Is there a physically universal cellular automaton or Hamiltonian?

It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we introduce a different notion of universality: a CA is called physically universal if every transformation on any finite region can be (approximately) implemented by the autonomous time evolution of the system after the complement of the region has been initialized in an appropriate way. We pose the question of whether physically universal CAs exist. Such CAs would provide a model of the world where the boundary between a physical system and its controller can be consistently shifted, in analogy to the Heisenberg cut for the quantum measurement problem. We propose to study the thermodynamic cost of computation and control within such a model because implementing a cyclic process on a microsystem may require a non-cyclic process for its controller, whereas implementing a cyclic process on system and controller may require the implementation of a non-cyclic process on a "meta"-controller, and so on. Physically universal CAs avoid this infinite hierarchy of controllers and the cost of implementing cycles on a subsystem can be described by mixing properties of the CA dynamics. We define a physical prior on the CA configurations by applying the dynamics to an initial state where half of the CA is in the maximum entropy state and half of it is in the all-zero state (thus reflecting the fact that life requires non-equilibrium states like the boundary between a hold and a cold reservoir). As opposed to Solomonoff's prior, our prior does not only account for the Kolmogorov complexity but also for the cost of isolating the system during the state preparation if the preparation process is not robust.Comment: 27 pages, 1 figur

SOUND SYNTHESIS WITH CELLULAR AUTOMATA

This thesis reports on new music technology research which investigates the use of cellular automata (CA) for the digital synthesis of dynamic sounds. The research addresses the problem of the sound design limitations of synthesis techniques based on CA. These limitations fundamentally stem from the unpredictable and autonomous nature of these computational models. Therefore, the aim of this thesis is to develop a sound synthesis technique based on CA capable of allowing a sound design process. A critical analysis of previous research in this area will be presented in order to justify that this problem has not been previously solved. Also, it will be discussed why this problem is worthwhile to solve. In order to achieve such aim, a novel approach is proposed which considers the output of CA as digital signals and uses DSP procedures to analyse them. This approach opens a large variety of possibilities for better understanding the self-organization process of CA with a view to identifying not only mapping possibilities for making the synthesis of sounds possible, but also control possibilities which enable a sound design process. As a result of this approach, this thesis presents a technique called Histogram Mapping Synthesis (HMS), which is based on the statistical analysis of CA evolutions by histogram measurements. HMS will be studied with four different automatons, and a considerable number of control mechanisms will be presented. These will show that HMS enables a reasonable sound design process. With these control mechanisms it is possible to design and produce in a predictable and controllable manner a variety of timbres. Some of these timbres are imitations of sounds produced by acoustic means and others are novel. All the sounds obtained present dynamic features and many of them, including some of those that are novel, retain important characteristics of sounds produced by acoustic means

Testing a deterministic implementation against a non-controllable non-deterministic stream X-machine

A stream X-machine is a type of extended finite state machine with an associated development approach that consists of building a system from a set of trusted components. One of the great benefits of using stream X-machines for the purpose of specification is the existence of test generation techniques that produce test suites that are guaranteed to determine correctness as long as certain well-defined conditions hold. One of the conditions that is traditionally assumed to hold is controllability: this insists that all paths through the stream X-machine are feasible. This restrictive condition has recently been weakened for testing from a deterministic stream X-machine. This paper shows how controllability can be replaced by a weaker condition when testing a deterministic system against a non-deterministic stream X-machine. This paper therefore develops a new, more general, test generation algorithm for testing from a non-deterministic stream X-machine