Semiautomata are abstractions of electronic devices that are deterministic finite-state machines having inputs but no outputs. Generalized semiautomata are obtained from stochastic semiautomata by dropping the restrictions imposed by probability. It is well-known that each stochastic semiautomaton can be decomposed into a sequential product of a dependent source and deterministic semiautomaton making partly use of the celebrated theorem of Birkhoff-von Neumann. It will be shown that each generalized semiautomaton can be partitioned into a sequential product of a generalized dependent source and a deterministic semiautomaton.
Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the concept of dynamic programming.
Stochastic Moore automata have in opposition to stochastic Mealy automata the same capabilities as general stochastic automata, but have the advantage that they are easier to access than their pure stochastic counterparts. Cascade decomposition of automata leads to a loop-free partitioning and in this way contributes to the analysis of automata. This paper shows that stochastic Moore automata can be decomposed into cascade products of stochastic Moore automata under mild conditions
Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the concept of dynamic programming.
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