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.     

基于图灵机的递归技术的实现陈晓亮[1] 卢朝辉[2] 宋文[1]

图灵机是通用的计算机模型,一般程序设计和以图灵机为机器模型的计算也是支持递归的。本文首先分析了递归的特征,利用多带图灵机作为计算模型,定义了递归技术转移 函数形式,提出了图灵机递归过程信息传递与保存的方法,给出了图灵机调用的实现,继而给出了图灵机递归技术的实现,同时证明了图灵机的调用与图灵机的递归调用是图灵可识别的。     

Probabilistic rebound Turing machines

This paper introduces a probabilistic rebound Turing machine (PRTM), and investigates the fundamental property of the machine. We first prove a sublogarithmic lower space bound on the space complexity of this model with bounded errors for recognizing specific languages. This lower bound strengthens a previous lower bound for conventional probabilistic Turing machines with bounded errors. We then show, by using our lower space bound and an idea in the proof of it, that

Full-size image

where £[PRTM(o(logn))] denotes the class of languages recognized by o(logn) space-bounded PRTMs with error probability less than . Furthermore, we show that there is an infinite space hierarchy for £[PRTM(o(logn))]. We finally show that £[PRTM(o(logn))] is not closed under concatenation, Kleene +, and length-preserving homomorphism. This paper answers two open problems in a previous paper.     

Three-dimensional parallel Turing machines

Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. Moreover, STMs which represent the individual processors of a parallel computer can multiply themselves in the course of computation. On the other hand, during the past 25 years or so, automata on a three-dimensional tape have been proposed as computational models of three-dimensional pattern processing, and several properties of such automata have been obtained. We proposed a three-dimensional parallel Turing machine (3-PTM), and dealt with a hardware-bounded 3-PTM whose inputs are restricted to cubic ones. We believe that this machine is useful in measuring the parallel computational complexity of three-dimensional images. In this article, we continue the study of 3-PTM, whose inputs are restricted to cubic ones, and investigate some of its accepting powers. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Turing machines, transition systems, and interaction

This paper presents persistent Turing machines (PTMs), a new way of interpreting Turing-machine computation, based on dynamic stream semantics. A PTM is a Turing machine that performs an infinite sequence of “normal” Turing machine computations, where each such computation starts when the PTM reads an input from its input tape and ends when the PTM produces an output on its output tape. The PTM has an additional worktape, which retains its content from one computation to the next; this is what we mean by persistence.A number of results are presented for this model, including a proof that the class of PTMs is isomorphic to a general class of effective transition systems called interactive transition systems; and a proof that PTMs without persistence (amnesic PTMs) are less expressive than PTMs. As an analogue of the Church-Turing hypothesis which relates Turing machines to algorithmic computation, it is hypothesized that PTMs capture the intuitive notion of sequential interactive computation.     

Theory of one-tape linear-time Turing machines

A theory of one-tape two-way one-head off-line linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in linear time, where the running time of a machine is defined as the length of any longest computation path. We explore structural properties of one-tape linear-time Turing machines and clarify how the machines’ resources affect their computational patterns and power.     

基于扩展通用图灵机的计算机病毒传染模型

在计算机基础理论模型——图灵机模型的基础上,提出了一种扩展的通用图灵机（EUTM）模型,这种模型突出了计算机病毒的传染特性,极大地简化了计算机病毒传染的形式描述,并根据EUTM模型给出了计算机病毒的形式定义,形式化描述了计算机病毒在单机和多机环境下的传染。最后指出了Fred Cohen关于病毒检测不可判定性定量证明的不足,并利用EUTM模型证明了病毒检测不可判定性定理。     

Some accepting powers of three-dimensional parallel Turing machines

Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. Moreover, STMs which represent the individual processors of a parallel computer can multiply themselves in the course of computation. On the other hand, during the past 25 years or so, automata on a three-dimensional tape have been proposed as computational models of three-dimensional pattern processing, and several properties of such automata have been obtained. We proposed a three-dimensional parallel Turing machine (3-PTM),¹ and dealt with a hardware-bounded 3-PTM whose inputs are restricted to cubic ones. We believe that this machine is useful in measuring the parallel computational complexity of three-dimensional images. Here, we continue the study of 3-PTM, whose inputs are restricted to cubic ones, and investigate some of its accepting powers. This work was presented in part at the First European Workshop on Artificial Life and Robotics, Vienna, Austria, July 12–13, 2007     

A note on alternating one-pebble Turing machines with sublogarithmic space

Inoue et al. [A. Inoue, A. Ito, K. Inoue, T. Okazaki, Some properties of one-pebble Turing machines with sublogarithmic space, Theoret. Comput. Sci. 341 (2005) 138-149] conjectured that the language {ww|w∈⁺{a,b}} is not accepted by any alternating one-pebble Turing machine with sublogarithmic space. In this paper we disprove the conjecture by showing that there exists an alternating one-pebble Turing machine accepting the language in loglogn space.     

