Local noncuppability in R/M

Given any [c], [a], [d] xxxxxxxxR/M such that [d] ≤ [a] ≤ [c], [a] is locally noncuppable between [c] and [d] if [d] < [a] ≤ [c] and [a] ∨ [b] < [c] for any [b] xxxxxxxxR/M such that [d] ≤ [b] < [c]. It will be shown that given any nonzero [c] xxxxxxxxR/M, there are [a], [d] xxxxxxxxR/M such that [d] < [a] ≤ [c] and [a] is locally noncuppable between [c] and [d].     

每个非零的 a∈ R/ M 中不存在极小元

证明了给定任何非零的递归可枚举图灵度 a存在递归可枚举图灵度 c   

Rwtt/Mwtt中的枝点元素

该文证明了在 Rwtt/ Mwtt中除了最大元和最小元外 ,每个元 c是枝点元素 ,即为某两个大于 c的元素的最大下界 ,其中 Rwtt/ Mwtt是递归可枚举弱真值表归约度集 Rwtt模可盖递归可枚举弱真值表归约度集 Mwtt的商     

基于量子逻辑的图灵机及其通用性

基于量子逻辑的自动机理论是量子计算模型的一个重要研究方向.该文研究了基于量子逻辑的图灵机(简称量子图灵机)及其一些变形,给出了包括非确定型量子图灵机l-VTM,确定型量子图灵机l-VDTM以及相应类型的多带量子图灵机,并引入量子图灵机基于深度优先与宽度优先识别语言的两种不同定义方式,证明了这两种定义方式在量子逻辑意义下是不等价的.进一步证明了l-VTM、l-VDTM与相应类型的多带量子图灵机之间的等价性.其次,给出了量子递归可枚举语言及量子递归语言的定义,并给出了二者的层次刻画,证明了l-VTM与l-VDTM不等价,但两者作为量子递归语言的识别器是等价的.最后,文中讨论了基于量子逻辑的通用图灵机的存在性问题,给出了一套合理编码系统,证明了基于量子逻辑的通用图灵机在其所取值的正交模格无限时不存在,而在其所取值的正交模格有限时是存在的.     

Plus cupping degrees do not form an ideal

~~Plus cupping degrees do not form an ideal~~     

R/M中的与R中的≤T的关系

证明存在递归可枚举图灵度a和c使得ca,并且对每个递归可枚举图灵度b≤_Ta, b≠c, 其中a是R/M中的一个元素,R/M是递归可枚举图灵度集R模可盖图灵度集M的商.     

一个高的钻石定理

证明存在一个保持最大元1的可计算枚举高度的钻石格.     

From Watson-Crick L systems to Darwinian P systems

Watson-Crick L systems are language generating devices making use ofWatson-Crick complementarity, a fundamental concept of DNA computing.These devices are Lindenmayer systems enriched with a trigger forcomplementarity transition: if a ``bad' string is obtained, then thederivation continues with its complement which is always a ``good'string. Membrane systems or P systems are distributed parallel computingmodels which were abstracted from the structure and the way offunctioning of living cells. In this paper, we first interpret theresults known about the computational completeness of Watson-Crick E0Lsystems in terms of membrane systems, then we introduce a related way ofcontrolling the evolution in P systems, by using the triggers not in theoperational manner (i.e., turning to the complement in a ``bad'configuration), but in a ``Darwinian' sense: if a ``bad' configurationis reached, then the system ``dies', that is, no result is obtained.The triggers (actually, the checkers) are given as finite state multisetautomata. We investigate the computational power of these P systems.Their computational completeness is proved, even for systems withnon-cooperative rules, working in the non-synchronized way, andcontrolled by only two finite state checkers; if the systems work in thesynchronized mode, then one checker for each system suffices to obtainthe computational completeness.     

Rwtt/ Mwtt中的枝点元素

该文证明了在 R_wtt/ M_wtt中除了最大元和最小元外 ,每个元 c是枝点元素 ,即为某两个大于 c的元素的最大下界 ,其中 R_wtt/ M_wtt是递归可枚举弱真值表归约度集 R_wtt模可盖递归可枚举弱真值表归约度集 M_wtt的商.     

R/M中的(≤)与R中的≤T的关系

证明存在递归可枚举图灵度a和c使得c(≤)a,并且对每个递归可枚举图灵度b≤Ta, b≠c, 其中a是R/M中的一个元素,R/M是递归可枚举图灵度集R模可盖图灵度集M的商.     

Approximation and universality of fuzzy Turing machines

Fuzzy Turing machines are the formal models of fuzzy algorithms or fuzzy computations. In this paper we give several different formulations of fuzzy Turing machine, which correspond to nondeterministic fuzzy Turing machine using max-＊ composition for some t-norm＊ （or NFTM＊, for short）, nondeterministic fuzzy Turing machine （or NFTM）, deterministic fuzzy Turing machine （or DFTM）, and multi-tape versions of fuzzy Turing machines. Some distinct results compared to those of ordinary Turing machines are obtained. First, it is shown that NFTM＊, NFTM, and DFTM are not necessarily equivalent in the power of recognizing fuzzy languages if the t-norm＊ does not satisfy finite generated condition, but are equivalent in the approximation sense. That is to say, we can approximate an NFTM＊ by some NFTM with any given accuracy; the related constructions are also presented. The level characterization of fuzzy recursively enumerable languages and fuzzy recursive languages are exploited by ordinary r.e. languages and recursive languages. Second, we show that universal fuzzy Turing machine exists in the approximated sense. There is a universal fuzzy Turing machine that can simulate any NFTM＊ on it with a given accuracy.     

M32R/D-integrating DRAM and microprocessor

Newly emerging portable multimedia systems demand low-energy processing. Until now, however, designers of microprocessors for PCs and engineering workstations have focused mostly on high speed. Microcontroller designers, on the other hand, have taken low power dissipation as a first priority. Today's portable multimedia system design calls for developers to combine these two approaches, lowering power consumption while maintaining reasonable performance. There are several approaches to reducing power dissipation. Using advanced process technology is one of them. Another approach merges a DRAM with a high-performance RISC processor on a single silicon chip-what we call embedded DRAM, or eRAM. This is exactly the concept that this new processor, M32R/D, embodies