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Interactive and probabilistic proofchecking
 Annals of Pure and Applied Logic
, 2000
"... The notion of efficient proofchecking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized and interac ..."
On Probabilistic Proof Systems . . .
, 2002
"... In this thesis we study the approximability of combinatorial optimization problems whose decision versions are NPcomplete. These problems cannot be solved exactly in polynomial time,unless P = NP. However,it may be possible to solve them approximately in polynomial time,i.e.,there might exist a pol ..."
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is at most c times the value of the produced solution,and for a minimization problem we say that an algorithm approximates within c if it finds a solution whose value is at most c times the optimum solution. The focus of this thesis is to use probabilistic proof systems to prove,for various problems
Probabilistic Proofs and Transferability
 Philosophia Mathematica
"... One of the central questions in the philosophy of mathematics concerns the nature of mathematical knowledge. The version of this question familiar from [Benacerraf, 1973] asks how knowledge of any mathematical proposition could be consistent with any picture of the semantics of mathematical language ..."
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. To begin to address this question, I note that there is some extremely close connection in mathematics between knowledge and proof. Mathematicians often say that a claim is not known until a proof has been given, and an account somewhat like this is presupposed in some naturalistic discussions
Probabilistic Proof Systems  A Survey
 IN SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1996
"... Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems  interactive proofs, zeroknowledge proofs, and probabilistic checkable proofs  stressing the essen ..."
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Various types of probabilistic proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems  interactive proofs, zeroknowledge proofs, and probabilistic checkable proofs  stressing
The Weizmann Workshop on Probabilistic Proof Systems
, 1994
"... The Weizmann Workshop on Probabilistic Proofs and Applications to Program Checking, Cryptography, and Hardness of Approximation was held at the Weizmann Institute of Science, on January 1013, 1994. The following report provides the abstracts of the talks given at the workshop, the list of participa ..."
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The Weizmann Workshop on Probabilistic Proofs and Applications to Program Checking, Cryptography, and Hardness of Approximation was held at the Weizmann Institute of Science, on January 1013, 1994. The following report provides the abstracts of the talks given at the workshop, the list
Combinatorial Constructions of Probabilistic Proof Systems
, 2010
"... Probabilistic proof systems is a paradigm of complexity theory whose study evolves around questions such as “how can we use randomness to prove and verify assertions?”, “what do we gain from using randomness in verification procedures?”, and “what assertions can be verified by probabilistic verifica ..."
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Probabilistic proof systems is a paradigm of complexity theory whose study evolves around questions such as “how can we use randomness to prove and verify assertions?”, “what do we gain from using randomness in verification procedures?”, and “what assertions can be verified by probabilistic
Probabilistic Proofs of Existence of Rare Events
"... In a typical probabilistic proof of a combinatorial result, one usually has to show that the probability of a certain event is positive. However, many of these proofs actually give more and show that the probability of the event considered is not only positive but is large. In fact, most probabilist ..."
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In a typical probabilistic proof of a combinatorial result, one usually has to show that the probability of a certain event is positive. However, many of these proofs actually give more and show that the probability of the event considered is not only positive but is large. In fact, most
Bounded Arithmetic and Formalizing Probabilistic Proofs
, 2014
"... The first theme of this thesis investigates the complexity class CC and its associated boundedarithmetic theory. Subramanian defined CC as the class of problems logspace reducible to the comparator circuit value problem (Ccv). Using the CookNguyen method we define the twosorted theory VCC whose ..."
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Subramanian’s work by showing that the problems in his paper are indeed complete for CC under manyone AC 0 reductions. We then prove the correctness of these reductions in VCC. The second theme of this thesis is formalizing probabilistic proofs in bounded arithmetic. In a series of papers, Jeˇrábek argued
Probabilistic Proofs and the Collective Epistemic Goals of Mathematicians
"... Mathematicians only use deductive proofs to establish that mathematical claims are true. They never use inductive evidence, such as probabilistic proofs, for this task. Don Fallis (1997 and 2002) has argued that mathematicians do not have good epistemic grounds for this complete rejection of probabi ..."
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Mathematicians only use deductive proofs to establish that mathematical claims are true. They never use inductive evidence, such as probabilistic proofs, for this task. Don Fallis (1997 and 2002) has argued that mathematicians do not have good epistemic grounds for this complete rejection
A probabilistic proof of the girthchromatic . . .
, 2013
"... This works presents a formalization of the GirthChromatic number theorem in graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. The proof uses the theory of Random Graphs to prove the existence with probabilistic arguments and is based on [1]. ..."
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This works presents a formalization of the GirthChromatic number theorem in graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. The proof uses the theory of Random Graphs to prove the existence with probabilistic arguments and is based on [1].
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