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We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1 map), are introduced. These Cellular Automata allow to test efficiently the Collatz conjecture for very large numbers.
Due to common misconceptions about the Church-Turing thesis, it has been widely assumed that the Turing machine provides an upper bound on what is computable. This is not so. The new field of hypercomputation studies models of computation…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
We study the emergence of information integration in cellular automata (CA) with respect to states in the long run. Information integration is in this case quantified by applying the information-theoretic measure known as total correlation…
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…
The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
Our concern is the behaviour of the elementary cellular automata with state set 0,1 over the cell set Z/nZ (one-dimensional finite wrap-around case), under all possible update rules (asynchronicity). Over the torus Z/nZ (n<= 11),we will see…
This paper is the continuation of our earlier considerations on cellular automata with Toom local rule (TCA) as the alternative to kinetic Ising systems. The arguments for TCA stationary states not being the equilibrium states are found in…
Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal…
We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…
It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…