490 research outputs found
Computation in Finitary Stochastic and Quantum Processes
We introduce stochastic and quantum finite-state transducers as
computation-theoretic models of classical stochastic and quantum finitary
processes. Formal process languages, representing the distribution over a
process's behaviors, are recognized and generated by suitable specializations.
We characterize and compare deterministic and nondeterministic versions,
summarizing their relative computational power in a hierarchy of finitary
process languages. Quantum finite-state transducers and generators are a first
step toward a computation-theoretic analysis of individual, repeatedly measured
quantum dynamical systems. They are explored via several physical systems,
including an iterated beam splitter, an atom in a magnetic field, and atoms in
an ion trap--a special case of which implements the Deutsch quantum algorithm.
We show that these systems' behaviors, and so their information processing
capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous
corrections and update
Reaction Cycles in Membrane Systems and Molecular Dynamics
We are considering molecular dynamics and (sequential) membrane systems
from the viewpoint of Markov chain theory. The first step is to understand the structure of
the configuration space, with respect to communicating classes. Instead of a reachability
analysis by traditional methods, we use the explicit monoidal structure of this space with
respect to rule applications. This leads to the notion of precycle, which is an element of
the integer kernel of the stoichiometric matrix. The generators of the set of precycles
can be effectively computed by an incremental algorithm due to Contejean and Devie.
To arrive at a characterization of cycles, we introduce the notion of defect, which is a
set of geometric constraints on a configuration to allow a precycle to be enabled, that
is, be a cycle. An important open problem is the effcient calculation of the defects. We
also discuss aspects of asymptotic behavior and connectivity, as well as give a biological
example, showing the usefulness of the method for model checking
- …