Space-bounded Church-Turing thesis and computational tractability of closed systems
arXiv:1905.03610 · doi:10.1103/PhysRevLett.115.098701
Abstract
We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory as the maximal amount of information that the evolving system can carry from one instant to the next. We show that memory is a limiting factor in computation even in lieu of any time limitations on the evolving system - such as when considering its equilibrium regime. We call this limitation the Space-Bounded Church Turing Thesis (SBCT). The SBCT is supported by a Simulation Assertion (SA), which states that predicting the long-term behavior of bounded-memory systems is computationally tractable. In particular, one corollary of SA is an explicit bound on the computational hardness of the long-term behavior of a discrete-time finite-dimensional dynamical system that is affected by noise. We prove such a bound explicitly.
arXiv comment6 pages
References in corpus (9)
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Ultimate physical limits to computation
- Computational capacity of the universe
- Simulation of topological field theories by quantum computers
- Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems
- On computational irreducibility and the predictability of complex physical systems
- Computable functions, quantum measurements, and quantum dynamics
- Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices
- Computability of Brolin-Lyubich Measure