1,151 research outputs found
Reversible Computation in Term Rewriting
Essentially, in a reversible programming language, for each forward
computation from state to state , there exists a constructive method to
go backwards from state to state . Besides its theoretical interest,
reversible computation is a fundamental concept which is relevant in many
different areas like cellular automata, bidirectional program transformation,
or quantum computing, to name a few.
In this work, we focus on term rewriting, a computation model that underlies
most rule-based programming languages. In general, term rewriting is not
reversible, even for injective functions; namely, given a rewrite step , we do not always have a decidable method to get from
. Here, we introduce a conservative extension of term rewriting that
becomes reversible. Furthermore, we also define two transformations,
injectivization and inversion, to make a rewrite system reversible using
standard term rewriting. We illustrate the usefulness of our transformations in
the context of bidirectional program transformation.Comment: To appear in the Journal of Logical and Algebraic Methods in
Programmin
Projective completions of Jordan pairs Part II. Manifold structures and symmetric spaces
We define symmetric spaces in arbitrary dimension and over arbitrary
non-discrete topological fields \K, and we construct manifolds and symmetric
spaces associated to topological continuous quasi-inverse Jordan pairs and
-triple systems. This class of spaces, called smooth generalized projective
geometries, generalizes the well-known (finite or infinite-dimensional) bounded
symmetric domains as well as their ``compact-like'' duals. An interpretation of
such geometries as models of Quantum Mechanics is proposed, and particular
attention is paid to geometries that might be considered as "standard models"
-- they are associated to associative continuous inverse algebras and to Jordan
algebras of hermitian elements in such an algebra
Group Averaging and Refined Algebraic Quantization
We review the framework of Refined Algebraic Quantization and the method of
Group Averaging for quantizing systems with first-class constraints. Aspects
and results concerning the generality, limitations, and uniqueness of these
methods are discussed.Comment: 4 pages, LaTeX 2.09 using espcrc2.sty. To appear in the proceedings
of the third "Meeting on Constrained Dynamics and Quantum Gravity", Nucl.
Phys. B (Proc. Suppl.
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