Related papers: Prof. Sch\"onhage's Mysterious Machines

In this paper, we prove that there is a strongly universal cellular automaton on the pentagrid with six states. For each cell c, Moore neighbourhood consists of the cells which share a vertex with c. Moreover, the rules are rotation…

We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…

We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We…

We present computer simulations run with a stochastic cellular automaton which describes $d=1$ particle systems connected to reservoirs which keep two different densities at the endpoints. We fix the parameters so that there is a phase…

There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…

It is known that elementary cellular automaton rule 110 is capable of supporting universal computation by emulating cyclic tag system. Since the whole information necessary to perform computation is stored in the configuration, it is…

Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.

Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular automata in [7]. We extend known results to…

This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with $\epsilon$-transitions. It gives an algorithm for testing the exponential ambiguity of an automaton $A$ in time…

The interactive computation paradigm is reviewed and a particular example is extended to form the stochastic analog of a computational process via a transcription of a minimal Turing Machine into an equivalent asynchronous Cellular…

We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with three states which is rotation invariant and which uses \`a la Moore neighbourhood. Moreover, at each step of the computation, the set of non…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

In this paper, we deal with the problem of implementing an abstract machine for a stochastic version of the Brane Calculus. Instead of defining an ad hoc abstract machine, we consider the generic stochastic abstract machine introduced by…

Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under…

It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new…

A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…

We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets…