TY - GEN N1 - http://www.edusoft.ro/brain/index.php/brain/article/view/97/201 ISSN: 2067-3957 ID - cogprints7751 UR - http://cogprints.org/7751/ A1 - Baianu, Professor I.C. A1 - Georgescu, Professor George A1 - Glazebrook, Professor James F. Y1 - 2010/07/12/ N2 - A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or ?ukasiewicz many-valued logic. A new theorem is proposed 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 with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms. PB - BRAIN KW - LM--algebraic logic KW - LM--logic algebras KW - algebraic category of LM-logic algebras KW - fundamental theorems of LM-logic algebra KW - non-linear genetic networks KW - nonlinear dynamics KW - Epigenomics KW - Cellular Interactomics KW - Immunology and hormonal regulatory systems KW - category theory KW - functors and natural transformations KW - toposes and Heyting logic algebras KW - quantum automata categories KW - limits and colimits KW - quantum automata homomorphisms KW - Abelian category KW - bicomplete categories KW - Quantum Relational Biology KW - generalised metabolic-replication KW - (M KW - R)--systems KW - complex bionetworks KW - quantum logic KW - non-commutative lattices KW - Hilbert space KW - quantum computers KW - computability of complex biological systems KW - Cartesian closed categories KW - extended quantum topos KW - category of groupoids KW - dynamic realisations of generalised (M KW - R)-systems (GMRs) KW - category of GMRs KW - compact subsystems of GMR TI - ?ukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems SP - 1 AV - public EP - 11 ER -