Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Skyrmion Logic System for Large-Scale Reversible Computation

Computational reversibility is necessary for quantum computation and inspires the development of computing systems in which information carriers are conserved as they flow through a circuit. While conservative logic provides an exciting vision for reversible computing with no energy dissipation, the large dimensions of information carriers in previous realizations detract from the system efficiency, and nanoscale conservative logic remains elusive. We therefore propose a non-volatile reversible computing system in which the information carriers are magnetic skyrmions, topologically-stable magnetic whirls. These nanoscale quasiparticles interact with one another via the spin-Hall and skyrmion-Hall effects as they propagate through ferromagnetic nanowires structured to form cascaded conservative logic gates. These logic gates can be directly cascaded in large-scale systems that perform complex logic functions, with signal integrity provided by clocked synchronization structures. The feasibility of the proposed system is demonstrated through micromagnetic simulations of Boolean logic gates, a Fredkin gate, and a cascaded full adder. As skyrmions can be transported in a pipelined and non-volatile manner at room temperature without the motion of any physical particles, this skyrmion logic system has the potential to deliver scalable high-speed low-power reversible Boolean and quantum computing.Comment: 24 pages, 7 figures, 3 table

Combined Integer and Floating Point Multiplication Architecture(CIFM) for FPGAs and Its Reversible Logic Implementation

In this paper, the authors propose the idea of a combined integer and floating point multiplier(CIFM) for FPGAs. The authors propose the replacement of existing 18x18 dedicated multipliers in FPGAs with dedicated 24x24 multipliers designed with small 4x4 bit multipliers. It is also proposed that for every dedicated 24x24 bit multiplier block designed with 4x4 bit multipliers, four redundant 4x4 multiplier should be provided to enforce the feature of self repairability (to recover from the faults). In the proposed CIFM reconfigurability at run time is also provided resulting in low power. The major source of motivation for providing the dedicated 24x24 bit multiplier stems from the fact that single precision floating point multiplier requires 24x24 bit integer multiplier for mantissa multiplication. A reconfigurable, self-repairable 24x24 bit multiplier (implemented with 4x4 bit multiply modules) will ideally suit this purpose, making FPGAs more suitable for integer as well floating point operations. A dedicated 4x4 bit multiplier is also proposed in this paper. Moreover, in the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. It is not possible to realize quantum computing without reversible logic. Thus, this paper also paper provides the reversible logic implementation of the proposed CIFM. The reversible CIFM designed and proposed here will form the basis of the completely reversible FPGAs.Comment: Published in the proceedings of the The 49th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS 2006), Puerto Rico, August 2006. Nominated for the Student Paper Award(12 papers are nominated for Student paper Award among all submissions

Anthropocentrism, Conservatism and Green Political Thought

In this paper I will examine a number of justifications for environmental concern, and show why all except for the (broadly) anthropocentric demonstrate problematic conservative logics that incline them towards socially conservative positions. Environmentalists would do best to take up an anthropocentric, or at least anthropogenic, defence of green values if they want to pair it with a progressive social politics

On polymorphic logical gates in sub-excitable chemical medium

In a sub-excitable light-sensitive Belousov-Zhabotinsky chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragment can conserve their shape and velocity vectors for extended time periods. The size and life span of a fragment depend on the illumination level of the medium. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. In computer simulations based on the Oregonator model we demonstrate that the outcomes of inter-fragment collisions can be controlled by varying the illumination level applied to the medium. We interpret these wave-fragments as values of Boolean variables and design collision-based polymorphic logical gates. The gate implements operation XNOR for low illumination, and it acts as NOR gate for high illumination. As a NOR gate is a universal gate then we are able to demonstrate that a simulated light sensitive BZ medium exhibits computational universality

Evolving localizations in reaction-diffusion cellular automata

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.Comment: Accepted for publication in Int. J. Modern Physics