,
to the assignment problem in Graph Theory,to the convex hull problem in Combinatorial
Geometry,and to the pathplanning problem in Articial Intelligence.This paper studies
two aspects of the problemthe informational and cryptographic ones:we prove that there
is no protocol that solves the RinS transferring a bounded number of bits,and we suggest
a protocol that allows robots to check whether their paths intersect,without revealing
additional information about their positions.
Brechka D.M.THE SEARCH FOR BRIDGES IN TAKEGRANT SECURITY
MODEL.An algorithmfor searching bridges in protection graph for TakeGrant protection
model is described.The proof of its correctness is given.
Devyanin P.N.RESULTS OF REALIZATION CONDITIONS ANALYSIS FOR
INFORMATION FLOWS BY MEMORY IN ROSL DPMODEL.The role DP
model of Linux operating systems is considered.Conditions for realization in it of informa
tion ows by memory are analysed.Some results of the analysis are presented.
Dolgikh A.N.MITIGATIONMETHODS FORILLEGAL INFORMATIONTIM
INGFLOWS ONTHE SOCKET PROGRAMINTERFACE.Some ways for creat
ing and implementing information timing ows based on sockets in GNU/Linux operating
systemare considered.Methods for mitigating thembased on the subjects blocking accesses
are proposed.
Kolegov D.N.HIERARCHICAL ROLEBASED ACCESS CONTROL.A new ac
cess control model is proposed.It is obtained by adding a hierarchy and type attributes to
elements of the RBAC model family.The allowed access rights of subjects to entities in it
are specied dependent on the values of the subject and entity attributes.
Kolegov D.N.,Hasanov B.S.\NETWORKSECURITYARCHITECTURES FUN
DAMENTALS"LABORATORY PRACTICE IN CISCO PACKET TRACER.
The laboratory practice named in the title includes a number of dierent network security
labs (secure routing,secure switching,Internet perimeter protection,etc.),studying games
and network security projects.All practical studies are performed in Cisco Packet Tracer
emulator.
Sviridov P.Y.RESEARCH OF MANDATORY AND ROLE BASED ACCESS
CONTROL IN RSBAC SYSTEM.The main properties of the access management
132 Прикладная дискретная математика.Приложение
system RSBAC are described,and,for the realization of them in DPmodel,an adequate
extension of the last is proposed.
Smolyaninov V.Y.SUFFICIENT CONDITIONS FOR ACCESS RIGHTS
STEALING IN DPMODEL OF DATABASE MANAGEMENT SYSTEMS.
For a security theoretical analysis of database management systems,a DPmodel of them
is suggested.Sucient conditions for stealing access rights in it are formulated.
Tkachenko N.O.BASED ON SELinux MANDATORY ACCESS CONTROL IN
DATABASE MANAGEMENT SYSTEM MySQL.The main steps for addition of
mandatory access control to relational database management system(RDBMS) MySQL are
proposed on the base of SELinux.These steps are the following:to set security contexts for
all entities of the RDBMS MySQL,to create the security policy module,to implement the
interaction of SELinux system and RDBMS MySQL hook functions,and to replace (fully
or partly) functions realizing discretionary access control in RDBMS with hook functions.
Chernov D.V.ATTRIBUTE BASED ACCESS CONTROL MODELS.The paper
presents reasons for necessity of more exible access control systems,like attribute based
access control (ABAC) system.General properties of ABAC are described.Several articles
which discuss how ABAC principles may be combined with other access control models and
how this models can be used are shown.
SECTION 4
Abrosimov M.B.,Komarov D.D.ON A COUNTEREXAMPLE TO A MINIMAL
VERTEX 1EXTENSION OF STARLIKE TREES.For a given graph G with n
nodes,we say that graph G
is its vertex extension if for each vertex v of G
the subgraph
G
v contains graph G up to isomorphism.A graph G
is a minimal vertex extension of
the graph G if G
has n +1 nodes and there is no vertex extension with n +1 nodes of G
having fewer edges than G
.A tree is called starlike if it has exactly one node of degree
greater than two.We give a lower and upper bounds of the edge number of a minimal
vertex extension of a starlike tree and present trees for which these bounds are achieved.
Abrosimov M.B.,Kuznetsov N.A.ON THE NUMBER OF MINIMAL VERTEX
AND EDGE 1EXTENSIONS OF CYCLES.For a given graph G with n nodes,we
say that graph G
is its vertex extension if for each vertex v of G
the subgraph G
v
contains graph G up to isomorphism.A graph G
is a minimal vertex extension of the
graph G if G
has n+1 nodes and there is no vertex extension with n+1 nodes of G having
fewer edges than G
.A graph G
is edge extension of graph G with n nodes if every graph
obtained by removing any edge from G
contains G.Edge extension of graph G with n
vertices is called minimal if among all edge extensions of graph G with n vertices it has the
minimum possible number of edges.We present the results of computational experiment
in which all minimal vertex and edge extensions of cycles up to 17 vertices were found.
