Anytime Algorithms for Non-Ending Computations

Mapping Intimacies ◽

10.31219/osf.io/9y5nv ◽

2017 ◽

Author(s):

Cristian S. Calude ◽

Damien Desfontaines

Keyword(s):

Stopping Time ◽

General Setting ◽

Anytime Algorithms ◽

Halting Problem ◽

Anytime Algorithm

A program which eventually stops but does not halt “too quickly” halts at a time which is algorithmically compressible. This result—originally proved in [4]—is proved in a more general setting. Following Manin [11] we convert the result into an anytime algorithm for the halting problem and we show that the stopping time (cut-off temporal bound) cannot be significantly improved

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Anytime Algorithms for Non-Ending Computations

International Journal of Foundations of Computer Science ◽

10.1142/s0129054115500252 ◽

2015 ◽

Vol 26 (04) ◽

pp. 465-475 ◽

Cited By ~ 3

Author(s):

Cristian S. Calude ◽

Damien Desfontaines

Keyword(s):

Stopping Time ◽

General Setting ◽

Anytime Algorithms ◽

Halting Problem ◽

Anytime Algorithm

A program which eventually stops but does not halt “too quickly” halts at a time which is algorithmically compressible. This result — originally proved in [4] — is proved in a more general setting. Following Manin [11] we convert the result into an anytime algorithm for the halting problem and we show that the stopping time (cut-off temporal bound) cannot be significantly improved.

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A probabilistic anytime algorithm for the halting problem

Computability ◽

10.3233/com-170073 ◽

2018 ◽

Vol 7 (2-3) ◽

pp. 259-271 ◽

Cited By ~ 3

Author(s):

Cristian S. Calude ◽

Monica Dumitrescu

Keyword(s):

Halting Problem ◽

Anytime Algorithm

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Meta-Level Control of Anytime Algorithms with Online Performance Prediction

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/208 ◽

2018 ◽

Cited By ~ 3

Author(s):

Justin Svegliato ◽

Kyle Hollins Wray ◽

Shlomo Zilberstein

Keyword(s):

Performance Prediction ◽

Intelligent Systems ◽

Computation Time ◽

Control Technique ◽

Level Control ◽

Anytime Algorithms ◽

Solution Quality ◽

Anytime Algorithm ◽

Control Techniques ◽

Meta Level

Anytime algorithms enable intelligent systems to trade computation time with solution quality. To exploit this crucial ability in real-time decision-making, the system must decide when to interrupt the anytime algorithm and act on the current solution. Existing meta-level control techniques, however, address this problem by relying on significant offline work that diminishes their practical utility and accuracy. We formally introduce an online performance prediction framework that enables meta-level control to adapt to each instance of a problem without any preprocessing. Using this framework, we then present a meta-level control technique and two stopping conditions. Finally, we show that our approach outperforms existing techniques that require substantial offline work. The result is efficient nonmyopic meta-level control that reduces the overhead and increases the benefits of using anytime algorithms in intelligent systems.

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A statistical anytime algorithm for the Halting Problem

Computability ◽

10.3233/com-190250 ◽

2020 ◽

Vol 9 (2) ◽

pp. 155-166

Author(s):

Cristian S. Calude ◽

Monica Dumitrescu

Keyword(s):

Halting Problem ◽

Anytime Algorithm

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General optimal stopping theorems for semi-Markov processes

Advances in Applied Probability ◽

10.2307/1427794 ◽

1993 ◽

Vol 25 (4) ◽

pp. 825-846 ◽

Cited By ~ 17

Author(s):

Frans A. Boshuizen ◽

José M. Gouweleeuw

Keyword(s):

Markov Processes ◽

Optimal Stopping ◽

Stopping Time ◽

General Setting ◽

The State ◽

Shock Models ◽

Special Cases ◽

Optimal Stopping Problems ◽

The Times ◽

Semi Markov Processes

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made.Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases.The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].

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Renormalisation and computation II: time cut-off and the Halting Problem

Mathematical Structures in Computer Science ◽

10.1017/s0960129511000508 ◽

2012 ◽

Vol 22 (5) ◽

pp. 729-751 ◽

Cited By ~ 9

Author(s):

YURI I. MANIN

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Hopf Algebra ◽

Quantum Field ◽

Theory Of Computation ◽

Anytime Algorithms ◽

Halting Problem

This is the second instalment in the project initiated in Manin (2012). In the first Part, we argued that both the philosophy and technique of perturbative renormalisation in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view.In this second part, we address some of the issues raised in Manin (2012) and develop them further in three contexts: a categorification of the algorithmic computations; time cut-off and anytime algorithms; and, finally, a Hopf algebra renormalisation of the Halting Problem.

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General optimal stopping theorems for semi-Markov processes

Advances in Applied Probability ◽

10.1017/s0001867800025775 ◽

1993 ◽

Vol 25 (04) ◽

pp. 825-846 ◽

Cited By ~ 6

Author(s):

Frans A. Boshuizen ◽

José M. Gouweleeuw

Keyword(s):

Markov Processes ◽

Optimal Stopping ◽

Stopping Time ◽

General Setting ◽

The State ◽

Shock Models ◽

Special Cases ◽

Optimal Stopping Problems ◽

The Times ◽

Semi Markov Processes

In this paper, optimal stopping problems for semi-Markov processes are studied in a fairly general setting. In such a process transitions are made from state to state in accordance with a Markov chain, but the amount of time spent in each state is random. The times spent in each state follow a general renewal process. They may depend on the present state as well as on the state into which the next transition is made. Our goal is to maximize the expected net return, which is given as a function of the state at time t minus some cost function. Discounting may or may not be considered. The main theorems (Theorems 3.5 and 3.11) are expressions for the optimal stopping time in the undiscounted and discounted case. These theorems generalize results of Zuckerman [16] and Boshuizen and Gouweleeuw [3]. Applications are given in various special cases. The results developed in this paper can also be applied to semi-Markov shock models, as considered in Taylor [13], Feldman [6] and Zuckerman [15].

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Products of 2 × 2 stochastic matrices with random entries

Journal of Applied Probability ◽

10.1017/s0021900200115943 ◽

1986 ◽

Vol 23 (04) ◽

pp. 1019-1024

Author(s):

Walter Van Assche

Keyword(s):

Rate Of Convergence ◽

Beta Distribution ◽

Stopping Time ◽

Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

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