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

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

Design, Fabrication, and Characterization of Conjugated Polymeric Electrochemical Memristors as Neuromorphic/Integrated Circuits

Organic materials are promising candidates for future electronic devices compared to the complementing inorganic materials due to their ease of processability, use, and disposal, low cost of fabrication, energy efficiency, and flexible nature toward implementation as flexible and non-conformal devices.With that in mind, electrochemical materials have been widely demonstrated with commercial use as sensors, displays, and a variety of other electronic devices. As Moore\u27s law predicts the increase in the density of transistors on a chip, the requirement to create either smaller transistors or the replacement of the transistor device entirely is apparent. Memory resistors, coined ``memristor , are variable resistive tuning devices that are capable of information processing and data storage in one device. This work focuses on the embodiment of a non-volatile conjugated polymeric electrochemical memristor. Three-terminal memristive systems are fabricated and studied using various electrochemicals (a self-doped PEDOT derivative, a polypyrrole, and a dithienopyrrole derivative) and are tested for their electronic properties and biomimicking capabilities. Optical absorbance properties are studied in order to verify the electrochemical material\u27s redox tuning potential for their respective oxidized and reduced chemical forms. The three-terminal device employed a post-synaptic ``read\u27\u27 channel where conductivity of the electrochemical material was equated to synaptic weight and was electronically decoupled from the pre-synaptic programming electrode by means of a polymeric gel electrolyte. Basic electronic characteristics are exhibited for these three devices such as state stability and retention, non-volatile voltage-driven conductivity tuning, input parameter characteristic trends, and power consumption per input program. Biological synapses consume, on the order of, 1 - 100 fJ of energy per synaptic energy. The electrochemical materials used in this study, at their most optimized input parameters, were capable of demonstrating a 4.16 fJ/mm2 power consumption per input pulse and lead to a promising candidate for implementation as future artificial neural networks. Biological mimicry was displayed for these devices in the form of paired-pulse facilitation and paired-pulse depression, both a form of short term memory which observes the effect the timescale between two incoming inputs has on the change in the final output signal. Toward the indication for the replacement of transistors with three-terminal memristors, basic circuit operations are achieved and demonstrated for these devices. These operations include both Boolean and elementary algebra, key features that demonstrate data processing and storage in-memory where the physical states of the conjugated polymer film represent either logical statements or arithmetic counting variables. The Boolean algebra demonstrated the use of a single memristive device equal to a variety of single logic gates (AND, NAND, OR and NOR) where, by wiring several devices in series, more advanced combinational logic gates can be achieved. Furthermore, each device was capable of displaying elementary algebra for the basic arithmetic functions of addition, subtraction, multiplication, and division. In regards to thin film deposition techniques, the self-doped PEDOT device employed roll-to-roll gravure printing, a high speed and high resolution commercially used deposition technique. The polypyrrole device was fabricated implementing an in-situ polymerization technique, referred to as vapor phase polymerization, and demonstrated the use of this technique toward non-conformal devices. The dithienopyrrole derivative was polymerized through the same vapor phase polymerization technique as the polypyrrole and used in tandem with screen printing in order to construct the final device, including the oxidant film, the silver electrodes, and the polymeric gel electrolyte

Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected works), Vol. 2

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang