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Assembly theory and its relationship with computational complexity [PDF]
npj ComplexityAssembly theory (AT) quantifies selection using the assembly equation, identifying complex objects through the assembly index, the minimal steps required to build an object from basic parts, and copy number, the observed instances of the object.
Christopher P. Kempes +6 more
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Computational complexity of time-dependent density functional theory [PDF]
New Journal of Physics, 2014 Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious
J D Whitfield +4 more
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Holographic local quench and effective complexity [PDF]
Journal of High Energy Physics, 2018 We study the evolution of holographic complexity of pure and mixed states in 1 + 1-dimensional conformal field theory following a local quench using both the “complexity equals volume” (CV) and the “complexity equals action” (CA) conjectures.
Dmitry Ageev +3 more
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The Computational Complexity of Density Functional Theory [PDF]
, 2014 Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach.
James Daniel Whitfield +5 more
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Some Applications of Coding Theory in Computational Complexity [PDF]
, 2004 Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory.
Luca Trevisan
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What Can Quantum Optics Say about Computational Complexity Theory? [PDF]
, 2015 Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory ...
Saleh Rahimi-Keshari +2 more
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Quantum game theory and the complexity of approximating quantum Nash equilibria [PDF]
Quantum, 2022 This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information.
John Bostanci, John Watrous
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Probabilistic Recursion Theory and Implicit Computational Complexity [PDF]
Scientific Annals of Computer Science, 2014 We show that probabilistic computable functions, i.e., those func- tions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene’s partial recursive functions.
U. Dal Lago, S. Zuppiroli, M. Gabbrielli
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Proof Compression and NP Versus PSPACE II: Addendum
Bulletin of the Section of Logic, 2022 In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding minimal Prawitz-style natural ...
Lew Gordeev, Edward Hermann Haeusler
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Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems
New Journal of Physics, 2022 Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems.
Adam Rupe +2 more
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