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NPcomplete problems and physical reality
 ACM SIGACT News Complexity Theory Column, March. ECCC
, 2005
"... Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Mal ..."
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Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, MalamentHogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing. ” The section on soap bubbles even includes some “experimental ” results. While I do not believe that any of the proposals will let us solve NPcomplete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics. 1
The tractable cognition thesis
 Cognitive Science: A Multidisciplinary Journal
, 2008
"... The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constra ..."
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Cited by 15 (2 self)
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The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computationallevel theories of cognition. To utilize this constraint, a precise and workable definition of “computational tractability ” is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomialtime computability, leading to the PCognition thesis. This article explains how and why the PCognition thesis may be overly restrictive, risking the exclusion of veridical computationallevel theories from scientific investigation. An argument is made to replace the PCognition thesis by the FPTCognition thesis as an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixedparameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified.
Computational universes
 Chaos, Solitons & Fractals
, 2006
"... Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science h ..."
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Cited by 9 (5 self)
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Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.
Quantum computation and quantum information
 International Journal of Parallel, Emergent and Distributed Systems
, 2006
"... The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Th ..."
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The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and errorcorrection are then discussed. Prospects for building a practical quantum computer are also analyzed. 1 Introduction and
Why philosophers should care about computational complexity
 In Computability: Gödel, Turing, Church, and beyond (eds
, 2012
"... One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed casethat onewouldbe wrong. In particular, I arguethat computational complexity theory—the field that ..."
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One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed casethat onewouldbe wrong. In particular, I arguethat computational complexity theory—the field that studies the resources (such as time, space, and randomness) needed to solve computational problems—leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume’s problem of induction, Goodman’s grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing
Quantum computability and complexity and the limits of quantum computation. http://www.cs.berkeley.edu/ kamil/quantum/qc4.pdf
, 2003
"... This paper will present an overview of the current beliefs of quantum complexity theorists and discuss in detail the impacts these beliefs may have on the future of the field. In section one we give a brief fundamental overview of classical complexity theory, defining the time and space hierarchies ..."
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This paper will present an overview of the current beliefs of quantum complexity theorists and discuss in detail the impacts these beliefs may have on the future of the field. In section one we give a brief fundamental overview of classical complexity theory, defining the time and space hierarchies and providing examples of problems that fit into several important categories thereon. In section two we introduce quantum complexity and discuss its relationship to classical complexity. Section three presents an overview of the successful existing quantum algorithms, and section four presents a discussion on the actual practical gains that might be realized by quantum computation. Finally in section five we speculate briefly on the direction we believe the field to be headed, and what might reasonably be expected in the future. 1 Introduction to Computability and Complexity In computability and complexity theory, all problems are reduced to language recognition, where a language is defined as a set of strings over some alphabet, typically {0, 1}. For example, L1 = {0, 00, 000, · · · } is the language that contains all strings that contain only the letter 0. Once we have a language L, there are some interesting questions we can ask about it. Given an input x, can a machine decide if x ∈ L? If so, how
Sadri Computational Power of the Quantum Turing Automata
 Proceedings of the IEEE conference on Information Technology Next Generations, ITNG
, 2007
"... Lots of efforts in the last decades have been done to prove or disprove whether the set of polynomially bounded problems is equal to the set of polynomially verifiable problems. This paper will present an overview of the current beliefs of quantum complexity theorists and discussion detail the impac ..."
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Lots of efforts in the last decades have been done to prove or disprove whether the set of polynomially bounded problems is equal to the set of polynomially verifiable problems. This paper will present an overview of the current beliefs of quantum complexity theorists and discussion detail the impacts these beliefs may have on the future of the field. We introduce a new form of Turing machine based on the concepts of quantum mechanics and investigate the domain of this novel definition for computation. The main object is to show the domain of these Computation machines and the new definition of Algorithms using these automata. In section one we give a brief fundamental overview of classical complexity theory, Turing machine and all the fundamental concepts required for the next chapters. In section two we describe various classes of classical complexity automata. In next chapter we introduce quantum complexity featuring Quantum Turing Machines and discuss its relationship to classical complexity. Section four presents a relationship between Quantum complexity classes based on the quantum Turing machines and Quantum oracles, and their relationship with corresponding classical complexity classes. And section five presents a discussion on the practical phenomena in problem solving using quantum computers. Finally in section five we speculate briefly on the direction we believe the field to be headed, and what might reasonably be expected in the future.
Halting in quantum Turing computation
, 705
"... Abstract The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa [1] as well as the objections raised by Myers [2], Kieu and Danos [3] and others. Final ..."
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Abstract The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa [1] as well as the objections raised by Myers [2], Kieu and Danos [3] and others. Finally, the relationship of the halting scheme to the quest for a universal quantum Turing machine is considered.