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Yuri Gurevich is a senior
scientist heading the Foundations of Software Engineering group
at Microsoft Research in Redmond, WA. He is Professor Emeritus of
Electrical Engineering and Computer Science at the University of
Michigan. Originally, he started his career as an algebraist. Later
he became a logician. Then he moved to computer science, where his
main projects have been Abstract State Machines, Average Case Computational
Complexity, and Finite Model Theory. Dr. Gurevich has been honored
as a Dr. Honoris Causa of the University of Limburg, Belgium (1998),
as a Fellow of the Association for Computing Machinery (1996), as
well as a Fellow of the John Simon Guggenheim Memorial Foundation
(1995).
Contributions to Algebra and Logic

For the first twenty years of his career Yuri Gurevich worked in
algebra and mathematical logic. One of the landmark results he obtained
was the decidability of the firstorder theory of ordered abelian
groups which answered a question posed by the great logician Alfred
Tarski. (Interestingly, Tarski announced that he had that decidability
result, but then acknowledged that the proof fell through). Another
landmark result of Gurevich relates to the Classical Decision Problem:
Classify the standard fragments of predicate logic into decidable
and undecidable. The problem attracted attention of many famous
logicians
including Gödel himself. Gurevich completed the desired classification.
Alongside Saharon Shelah, Gurevich made a major contribution into
the study of the monadic secondorder theory of orders and trees.
His work in this early period addressed a wide spectrum of problems,
some involving advanced set theory, and showed enormous versatility.
In the early eighties he had become one of the world's leading mathematical
logicians.
Contributions to Average Case Computational Complexity

In applications, NP problems often come with probability distribution
on instances. Typically, it suffices to solve the problem fast on
average. It turns out that many NP complete (and thus worstcase
intractable) problems do have feasible averagecase solutions with
respect to natural probability distributions. For example, Gurevich
and Shelah constructed an algorithm that solves the Hamiltonian
circuit problem in linear time on average with respect to the uniform
probability distribution. However, the situation is not always so
rosy. Leonid Levin and Yuri Gurevich developed a theory of averagecase
complexity and provided numerous examples of averagecase intractable
NP problems with natural probability distributions.
Contributions to Finite Model Theory

Yuri Gurevich is one of the founders of and major contributors to
finite model theory. He discovered that numerous classical modeltheoretic
results fail in the finite case. He showed that, over finite models,
primitive recursive functions are exactly those logspace computable,
and that recursive (a la HerbrandGödelKleene) functions are
exactly those polynomial time computable. Gurevich and Shelah showed
that, over finite models, firstorder logic with the least fixedpoint
operator is exactly as expressible as firstorder logic with the
inflationary fixedpoint operator. Ajtai and Gurevich showed that,
as far as expressivity over finite models is concerned, firstorder
logic and datalog have trivial intersection. In 1988, Gurevich published
a conjecture that, in the case of arbitrary finite models (as opposite
to ordered finite models), there is no logic that captures polynomial
time. These are only some of the important results of Gurevich in
the area.
Contributions to the Theory of Abstract State Machines

Dr. Gurevich's fundamental work on the theory of Abstract State
Machines (ASMs), originally called evolving algebras, is of fundamental
importance for theoretical and applied computing science. He formulated
the ASM thesis according to which ASMs provide a universal model
of computation in a stronger sense than Turing Machines. ASMs
stepforstep simulate arbitrary algorithms on their natural levels
of abstraction. The ASM thesis applies to sequential, parallel and
distributed algorithms. Recently Gurevich was able to prove the
version of the thesis for sequential algorithms. After that, Andreas
Blass and Yuri Gurevich proved the version of the thesis for parallel
algorithms.
The significance of the theoretical concepts developed by Gurevich
is confirmed by the substantial impact they have on mathematical
modeling of discrete dynamic systems. Indeed, the definition of
ASMs have triggered hundreds of research papers in applied computer
science. This success is well documented in the annotated ASM bibliography
on the ASM web site. There
is a wellestablished international ASM community which holds regular
conferences and workshops.
Beyond academic research, ASMs have been used in industry as a
practical tool for system modeling by leading companies such as
Siemens (Munich), and Microsoft (Redmond). Furthermore, ASMs have
been adopted as a basis for international standardization of complex
modeling and programming languages. For instance, the International
Telecommunication Union (former CCITT) has approved the ASMbased
model of their specification and design language SDL as the current
standard. 