相关论文: Prof. Sch\"onhage's Mysterious Machines

A brief introduction to Wolfram's work on cellular automata.

A theory of one-tape (one-head) linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues…

We provide a short proof for the twisted multiplicativity property of the operator-valued S-transform. This is my contribution to the topical collection ''Multivariable Operator Theory. The J\"org Eschmeier Memorial'' of Complex Analysis…

Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…

This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are…

In this paper we explore the power of tile self-assembly models that extend the well-studied abstract Tile Assembly Model (aTAM) by permitting tiles of shapes beyond unit squares. Our main result shows the surprising fact that any aTAM…

We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these…

We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to…

This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…

Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g.…

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…

We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement…

We study the complexity of inverse cellular automata on configurations of bounded size. Deciding injectivity in this setting is co-NP-complete by a theorem of Durand. We give a simpler proof of this theorem by a direct reduction from UNSAT…

SIMD||DNA is a model of DNA strand displacement allowing parallel in-memory computation on DNA storage. We show how to simulate an arbitrary 3-symbol space-bounded Turing machine with a SIMD||DNA program, giving a more direct and efficient…

It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed…

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…

(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the…

Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…

A cellular automaton that is a generalization of the box-ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: nonautonomous discrete KP lattice and…

We consider reversible and surjective cellular automata perturbed with noise. We show that, in the presence of positive additive noise, the cellular automaton forgets all the information regarding its initial configuration exponentially…