Machine Models and Simulations

Boas, Peter van Emde

doi:10.1016/b978-0-444-88071-0.50006-0

Cited by 186 publications

(99 citation statements)

References 76 publications

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“…This can be seen in the statement of the quantitative Church's thesis in van Emde Boas [1990], where the word "physical" in the above phrasing is replaced with the word "reasonable." It is difficult to imagine any definition of "reasonable" in this context which does not mean "physically realizable," i.e., that this computing machine could actually be built and would work.…”

Section: Introductionmentioning

confidence: 99%

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Shor¹

1997

SIAM J. Comput.

6,393

4,713

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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

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Section: Introductionmentioning

confidence: 99%

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Shor¹

1997

SIAM J. Comput.

6,393

4,713

View full text Add to dashboard Cite

show abstract

“…[11]). Its members fulfill the so-called Parallel Computation Thesis which states that sequential polynomial space is equivalent to parallel polynomial time on devices from this class.…”

Section: Corollary 1 For Any S(t)mentioning

confidence: 99%

Beyond the Turing Limit: Evolving Interactive Systems

Leeuwen

Wiedermann

2001

Lecture Notes in Computer Science

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Abstract:Modern networked computing systems follow scenarios that differ from those modeled by classical Turing machines. For example, their architecture and functionality may change over time as components enter or disappear. Also, as a rule their components interact with each other and with the environment at unpredictable times and in unpredictable manners, and they evolve in ways that are not pre-programmed. Finally, although the life span of the individual components may be finite, the life span of the systems as a whole is practically unlimited. The examples range from families of cognitive automata to (models of) the Internet and to communities of intelligent communicating agents.We present several models for describing the computational behaviour of evolving interactive systems, in order to characterize their computational power and efficiency. The analysis leads to new models of computation, including 'interactive' Turing machines (ITM's) with advice and new, natural characterizations of non-uniform complexity classes. We will argue that ITM's with advice can serve as an adequate reference model for capturing the essence of computations by evolving interactive systems, showing that 'in theory' the latter are provably more powerful than classical systems.

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“…For our runtime considerations we assume the random access machine (RAM) model [35]. In addition, we assume that elementary operations (addition, subtraction, multiplication, modulo) require constant time.…”

Section: Turing Machine Acceptancementioning

confidence: 99%

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

Bruner

Lackner

2015

Algorithmica

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The NP-complete Permutation Pattern Matching problem asks whether a k-permutation P is contained in a n-permutation T as a pattern. This is the case if there exists an order-preserving embedding of P into T . In this paper, we present a fixed-parameter algorithm solving this problem with a worst-case runtime of O(1.79 run(T ) · n · k), where run(T ) denotes the number of alternating runs of T . This algorithm is particularly well-suited for instances where T has few runs, i.e., few ups and downs. Moreover, since run(T ) < n, this can be seen as a O(1.79 n · n · k) algorithm which is the first to beat the exponential 2 n runtime of brute-force search. Furthermore, we prove that under standard complexity theoretic assumptions such a fixedparameter tractability result is not possible for run(P ).

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Machine Models and Simulations

Cited by 186 publications

References 76 publications

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Beyond the Turing Limit: Evolving Interactive Systems

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

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