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TIME TRAVEL: A NEW HYPERCOMPUTATIONAL PARADIGM
, 2009
"... Assuming that all objections to time travel are set aside, it is shown that a computational system with closed timelike curves is a powerful hypercomputational tool. Speci cally, such a system allows us to solve four out of five problems recently advanced as counterexamples to the fundamental princi ..."
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Cited by 6 (3 self)
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Assuming that all objections to time travel are set aside, it is shown that a computational system with closed timelike curves is a powerful hypercomputational tool. Speci cally, such a system allows us to solve four out of five problems recently advanced as counterexamples to the fundamental principle of universality in computation. The fifth counterexample, however, remains unassailable, indicating that universality in computation cannot be achieved, even with the help of such an extraordinary ally as time travel.
Computations with Uncertain Time Constraints: Effects on Parallelism and Universality
, 2008
"... It is known that there exist computational problems that can be solved on a parallel computer, yet are impossible to be solved sequentially. Specifically, no general purpose sequential model of computation, such as the Turing Machine or the Random Access Machine, can simulate a large family of compu ..."
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Cited by 1 (0 self)
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It is known that there exist computational problems that can be solved on a parallel computer, yet are impossible to be solved sequentially. Specifically, no general purpose sequential model of computation, such as the Turing Machine or the Random Access Machine, can simulate a large family of computations (for example, solutions to certain realtime problems), each of which is capable of being carried out readily by a particular parallel computer. We extend 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 the input data available. A second type of time constraints refers to uncertain deadlines for tasks. Our main objective 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 here, prove once more that it is impossible to define a ‘universal computer’, that is, a computer able to compute all computable functions. Finally, one of the contributions of this paper is to promote the study of a topic, conspicuously absent to date from theoretical computer science, namely, the role of physical time and physical space in computation. The focus of our work is to analyze the effect of external natural phenomena on the various components of a computational process, namely, the input phase, the calculation phase (including the algorithm and the computing agents themselves), and the output phase.
Technical Report 2013608 WHAT IS COMPUTATION?
"... Abstract Three conditions are usually given that must be satisfied by a process in order for it to be called a computation, namely, there must exist a finite length algorithm for the process, the algorithm must terminate in finite time for valid inputs and return a valid output, and finally the alg ..."
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Abstract Three conditions are usually given that must be satisfied by a process in order for it to be called a computation, namely, there must exist a finite length algorithm for the process, the algorithm must terminate in finite time for valid inputs and return a valid output, and finally the algorithm must never return an output for invalid inputs. These three conditions are advanced as being necessary and sufficient for the process to be computable by a universal model of computation. In fact, these conditions are neither necessary, nor sufficient. On the one hand, recently defined paradigms show how certain processes that do not satisfy one or more of the aforementioned properties can indeed be carried out in principle on new, more powerful, types of computers, and hence can be considered as computations. Thus the conditions are not necessary. On the other hand, contemporary work in unconventional computation has demonstrated the existence of processes that satisfy the three stated conditions, yet contradict the ChurchTuring Thesis, and more generally, the principle of universality in computer science. Thus the conditions are not sufficient.
Time Indeterminacy, NonUniversality in Computation, and the Demise of the ChurchTuring Thesis
, 2011
"... It is known that there exist computational problems that can be solved on a parallel computer, yet are impossible to be solved sequentially. Specifically, no general purpose sequential model of computation, such as the Turing Machine or the Random Access Machine, can simulate a large family of compu ..."
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It is known that there exist computational problems that can be solved on a parallel computer, yet are impossible to be solved sequentially. Specifically, no general purpose sequential model of computation, such as the Turing Machine or the Random Access Machine, can simulate a large family of computations (for example, solutions to certain realtime problems), each of which is capable of being carried out readily by a particular parallel computer. We extend 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 the input data available. A second type of time constraints refers to uncertain deadlines on when outputs are to be produced. Our main objective 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 here, prove once more that it is impossible to define a ‘universal computer’, that is, a computer able to perform (through simulation or
TimeSensitive Computational Models with a Dynamic Time Component
"... 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 realtime ..."
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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 realtime 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 itisvery 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.