Abrosimov M.B.,Modenova O.V.ON DIGRAPHS WITH A SMALL NUMBER
OF ARCS IN A MINIMAL 1VERTEX EXTENSION.A graph G
nodes is vertex
extension of graph G with n nodes if every graph obtained by removing any vertex fromG
contains G.Vertex extension of graph G with n + 1 vertices is called minimal if among
all vertex extensions of graph G with n +1 vertices it has the minimum possible number
of edges.We study digraphs,whose minimal vertex extensions have a specied number
of additional arcs.A solution is given when the number of additional arcs is equal to one
or two.
Аннотации докладов на английском языке 133
Bondarenko P.P.ON MINIMAL EXTENSIONS OF SPECIAL TYPE BLACK
WHITE PATHS.The circles and circuits with two vertices of one type and with other
vertices of another type are considered.Their minimal vertex and edge extensions are
studied.A connection between vertex extensions of some of such circuits and circles are
described.
Grunsky I.S.,Sapunov S.V.DETERMINISTIC LABELLING OF GRAPH VER
TICES BY WALKING AGENT.This paper is devoted to the problem of online
labelling of graph vertices by walking agent so that all vertices in the neighbourhood of the
current vertex have dierent labels (i.e.deterministic labelling).This problem arises in
the navigation of mobile robots using topological maps of an environment.Here,a method
for deterministic labelling is proposed for an agent of two types diering by the size of the
observed neighbourhood of the current vertex.
Zharkova A.V.ON INDICES IN DYNAMIC SYSTEMOF BINARY VECTORS
ASSOCIATED WITH CYCLES ORIENTATIONS.An algorithm is proposed for
computation of indices in dynamic system of binary vectors associated with cycles orien
tations.Evolutionary function of the system transforms vectors according to the following
rules:if both the initial component is 0 and the nal one is 1 they are replaced by 1 and 0
respectively,and all digrams 10 are replaced simultaneously by 01.Maximal index of a
subsystem formed by vectors of a given dimension is found.
Karmanova E.O.GRAPH CONGRUENCES:SOME COMBINATORIAL PRO
PERTIES.A congruence relation of a path is an equivalence relation on the set of its
vertices all of whose classes are independent subsets.It is proved (theorem 1) that the
number of all congruence relations of a path with m edges equals to the number of all
equivalence relations on a melement set.For a given connected graph G theorem 2 deter
mines the length of the shortest path whose quotientgraph is G.
Magomedov A.M.ONINTERVAL EDGE COLOURING.It is shown that there is a
(6,3)biregular graph G = (X;Y;E),such that jXj +jY j = 33,with no interval 6colourings,
and it is proved that the colouring problem for bipartite multigraph G = (X;Y;E) is
NPcomplete even if jXj = 2.
Magomedov T.A.MATCHINGS CONSTRUCTIONPROCEDURE.Conditions for
the existence of consecutive matchings in a bipartite graph are considered.
Sennikova L.I.,Kochkarov A.A.A PARALLEL ALGORITHMFOR SEARCHING
THE MINIMUMWEIGHT SPANNING TREE ON PREFRACTAL GRAPH.
Prefractal (fractal) graphs are models of complex selfsimilar structures.Hence,there is
a need in theoretical studies related to processing prefractal graph models.In view of a
large dimension of prefractal graphs,it is advisable to analyze these models on parallel
computational systems.In this paper,a parallel algorithm for searching the minimum
weight spanning tree of a prefractal graph is suggested.The parallelization of the algorithm
is based on the use of selfsimilarity properties of prefractal graphs.
Tatarinov E.A.GRAPHRECONSTRUCTIONBYAUTOMATATEAM.The pa
per is devoted to analysis and modication of the Basic Algorithm for graph reconstruction
by agent,moving through graph edges,reading and modifying marks on the elements of
the graph.The algorithm uses an implicit enumeration of graph vertices.The modication
of the Basic Algorithm implements the reconstruction by automata team.In this case,the
134 Прикладная дискретная математика.Приложение
upper bound on the time complexity of the algorithm depends on the number of agents in
the automata team that perform the reconstruction.
SECTION 5
Bannykh A.G.MASS UPDATES ON MULTIDIMENSIONAL DATA.A problem
of ecient implementation of mass updates on multidimensional data is studied.For a
specic range of operations,a exible solution is proposed.The solution is applicable if
the data elements form an abelian group with some operator +.In that case,the proposed
method allows eective sum calculation and addition of the same value to the rectangular
areas.
Burlakov A.S.ANALYSIS OF ALGORITHMS OF EXECUTABLE FILES IN A
COMPUTER EMULATOR WITH A CHANGEABLE SPECIFICATION.The
report addresses to issues related to the description of the semantics of machine instructions.
This includes the analysis of expressions.It also discusses the methods for dynamic analysis
of applications executed within the builtin environment,such as tracing the progress of
the program and the construction of the graph of conditional transitions.
