11,519 research outputs found
Transition Systems for Model Generators - A Unifying Approach
A fundamental task for propositional logic is to compute models of
propositional formulas. Programs developed for this task are called
satisfiability solvers. We show that transition systems introduced by
Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers
can be adapted for solvers developed for two other propositional formalisms:
logic programming under the answer-set semantics, and the logic PC(ID). We show
that in each case the task of computing models can be seen as "satisfiability
modulo answer-set programming," where the goal is to find a model of a theory
that also is an answer set of a certain program. The unifying perspective we
develop shows, in particular, that solvers CLASP and MINISATID are closely
related despite being developed for different formalisms, one for answer-set
programming and the latter for the logic PC(ID).Comment: 30 pages; Accepted for presentation at ICLP 2011 and for publication
in Theory and Practice of Logic Programming; contains the appendix with
proof
An Introduction to Nuclear Supersymmetry: a Unification Scheme for Nuclei
The main ideas behind nuclear supersymmetry are presented, starting from the
basic concepts of symmetry and the methods of group theory in physics. We
propose new, more stringent experimental tests that probe the supersymmetry
classification in nuclei and point out that specific correlations should exist
for particle transfer intensities among supersymmetric partners. We also
discuss possible ways to generalize these ideas to cases where no dynamical
symmetries are present. The combination of these theoretical and experimental
studies may play a unifying role in nuclear phenomena.Comment: 40 pages, 11 figures, lecture notes `VIII Hispalensis International
Summer School: Exotic Nuclear Physics', Oromana, Sevilla, Spain, June 9-21,
200
Coupling of quantum angular momenta: an insight into analogic/discrete and local/global models of computation
In the past few years there has been a tumultuous activity aimed at
introducing novel conceptual schemes for quantum computing. The approach
proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling
theory of SU(2) angular momenta and can be viewed as a generalization to
arbitrary values of the spin variables of the usual quantum-circuit model based
on `qubits' and Boolean gates. Computational states belong to
finite-dimensional Hilbert spaces labelled by both discrete and continuous
parameters, and unitary gates may depend on quantum numbers ranging over finite
sets of values as well as continuous (angular) variables. Such a framework is
an ideal playground to discuss discrete (digital) and analogic computational
processes, together with their relationships occuring when a consistent
semiclassical limit takes place on discrete quantum gates. When working with
purely discrete unitary gates, the simulator is naturally modelled as families
of quantum finite states--machines which in turn represent discrete versions of
topological quantum computation models. We argue that our model embodies a sort
of unifying paradigm for computing inspired by Nature and, even more
ambitiously, a universal setting in which suitably encoded quantum symbolic
manipulations of combinatorial, topological and algebraic problems might find
their `natural' computational reference model.Comment: 17 pages, 1 figure; Workshop `Natural processes and models of
computation' Bologna (Italy) June 16-18 2005; to appear in Natural Computin
Coset Realization of Unifying W-Algebras
We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and
sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely
generated. Furthermore, we discuss in detail their role as unifying W-algebras
of Casimir W-algebras. We show that it is possible to give coset realizations
of various types of unifying W-algebras, e.g. the diagonal cosets based on the
symplectic Lie algebras sp(2n) realize the unifying W-algebras which have
previously been introduced as `WD_{-n}'. In addition, minimal models of WD_{-n}
are studied. The coset realizations provide a generalization of
level-rank-duality of dual coset pairs. As further examples of finitely
nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras
which on the quantum level has different properties than in the classical case.
We demonstrate in some examples that the classical limit according to Bowcock
and Watts of these nonfreely finitely generated quantum W-algebras probably
yields infinitely nonfreely generated classical W-algebras.Comment: 60 pages (plain TeX) (final version to appear in Int. J. Mod. Phys.
A; several minor improvements and corrections - for details see beginning of
file
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