Courcelle’s theorem—A game-theoretic approach

Courcelle’s theorem states that every problem definable in Monadic Second-Order logic can be solved in linear time on structures of bounded treewidth, for example, by constructing a tree automaton that recognizes or rejects a tree decomposition of the structure. Existing, optimized software like the MONA tool can be used to build the corresponding tree automata, which for bounded treewidth are of constant size. Unfortunately, the constants involved can become extremely large—every quantifier alternation requires a power set construction for the automaton. Here, the required space can become a problem in practical applications.In this paper, we present a novel, direct approach based on model checking games, which avoids the expensive power set construction. Experiments with an implementation are promising, and we can solve problems on graphs where the automata-theoretic approach fails in practice.     

Interpretability assessment of fuzzy knowledge bases: A cointension based approach

Computing with words (CWW) relies on linguistic representation of knowledge that is processed by operating at the semantical level defined through fuzzy sets. Linguistic representation of knowledge is a major issue when fuzzy rule based models are acquired from data by some form of empirical learning. Indeed, these models are often requested to exhibit interpretability, which is normally evaluated in terms of structural features, such as rule complexity, properties on fuzzy sets and partitions. In this paper we propose a different approach for evaluating interpretability that is based on the notion of cointension. The interpretability of a fuzzy rule-based model is measured in terms of cointension degree between the explicit semantics, defined by the formal parameter settings of the model, and the implicit semantics conveyed to the reader by the linguistic representation of knowledge. Implicit semantics calls for a representation of user’s knowledge which is difficult to externalise. Nevertheless, we identify a set of properties - which we call “logical view” - that is expected to hold in the implicit semantics and is used in our approach to evaluate the cointension between explicit and implicit semantics. In practice, a new fuzzy rule base is obtained by minimising the fuzzy rule base through logical properties. Semantic comparison is made by evaluating the performances of the two rule bases, which are supposed to be similar when the two semantics are almost equivalent. If this is the case, we deduce that the logical view is applicable to the model, which can be tagged as interpretable from the cointension viewpoint. These ideas are then used to define a strategy for assessing interpretability of fuzzy rule-based classifiers (FRBCs). The strategy has been evaluated on a set of pre-existent FRBCs, acquired by different learning processes from a well-known benchmark dataset. Our analysis highlighted that some of them are not cointensive with user’s knowledge, hence their linguistic representation is not appropriate, even though they can be tagged as interpretable from a structural point of view.     

All-optical reconfigurable logic operations with the help of terahertz optical asymmetric demultiplexer

An all-optical reconfigurable logic operation essentially constitutes a key technology for avoiding complex and speed limited optoelectronics conversions and performing various processing tasks. All-optical reconfigurable logic operations with the help of terahertz optical asymmetric demultiplexer (TOAD) is proposed and described. The paper describes the all-optical reconfigurable logic operations using a set of all-optical multiplexer and optical switches. We have tried to exploit the advantages of TOAD-based switch to design an integrated all-optical circuit which can perform the different logic operations AND, XOR, NOR and NOT. Numerical simulation confirming described methods is given in this paper.     

A method of developing all-optical mono-stable multivibrator system exploiting the Kerr non-linearity of medium

Optics has already been established as a potential candidate for conduction of digital logic and arithmetic operation in communication and computation processes. Different proposals have been reported by different scientists to make optics meaningful signal for conduction of the above operations. As it is well known that the memory device is a basic building block of any computation and communication system hence developing systems such as digital memory, multivibrator, etc. are the obvious requirements for optical communication as well as computation systems also. As the role of switching devices is an essential part of any processing system, many proposals were seen where all-optical switches using the combination of linear and non-linear materials were used, to implement the logic elements.In this context, the authors propose a new scheme for implementation of an all-optical mono-stable multivibrator using the non-linear material based switches and high refractive index based material. This multivibrator can generate a time pulse of definite width.     

Designing of an all-optical scheme for single input ternary logical operations

In this paper, for the first time to our knowledge, we propose and describe a novel design of single circuit capable of generating all the possible 27 logic functions for single input ternary (3-valued) logic system in all-optical domain. Here the different logical states have been represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch plays a significant role as ultra-fast all-optical switching device. Proposed all-optical circuit is numerically investigated and simulated.     

磁性量子元胞自动机逻辑电路的转换特性研究

本文研究了磁性量子元胞自动机反相器和择多逻辑门等基本逻辑电路在不同纳磁体厚度和间距下的转换特性.采用单畴近似LLG方程对纳磁体以及电路进行了建模和仿真,结果表明更厚的纳磁体需要更大的转换磁脉冲,大厚度纳磁体逻辑电路表现出较慢的转换;相同厚度和间距下,择多逻辑门比反相器的转换时间略长.此外,模拟结果还表明纳磁体间距对反相器的转换过程影响明显,而对择多逻辑门则影响较小. 关键词： 磁性量子元胞自动机 转换特性 厚度和间距 逻辑电路     

Modules with Few Types Over A Serial Ring and Over A Commutative Prüfer Ring

It is proved that the theory of a module M over a countable serial ring has few models iff M is ∑-pure—injective iff the theory of M has few types. It is also proved that the theory of a module M over a countable commutative Prüfer ring has few types if and only if M is ∑-pure—injective.     

A simulated colorimetric INHIBIT logic gate based on 2-(2-thiazolylazo)-p-cresol

ABSTRACT

2-(2-Thiazolylazo)-p-cresol system achieved distinct optical output signal by controlling pH and mercury-ion complexation. The 2-(2-thiazolylazo)-p-cresol with mercury ion existed as an equilibrium mixture of both an azo and hydrazone tautomeric forms at 372 and 425?nm, respectively, along with the appearance of a new absorption peak at 610?nm (visual color of green), which was attributed to the binding of mercury ion with 2-(2-thiazolylazo)-p-cresol. Furthermore, the addition of proton led to the perturbation of the conjugation between 2-(2-thiazolylazo)-p-cresol and mercury ion and absence of absorption at 610?nm (visual color of yellow). 2-(2-thiazolylazo)-p-cresol could thus be applied to develop an effective simulated colorimetric INHIBIT logic gate with mercury ion and proton as inputs. Consequently, green color with the absorption peak at 610?nm was outputted from yellow color of 2-(2-thiazolylazo)-p-cresol in the presence of mercury ion as an input signal at pH 7.0.