3 research outputs found
Hardware-Oriented Group Solutions for Hard Problems
Group and individual solutions are considered for hard problems such as
satisfiability problem. Time-space trade-off in a structured active memory
provides means to achieve lower time complexity for solutions of these
problems
Superrecursive Features of Interactive Computation
Functioning and interaction of distributed devices and concurrent algorithms
are analyzed in the context of the theory of algorithms. Our main concern here
is how and under what conditions algorithmic interactive devices can be more
powerful than the recursive models of computation, such as Turing machines.
Realization of such a higher computing power makes these systems
superrecursive. We find here five sources for superrecursiveness in
interaction. In addition, we prove that when all of these sources are excluded,
the algorithmic interactive system in question is able to perform only
recursive computations. These results provide computer scientists with
necessary and sufficient conditions for achieving superrecursiveness by
algorithmic interactive devices
Mathematical Models in Schema Theory
In this paper, a mathematical schema theory is developed. This theory has
three roots: brain theory schemas, grid automata, and block-shemas. In Section
2 of this paper, elements of the theory of grid automata necessary for the
mathematical schema theory are presented. In Section 3, elements of brain
theory necessary for the mathematical schema theory are presented. In Section
4, other types of schemas are considered. In Section 5, the mathematical schema
theory is developed. The achieved level of schema representation allows one to
model by mathematical tools virtually any type of schemas considered before,
including schemas in neurophisiology, psychology, computer science, Internet
technology, databases, logic, and mathematics