Dmitriy Yu. Cherukhin cherukhin at gmail dot com (+7 495)

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 ( ) Outstanding Ph.D. thesis (2000)

Job Experience 1 Lomonosov Moscow State University, Mechanics and Mathematics Faculty, Discrete Mathematics Department – : 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 – 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 B 1 is better that a basis B 2 iff over the basis B 1, we can represent any Boolean function more effectively (i.e. with smaller complexity) then over the basis B 2 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 x1x1 x2x2 f1f1 x3x3 f2f2 f3f3 f4f4 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 n 1.5 (2005); previous best bound is n log 2 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