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A Methodology for Automated Verification of Rosetta Specification Transformations
The Rosetta system-level design language is a specification language created to support design and analysis of heterogeneous models at varying levels of abstraction. These abstraction levels are represented in Rosetta as domains, specifying a particular semantic vocabulary and modeling style. The following dissertation proposes a framework, semantics and methodology for automated verification of safety preservation over specification transformations between domains. Utilizing the ideas of lattice theory, abstract interpretation and category theory we define the semantics of a Rosetta domain as well as safety of specification transformations between domains using Galois connections and functors. With the help of Isabelle, a higher order logic theorem prover, we verify the existence of Galois connections between Rosetta domains as well as safety of transforming specifications between these domains. The following work overviews the semantic infrastructure required to construct the Rosetta domain lattice and provides a methodology for verification of transformations within the lattice
Mass problems and intuitionistic higher-order logic
In this paper we study a model of intuitionistic higher-order logic which we
call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the
category of sheaves of sets over the topological space consisting of the Turing
degrees, where the Turing cones form a base for the topology. We note that our
Muchnik topos interpretation of intuitionistic mathematics is an extension of
the well known Kolmogorov/Muchnik interpretation of intuitionistic
propositional calculus via Muchnik degrees, i.e., mass problems under weak
reducibility. We introduce a new sheaf representation of the intuitionistic
real numbers, \emph{the Muchnik reals}, which are different from the Cauchy
reals and the Dedekind reals. Within the Muchnik topos we obtain a \emph{choice
principle} and a \emph{bounding principle} where range over Muchnik
reals, ranges over functions from Muchnik reals to Muchnik reals, and
is a formula not containing or . For the convenience of the
reader, we explain all of the essential background material on intuitionism,
sheaf theory, intuitionistic higher-order logic, Turing degrees, mass problems,
Muchnik degrees, and Kolmogorov's calculus of problems. We also provide an
English translation of Muchnik's 1963 paper on Muchnik degrees.Comment: 44 page
Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions
We show how to perform universal Hamiltonian and adiabatic computing using a
time-independent Hamiltonian on a 2D grid describing a system of hopping
particles which string together and interact to perform the computation. In
this construction, the movement of one particle is controlled by the presence
or absence of other particles, an effective quantum field effect transistor
that allows the construction of controlled-NOT and controlled-rotation gates.
The construction translates into a model for universal quantum computation with
time-independent 2-qubit ZZ and XX+YY interactions on an (almost) planar grid.
The effective Hamiltonian is arrived at by a single use of first-order
perturbation theory avoiding the use of perturbation gadgets. The dynamics and
spectral properties of the effective Hamiltonian can be fully determined as it
corresponds to a particular realization of a mapping between a quantum circuit
and a Hamiltonian called the space-time circuit-to-Hamiltonian construction.
Because of the simple interactions required, and because no higher-order
perturbation gadgets are employed, our construction is potentially realizable
using superconducting or other solid-state qubits.Comment: 33 pages, 5 figure
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