A relationship between Turing machines and finite automata on four-dimensional input tapes

Due to the advances in computer animation, motion image processing, virtual reality systems, and so forth recently, it is useful for analyzing computation of multi-dimensional information processing to explicate the properties of four-dimensional automata. From this point of view, we first proposed four-dimensional automata in 2002, and investigated their several accepting powers. In this paper, we coutinue the study, and mainly concentrate on investigating the relationship between the accepting powers of four-dimensional finite automata and seven-way four-dimensional tape-bounded Turing Machines. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

A Turing machine time hierarchy

The time separation results concerning classes of languages over a single-letter alphabet accepted by multi-tape nondeterministic Turing machines, well-known from Seiferas, Fischer and Meyer (1978), are supplemented. Moreover, via a universal machine a modified time complexity measure UTIME of Turing machines computations which is sensitive to multiplication by constants (i.e., UTIME(t) ? UTIME(kt), where UTIME(t) is the class of languages of complexity not larger than t) is introduced. On the level of this measure, the results concerning languages over one- and two-letter alphabets are refined. The proof tools are versions of a translational diagonalization and of an unpadding technique.     

Hopfield网的图灵等价性

本文给出了用Ｈｏｐｆｉｅｌｄ网计算部分递归函数的构造性证明．由于部分递归函数与图灵机等价，故Ｈｏｐｆｉｅｌｄ网与图灵机等价．     

Simulating reversible Turing machines and cyclic tag systems by one-dimensional reversible cellular automata

In this paper, we investigate how 1-D reversible cellular automata (RCAs) can simulate reversible Turing machines (RTMs) and cyclic tag systems (CTSs). A CTS is a universal string rewriting system proposed by M. Cook. First, we show that for any m-state n-symbol RTM there is a 1-D 2-neighbor RCA with a number of states less than (m+2n+1)(m+n+1) that simulates it. It improves past results both in the number of states and in the neighborhood size. Second, we study the problem of finding a 1-D RCA with a small number of states that can simulate any CTS. So far, a 30-state RCA that can simulate any CTS and works on ultimately periodic infinite configurations has been given by K. Morita. Here, we show there is a 24-state 2-neighbor RCA with this property.     

K带实时图灵机计算能力与图灵机带数的关系

本文证明了对任意整数k,至少存在一个语言能被k带实时图灵机接受,但不能被(k—1)带实时图灵机所接受,从而证明了k带图灵机计算能力严格强于(k-1)带实时图灵机。     

Zeno machines and hypercomputation

This paper reviews the Church–Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of “hypercomputation”, concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is suggested that claims to have “broken the Turing barrier” could be toned down and that the important and well-founded rôle of Turing computability in the mathematical sciences stands unchallenged.     

图灵机的哲学意义

人类在创造人工自然的过程在中,如果不遵循自然规律而一意孤行,其结果必然对天然自然造成级大破坏,人类最终将自食苦果,计算机技术的发展也不例外。     

Quotient structures of intuitionistic fuzzy finite state machines

Quotient structures of intuitionistic fuzzy finite state machines are discussed. We give congruence relations which can be naturally introduced in such a way that each associates a semigroup with an intuitionistic fuzzy finite state machine. We also introduce the notion of intuitionistic admissible relation, and give its characterization. An isomorphism between an intuitionistic fuzzy finite state machine and the quotient structure of another intuitionistic fuzzy finite state machine is established.     

基于遗传算法的可变机器约束模糊作业调度

对同时考虑模糊加工时间和模糊交货期,以及工件的某道工序有多台机器可供选择的模糊作业车间调度问题进行了研究,在 Giffler & Thompson算法的基础上引入了基于优先规则的冲突处理方法,并且设计了相应的遗传算子,保证遗传操作后的染色体搜索空间仍然属于活动调度集,最后通过仿真实验,验证了该算法的有效性。     

The equivalence between fuzzy Mealy and fuzzy Moore machines

We study the relationships between fuzzy Mealy and fuzzy Moore machines in the frame of truth values in a lattice-ordered monoid. In particular, we show that lattice-valued sequential-like machines and lattice-valued finite Moore machines are equivalent in the sense they exhibit the same input–output characteristics.