X-machines and the halting problem: Building a super-turing machine

Stannett, Mike

doi:10.1007/bf01888233

Cited by 38 publications

(21 citation statements)

References 4 publications

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“…This Turing machine is not able to simulate a more powerful machine capable of carrying these tasks to completion. This confirms, once again, the previously established result [9,11,15,16,17,18] that the Turing machine is in fact not universal, as it cannot simulate a task computable on a particular parallel machine.…”

Section: Resultssupporting

confidence: 87%

Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

Nagy

Akl

2011

Lecture Notes in Computer Science

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It is known that a parallel computer can solve problems that are impossible to be solved sequentially. That is, any general purpose sequential model of computation, such as the Turing machine or the random access machine (RAM), cannot simulate certain computations, for example solutions to real-time problems, that are carried out by a specific parallel computer. This paper extends the scope of such problems to the class of problems with uncertain time constraints. The first type of time constraints refers to uncertain time requirements on the input data, that is when and for how long are input data available. A second type of time constraints refers to uncertain deadlines for tasks. The main contribution of this paper is to exhibit computational problems in which it is very difficult to find out (read compute) what to do and when to do it. Furthermore, problems with uncertain time constraints, as described in this paper, prove once more, that it is impossible to define a universal computer, that is, a computer able to simulate all computable functions.

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Section: Resultssupporting

confidence: 87%

Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

Nagy

Akl

2011

Lecture Notes in Computer Science

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“…Generally, the automaton to recognize a set not to be r.e. is called a super-Turing machine [22,23]. Every super-Turing machine recognizes a set to be beyond r.e.…”

Section: Discussionmentioning

confidence: 99%

Dynamics and computation in functional shifts

Namikawa¹,

Hashimoto²

2004

Nonlinearity

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Abstract. We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift that is defined by a set of bi-infinite sequences of some functions on a set of symbols. To analyze the complexity of functional shifts, we measure them in terms of topological entropy, and locate their languages in the Chomsky hierarchy. Through this study, we argue that considering functional shifts from the viewpoints of both dynamics and computation give us opposite results about the complexity of systems. We also describe a new class of shift spaces whose languages are not recursively enumerable. §

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“…Using real numbers can, as always, create a number of fundamental problems related to computability etc., e.g. [19].…”

Section: A Probabilistic Languagementioning

confidence: 99%

On Dynamical Probabilities, or: How to Learn to Shoot Straight

Wiklicky¹

2016

Lecture Notes in Computer Science

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Abstract. In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involved are represented by constants, i.e. one deals with static probabilities. In this paper we investigate a semantical framework which allows for changing, i.e. dynamic probabilities which is still based on time-homogenous DTMCs, i.e. the transition matrix representing the semantics of a program does not change over time.

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X-machines and the halting problem: Building a super-turing machine

Cited by 38 publications

References 4 publications

Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

Dynamics and computation in functional shifts

On Dynamical Probabilities, or: How to Learn to Shoot Straight

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