Bykova V.V.METHODS FORDESIGNINGFPTALGORITHMS ONGRAPHS
OF LIMITED TREEWIDTH.A method for designing FPTalgorithms by means of
dynamic programming based on the tree decomposition is investigated.Some problems
limiting the application of this method in practice are pointed.The problem of memory is
solved by using a binary tree decomposition of the separator,which reduces the theoretical
and the actual size of the dynamic programming tables.The technique of tables in the
language of relational algebra is described.
Glotov I.N.,Ovsyannikov S.V.,Trenkaev V.N.ABOUTDISTRIBUTEDDATABASE
MANAGEMENT SYSTEMBASED ON MariaDB SERVER.The paper presents
a distributed database management system (DDBMS) based on MariaDB server.The dis
tinguishing feature of the DDBMS is a partition of MariaDB server.The MariaDB server
core and remote storage engine are placed on dierent machines and interact through a
network.
Zaikin O.S.,Posypkin M.A.,Semenov A.A.USING VOLUNTEER COMPUTA
TION TO SOLVE CRYPTOGRAPHIC PROBLEMS.In the paper a technology
for solving cryptographic problems in volunteer computing projects is described.Authors
have implemented volunteer project SAT@home in which a successful cryptanalysis of the
keystream generator A5/1 was performed.
Mikhailov A.A.DELPHI OBJECT FILES ANALYSIS USINGSPECIFICATION
OF MACHINE COMMANDS SEMANTICS.The object Delphi les decompilation
problemis considered.The DCU format specication in Flext and disassembler DCU32INT
of the DCU format specication are made use for the Delphi compiled les analysis.Mech
anism of the code semantics description for Intel x86 processors is developed.Using this
gives much of opportunities and makes the decompilation process more eective.
Saukh A.M.ANALYSIS OF SOME PROGRAM SOURCES SEMANTIC AS
PECTS BASED ON FORMAL SYNTAX AND SEMANTICS SPECIFICA
TIONS.In this work,the problem of syntax and semantic analysis of program sources
written in dierent languages is considered.The programming language is considered to
be specied by describing the lexis as a set of regular expressions and the syntax as a
Аннотации докладов на английском языке 135
contextfree grammar with a set of controlling structures matching grammar rules.These
controlling structures manage abstract syntax tree building and other analysis tasks.All
these allow performing some sort of semantic analysis against the source written in the
specied language.
SECTION 6
Andreeva L.N.,Poteryaeva V.A.INVOLUTIONS NUMERATION.Two algorithms
for involutions numeration are proposed in this paper:an algorithm nding index of the
given involution and an algorithm constructing involution by means of the given index.
Zachesov Y.L.,Grishin A.M.ABSENCE OF DYNAMISM AT METHOD NFS.
At present,the number eld sieve (NFS) and a software package GGNFS are the primary
tools for solving the factorization problem.Extrapolation of the data complexity of the
algorithm NFS shows that it is impossible to apply this algorithm for factoring 768bit or
more modules.This work compares the evaluation of laborintensiveness of subexponential
algorithms of whole number factorization and evaluation of productivity of supercomputers
fromthe Top 500 list.The conclusion following fromthe comparison is that these algorithms
are now nondynamic.
Filina M.V.,Zubkov A.M.EXACT COMPUTATION OF DISTRIBUTIONS BY
MEANS OF MARKOV CHAINS.The machinery of Markov chains may be used for
the exact computation of distributions of some statistics.Numerical results reveal some
unexpected dierences between exact and asymptotic distributions.
Medvedev A.V.BOOLEAN FUNCTION ABSOLUTE NONLINEARITY CAL
CULATION ON GPU.The algorithm for calculating the absolute nonlinearity of
Boolean function on CUDAenabled GPUs is proposed.Experiments showed that com
putation on GPU is 106 times faster than on one core of CPU.
Semenov A.A.,Ignatiev A.S.ABOUT CONVERGENCE OF A HYBRID
SAT+ROBDDDERIVATION.In the paper,the authors consider a new property of a
hybrid SAT+ROBDDderivation.This property consists in a convergence with respect to
the number of paths to a terminal vertex"1"in a ROBDD which represents database of
con icts accumulated during the process of nonchronological DPLL.
Usatyuk V.S.THE IMPLEMENTATION OF THE PARALLEL ORTHOGO
NALIZATION ALGORITHMS IN THE SHORTEST INTEGER LATTICES
BASIS PROBLEM.This article presents a way to signicantly increase the performance
of lattice basis reduction algorithms (hundredfold to three hundred times) by replacing re
cursive orthogonalization GramSchmidt algorithmby parallel QRalgorithms.The paper
contains a comparison between implementation of serial columnmajor Gram  Schmidt
and parallel algorithms on NVIDIA CUDA GPU framework using Givens rotation,multi
core CPU Intel Math Kernel library,and Householder transformation.
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