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Related Concept Videos

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Causality or causation is a fundamental concept in epidemiology, vital for understanding the relationships between various factors and health outcomes. Despite its importance, there's no single, universally accepted definition of causality within the discipline. Drawing from a systematic review, causality in epidemiology encompasses several definitions, including production, necessary and sufficient, sufficient-component, counterfactual, and probabilistic models. Each has its strengths and...
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Associative learning, a core principle in behavioral psychology, involves forming connections between events and facilitating learned responses. This concept is vividly illustrated by classical conditioning, a process extensively studied by the Russian physiologist Ivan Pavlov. Pavlov's pioneering research on dogs' digestive systems led to the discovery that behaviors can be learned through association, laying the groundwork for classical conditioning.
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Related Experiment Video

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Measuring Active and Passive Tameness Separately in Mice
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Computational tameness of classical non-causal models.

Ämin Baumeler1,2, Stefan Wolf1,2

  • 1Faculty of Informatics, Università della Svizzera italiana, via G. Buffi 13, 6900 Lugano, Switzerland.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2018
PubMed
Summary

Classical deterministic closed timelike curves (CTCs) are computationally limited to problems within the UP∩coUP complexity class, like factorization. This finding suggests CTCs cannot efficiently solve NP-complete problems, making their existence less implausible.

Keywords:
causalityclosed timelike curvescomplexity theorynon-causal computationunambiguous polynomial time

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Area of Science:

  • Theoretical computer science
  • Quantum computing
  • Cosmology

Background:

  • The computational power of non-causal systems, particularly closed timelike curves (CTCs), is a subject of theoretical interest.
  • Previous models suggested CTCs could efficiently solve NP-complete problems, raising questions about their physical plausibility.

Purpose of the Study:

  • To precisely characterize the computational power of classical deterministic CTCs.
  • To determine if these CTCs can efficiently solve problems outside the UP∩coUP complexity class.

Main Methods:

  • Analysis of the non-causal circuit model, replacing global causality with logical consistency.
  • Characterization of computational power using complexity classes, specifically UP∩coUP.
  • Investigation of the implications for solving NP-complete problems.

Main Results:

  • The computational power of the non-causal circuit model is fully characterized by the complexity class UP∩coUP.
  • Factorization is an example of a problem solvable within this class.
  • Classical deterministic CTCs cannot efficiently solve problems outside UP∩coUP.

Conclusions:

  • Classical deterministic CTCs are restricted to solving problems within UP∩coUP, unlike some other CTC models.
  • These CTCs cannot efficiently solve NP-complete problems unless NP=UP∩coUP=coNP.
  • The limited computational power makes the existence of these specific CTCs in nature appear less implausible.