P systems without multiplicities of symbol-objects

In this paper we investigate P systems whose compartments contain sets of symbol-objects rather than multisets of objects, as it is common in membrane computing. If the number of membranes cannot grow, then in this framework we can characterize exactly the regular languages. If membrane creation or membrane division is allowed, then the Parikh sets of recursively enumerable languages can be generated. The last result also implies the universality of P systems with active membranes (with multisets of symbol-objects) without polarizations.     

An overview of MiMo2

The MiMo2 translation system combines several leading ideas in the areas of linguistics, computation and translation. In the area of translation we follow the ideas of Landsbergen (1987) by assuming that translation is symmetric; and combine these ideas with the advantages of a transfer approach. Computationally the system focuses on computability and declarativity. The linguistics of the system is based on a lexicalistic and sign-based approach to grammar.MiMo2 is a sideline project of the Dutch Eurotra team in Utrecht. An extended version of this article was presented at the machine translation workshop in Austin, Texas, June 1990.     

关于实数的可计算性

给出了图灵机和可计算数之间的关系和可计算数的若干性质，提出了半可计算数的概念，并在此基础上结合集合的算术层次对实数集进行了算术分层，这一思想对于从可计算性角度理解实数具有借鉴意义。     

On stability and solvability (or,when does a neural network solve a problem?)

The importance of the Stability Problem in neurocomputing is discussed, as well as the need for the study of infinite networks. Stability must be the key ingredient in the solution of a problem by a neural network without external intervention. Infinite discrete networks seem to be the proper objects of study for a theory of neural computability which aims at characterizing problems solvable, in principle, by a neural network. Precise definitions of such problems and their solutions are given. Some consequences are explored, in particular, the neural unsolvability of the Stability Problem for neural networks.     

四维时空高效利用的装箱调度问题及其可计算性证明

提出了四维时空中考虑时间因素的一个长方体装箱工作的优化调度问题.已知一个形状大小任意给定的长方体形的箱子和有限个形状大小分别任意给定的长方体形的刚性物体,又知每个物体须在箱中连续烘烤的时间长度,问应如何安排每个物体的入箱时刻,以及至出箱前这段时间内它在每个时刻上的位置和方向,才能使整个箱子的被使用时间最少.问题中涉及的箱子及诸长方形刚体的长、宽、高以及各刚体须连续烘烤的时间长度均为分别任意给定的正实数.与经典装箱问题的不同之处在于,各物体在箱子内可以随时间而改变其位置和方向,从而使四维时空得到更真实、更充分的利用.进一步地,通过枚举长方体的各种排列,并证明对每一种排列,按照某种贪心策略可得到该排列下问题的最优解,从而给出了原问题具有可计算性的严格证明.在此基础上,今后有望对此问题发展出各种有效的实用求解算法.     

THEORY OF CYBERNETIC AND INTELLIGENT MACHINE BASED ON LIE COMMUTATORS

Many attempts^{1, 7, 8, 35} have been made to overcome the limit imposed by the Turing Machine³⁴ to realise general mathematical functions and models of (physical) phenomena.

They center around the notion of computability.

In this paper we propose a new definition of computability which lays the foundations for a theory of cybernetic and intelligent machines in which the classical limits imposed by discrete algorithmic procedures are offset by the use of continuous operators on unlimited data. This data is supplied to the machine in a totally parallel mode, as a field or wave.

This theory of machines draws its concepts from category theory, Lie algebras, and general systems theory. It permits the incorporation of intelligent control into the design of the machine as a virtual element. The incorporated control can be realized in many (machine) configurations of which we give three:

a) a quantum mechanical realization appropriate to a possible understanding of the quantum computer and other models of the physical microworld,

b) a stochastic realization based on Kolmogorov-Gabor theory leading to a possible understanding of generalised models of the physical or thermodynamic macroworld, and lastly

c) a classical mechanical realization appropriate lo the study of a new class of robots.

Particular applications at a fundamental level are cited in geometry, mathematics, biology, acoustics, aeronautics, quantum mechanics, general relativity and. Markov chains. The proposed theory therefore opens a new way towards understanding the processes that underlie intelligence.     

‘Real’ information is not flat – and why it matters

We consider Luciano Floridi's proposal for a structural realism based on an Informational Structural Realism which, as he describes in his book (p. 339): ‘As a form of realism … is committed to the existence of a mind-independent reality addressed by, and constraining knowledge’. In doing this, we inform and reform aspects of the argument within a mathematical and, specifically, computability theoretic context.     

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.     

知识库系统的逻辑基础

针对知识库系统的研究现状和存在的问题,分析了用经典一阶谓词逻辑作为知识库系统逻辑基础的不充分性,根据知识库系统的特点和需求,指出可计算性逻辑既能为知识库系统提供合理的逻辑基础,义能弥补经典逻辑作为知识库系统逻辑基础的不足.并在此基础上用证明论方法,建立了一个基于可计算性逻辑的完备子集CL4的知识库系统的公理系统,显示出易于表达、操作简单的特点.