COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)

Quantum Genetics, Quantum Automata and Quantum Computation

The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983,2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens(Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in Lukasiewicz Logic Algebras

Relational semantics of linear logic and higher-order model-checking

In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of any higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree automata (ATA) of the same signature. Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion scheme. We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities) in higher-order model-checking. We show in particular how to reunderstand in this way the type-theoretic approach to higher-order model-checking developed by Kobayashi and Ong. We briefly explain in the end of the paper how his analysis driven by linear logic results in a new and purely semantic proof of decidability of the formulas of the monadic second-order logic for higher-order recursion schemes.Comment: 24 pages. Submitte

Reachability analysis of first-order definable pushdown systems

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1

Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

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 Łukasiewicz 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

Automata theory in nominal sets

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts