Asymptotic properties of free monoid morphisms

Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^\omega(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $\sigma$ and a coding $\tau$ such that $w =\tau(\sigma^\omega(b))$. Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution is an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing $\sigma$ and $\tau$ from $f$ and $g$.Comment: 25 page

The Algebraic View of Computation

We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.Comment: 13 pages, final version will be published elsewher

Fault-tolerant computer study

A set of building block circuits is described which can be used with commercially available microprocessors and memories to implement fault tolerant distributed computer systems. Each building block circuit is intended for VLSI implementation as a single chip. Several building blocks and associated processor and memory chips form a self checking computer module with self contained input output and interfaces to redundant communications buses. Fault tolerance is achieved by connecting self checking computer modules into a redundant network in which backup buses and computer modules are provided to circumvent failures. The requirements and design methodology which led to the definition of the building block circuits are discussed

A Lightweight Privacy-Preserved Spatial and Temporal Aggregation of Energy Data

Smart grid provides fine-grained real time energy consumption, and it is able to improve the efficiency of energy management. It enables the collection of energy consumption data from consumer and hence has raised serious privacy concerns. Energy consumption data, a form of personal information that reveals behavioral patterns can be used to identify electrical appliances being used by the user through the electricity load signature, thus making it possible to further reveal the residency pattern of a consumer’s household or appliances usage habit. This paper proposes to enhance the privacy of energy con- sumption data by enabling the utility to retrieve the aggregated spatial and temporal consumption without revealing individual energy consumption. We use a lightweight cryptographic mech- anism to mask the energy consumption data by adding random noises to each energy reading and use Paillier’s additive homo- morphic encryption to protect the noises. When summing up the masked energy consumption data for both Spatial and Temporal aggregation, the noises cancel out each other, hence resulting in either the total sum of energy consumed in a neighbourhood at a particular time, or the total sum of energy consumed by a household in a day. No third party is able to derive the energy consumption pattern of a household in real time. A proof-of- concept was implemented to demonstrate the feasibility of the system, and the results show that the system can be efficiently deployed on a low-cost computing platform