期刊名称：Brain. Broad Research in Artificial Intelligence and Neuroscience
印刷版ISSN：2067-3957
出版年度：2010
卷号：1
页码：1-11
语种：English
出版社：EduSoft publishing
摘要：The fundamentals of Lukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the SchrÄodinger representation, with both initial and boundary conditions in space-time. A new theorem is proven which states that the category of quantum automata and automata-homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)-Systems which are open, dynamic biosystem networks [4] with de¯ned biological relations that represent physiological functions of primordial(s), single cells and the simpler organisms. A new category of quantum computers is also defined in terms of reversible quantum automata with quantum state spaces represented by topological groupoids that admit a local characterization through unique, quantum Lie algebroids. On the other hand, the category of n-Lukasiewicz algebras has a subcategory of centered n-Lukasiewicz algebras (as proven in ref. [2]) which can be employed to design and construct subcategories of quantum automata based on n-Lukasiewicz diagrams of existing VLSI. Furthermore, as shown in ref. [2] the category of centered n-Lukasiewicz algebras and the category of Boolean algebras are naturally equivalent. A `no-go' conjecture is also proposed which states that Generalized (M,R)-Systems complexity prevents their complete computability (as shown in refs. [5]-[6]) by either standard, or quantum, automata.
关键词：LM-logic algebra, algebraic category of LM-logic algebras, fundamental theorems of LM-logic algebra, many-valued logics of highly com- plex systems and Categorical Ontology, quantum automata categories, limits and colimits, bicomplete categories etc.
