114,086 research outputs found
Verification of model transformations
Model transformations are a central element of model-driven
development (MDD) approaches such as the model-driven architecture (MDA). The correctness of model transformations is critical to their effective use in practical software development, since users must be able
to rely upon the transformations correctly preserving the semantics of models. In this paper we define a formal semantics for model transformations, and provide techniques for proving the termination, confluence and correctness of model transformations
All Symmetries of Non-Einsteinian Gravity in
The covariant form of the field equations for two--dimensional --gravity
with torsion as well as its Hamiltonian formulation are shown to suggest the
choice of the light--cone gauge. Further a one--to--one correspondence between
the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz
transformations is established, thus proving that there are no hidden local
symmetries responsible for the complete integrability of the model. Finally the
constraint algebra is shown to have no quantum anomalies so that Dirac's
quantization should be applicable.Comment: LaTex, 16 pages, TUW9207, (Some smaller corrections, cross-references
updated
The Parisi-Sourlas Mechanism in Yang-Mills Theory?
The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using
the new scalar degrees of freedom derived from the non-linear gauge condition,
we show that the non-perturbative sector of Yang-Mills theory is equivalent to
a 4D O(1,3) sigma model in a random field. We then show that the leading term
of this equivalent theory is invariant under supersymmetry transformations
where (x^{2}+\thetabar\theta) is unchanged. This leads to dimensional reduction
proving the equivalence of the non-perturbative sector of Yang-Mills theory to
a 2D O(1,3) sigma model.Comment: 13 pages, LATE
How hard is it to verify flat affine counter systems with the finite monoid property ?
We study several decision problems for counter systems with guards defined by
convex polyhedra and updates defined by affine transformations. In general, the
reachability problem is undecidable for such systems. Decidability can be
achieved by imposing two restrictions: (i) the control structure of the counter
system is flat, meaning that nested loops are forbidden, and (ii) the set of
matrix powers is finite, for any affine update matrix in the system. We provide
tight complexity bounds for several decision problems of such systems, by
proving that reachability and model checking for Past Linear Temporal Logic are
complete for the second level of the polynomial hierarchy , while
model checking for First Order Logic is PSPACE-complete
Quantum gauge symmetries in Noncommutative Geometry
We discuss generalizations of the notion of i) the group of unitary elements
of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations
and iii) (real) automorphisms, in the framework of compact quantum group theory
and spectral triples. The quantum analogue of these groups are defined as
universal (initial) objects in some natural categories. After proving the
existence of the universal objects, we discuss several examples that are of
interest to physics, as they appear in the noncommutative geometry approach to
particle physics: in particular, the C*-algebras M_n(R), M_n(C) and M_n(H),
describing the finite noncommutative space of the Einstein-Yang-Mills systems,
and the algebras A_F=C+H+M_3(C) and A^{ev}=H+H+M_4(C), that appear in
Chamseddine-Connes derivation of the Standard Model of particle physics
minimally coupled to gravity. As a byproduct, we identify a "free" version of
the symplectic group Sp(n) (quaternionic unitary group).Comment: 31 pages, no figures; v2: minor changes, added reference
Totally correct logic program transformations via well-founded annotations
We address the problem of proving the total correctness of transformations of definite logic programs. We consider a general transformation rule, called clause replacement,
which consists in transforming a program P into a new program Q by replacing a set Î1 of
clauses occurring in P by a new set Î2 of clauses, provided that Î1 and Î2 are equivalent in the least Herbrand model M(P) of the program P.
We propose a general method for proving that transformations based on clause replacement are totally correct, that is, M(P) = M(Q). Our method consists in showing that the
transformation of P into Q can be performed by: (i) adding extra arguments to predicates,
thereby deriving from the given program P an annotated program P, (ii) applying a variant
of the clause replacement rule and transforming the annotated program P into a terminating
annotated program Q, and (iii) erasing the annotations from Q, thereby getting Q.
Our method does not require that either P or Q are terminating and it is parametric with
respect to the annotations. By providing different annotations we can easily prove the total correctness of program transformations based on various versions of the popular unfolding, folding, and goal replacement rules, which can all be viewed as particular cases of our clause replacement rule
Well-definedness of Streams by Transformation and Termination
Streams are infinite sequences over a given data type. A stream specification
is a set of equations intended to define a stream. We propose a transformation
from such a stream specification to a term rewriting system (TRS) in such a way
that termination of the resulting TRS implies that the stream specification is
well-defined, that is, admits a unique solution. As a consequence, proving
well-definedness of several interesting stream specifications can be done fully
automatically using present powerful tools for proving TRS termination. In
order to increase the power of this approach, we investigate transformations
that preserve semantics and well-definedness. We give examples for which the
above mentioned technique applies for the ransformed specification while it
fails for the original one
Proving theorems by program transformation
In this paper we present an overview of the unfold/fold proof method, a method for proving theorems about programs, based on program transformation. As a metalanguage for specifying programs and program properties we adopt constraint logic programming (CLP), and we present a set of transformation rules (including the familiar unfolding and folding rules) which preserve the semantics of CLP programs. Then, we show how program transformation strategies can be used, similarly to theorem proving tactics, for guiding the application of the transformation rules and inferring the properties to be proved. We work out three examples: (i) the proof of predicate equivalences, applied to the verification of equality between CCS processes, (ii) the proof of first order formulas via an extension of the quantifier elimination method, and (iii) the proof of temporal properties of infinite state concurrent systems, by using a transformation strategy that performs program specialization
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