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Algorithms: A quest for absolute definitions
 Bulletin of the European Association for Theoretical Computer Science
, 2003
"... y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTurin ..."
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Cited by 19 (9 self)
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y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTuring thesis and contrast Church's and Turing's approaches, and we finish with some recent investigations.
On Kolmogorov machines and related issues
 Bull. of Euro. Assoc. for Theor. Computer Science
, 1988
"... I felt honored and uncertain when Grzegorsz Rozenberg, the president of EATCS, proposed that I write a continuing column on logic in computer science in this Bulletin. Writing essays wasn’t my favorite subject in high school. After some hesitation, I decided to give it a try. I’ll need all the help ..."
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Cited by 6 (2 self)
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I felt honored and uncertain when Grzegorsz Rozenberg, the president of EATCS, proposed that I write a continuing column on logic in computer science in this Bulletin. Writing essays wasn’t my favorite subject in high school. After some hesitation, I decided to give it a try. I’ll need all the help I can get from you: criticism, comments, queries, suggestions, etc. Andrei Nikolayevich Kolmogorov died a few months ago. In recent years he chaired the Department of Mathematical Logic at the Moscow State University. In a later article or articles, I hope to discuss Kolmogorov’s ideas on randomness and information complexity; here let me take up the issue of Kolmogorov machines and their close relatives, Schönhage machines. I believe, we are a bit too faithful to the Turing model. It is often easier to explain oneself in a dialog. To this end, allow me to introduce my imaginary student Quizani. • Quizani: I think you should introduce yourself too. Don’t assume everyone knows you. • Author: All right. I grew up in the Soviet Union and started my career in the Ural University as an algebraist and selftaught logician. In 1973, I emigrated to Israel where I did logic and taught at BenGurion
In Some Curved Spaces, One Can Solve NPHard Problems in Polynomial Time
"... In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved s ..."
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Cited by 6 (6 self)
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In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NPhard. It is well known that many important practical problems are NPhard; see, e.g., [11, 14, 27]. Under the usual hypothesis that P̸=NP, NPhardness has the following intuitive meaning: every algorithm which solves all instances of the corresponding problem requires, for
In Some Curved Spaces, We Can Solve NPHard Problems in Polynomial Time: Towards Matiyasevich’s Dream
"... In late 1970s and early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 ..."
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In late 1970s and early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NPhard. It is well known that many important practical problems are NPhard; see, e.g., [7, 9, 22]. Under the usual hypothesis that P̸=NP, NPhardness has the following intuitive meaning: every algorithm which solves all the instances of the corresponding problem requires,