Dmitriy Yu. Cherukhin

cherukhin at gmail dot com

(+7 495) 454-91-12

Personal information

• Date of birth: October 30, 1976

• Place of birth: Kerch, Ukraine

• Gender: male

• Marital status: married

• Children: none

Educational background

• Lomonosov Moscow State University, Mechanics and Mathematics Faculty, Discrete Mathematics Department

• 1998: M.Sc., major - Mathematics, minor - Computer Science

• 2000: Ph.D. in Computer Science• Specialization: Complexity of Boolean

functions, lower bounds

Achievements

• Participation in many mathematical competitions for schools; the best result – personal Second Diploma in All-U.S.S.R. Mathematical Competition (1991)

• Personal grants from Soros Foundation (1998-2000)

• Outstanding Ph.D. thesis (2000)

Job Experience 1

• Lomonosov Moscow State University, Mechanics and Mathematics Faculty, Discrete Mathematics Department

• 11.2000 – 06.2008: Assistant Professor

• Teaching; courses: Discrete Mathematics, Introduction to Mathematical Logic

• Scientific work (see later)

Job Experience 2

• Lomonosov Moscow State University, Mechanics and Mathematics Faculty, Laboratory for Computational Methods

• 06.2008 – the present: Researcher

• Teaching; course: Algebra; location: Branch of Moscow State University in Baku, Azerbaijan

Scientific work

• 19 papers published in Russian refereeing scientific journals; most of them are translated into English

• Participating in many Russian scientific conferences and international conference CSR-2008, Moscow (proceedings are in Lecture Notes in Computer Science, Springer)

Research results: Boolean bases 1

• The comparison of Boolean bases problem• Let us represent Boolean functions by formulas

over different bases• For example, here is the representation of the

function xor by a formulae over the basis {and, or, not}:

• X xor Y = (X and (not Y)) or ((not X) and Y)• The complexity of this formulae is 4

Research results: Boolean bases 2

• We say that a basis B1 is better that a basis B2 iff over the basis B1, we can represent any Boolean function more effectively (i.e. with smaller complexity) then over the basis B2

• The problem is to describe the relation ‘better’ between any finite bases

• The problem was stated by Lupanov in 1961; an algorithmic criterion for comparison of any bases was given by me (1999, Ph.D. thesis)

Research results: finite depth 1

• The problem of deriving high lower bounds of complexity for explicitly given functions

• We consider circuits with:

• - arbitrary Boolean gates f : {0,1}n {0,1}

• - unbounded fan-in (n is unlimited)

• - bounded depth d

• The complexity is the number of edges

Research results: finite depth 2

• Here is an example of a circuit; the depth is 2 and the complexity is 8

x1 x2

f1

x3

f2

f3 f4

Level 2

Level 1

Research results: finite depth 3

• For any finite depth we prove a lower bound of complexity for the Boolean convolution

• This lower bound is the best known for any even depth and for depth 3

• For depth 2 our bound is n1.5 (2005); previous best bound is n log2 n / log log n (Radhakrishnan J., Ta-Shma A., 1997)

Hobby: programming

• I wrote the DuS operation system from the zero start point (for Intel-32 architecture)

• The main conception: there are no system functions; every process has its own set of external functions given by its parent

• Multitasking, multi-user with protection• Hard: keyboard, mouse, VESA, ATA HDD• Soft: Commander, text, graphics, C, TeX

Future plans with Big Company

• Research (Mathematics, Computer Science) and/or programming

• 1 year (preferred)

• Location: Big Country or Russia