206,421 research outputs found
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
Implementing a Unification Algorithm for Protocol Analysis with XOR
In this paper, we propose a unification algorithm for the theory which
combines unification algorithms for E\_{\std} and E\_{\ACUN} (ACUN
properties, like XOR) but compared to the more general combination methods uses
specific properties of the equational theories for further optimizations. Our
optimizations drastically reduce the number of non-deterministic choices, in
particular those for variable identification and linear orderings. This is
important for reducing both the runtime of the unification algorithm and the
number of unifiers in the complete set of unifiers. We emphasize that obtaining
a ``small'' set of unifiers is essential for the efficiency of the constraint
solving procedure within which the unification algorithm is used. The method is
implemented in the CL-Atse tool for security protocol analysis
On the Possibility of Optical Unification in Heterotic Strings
Recently J. Giedt discussed a mechanism, entitled optical unification,
whereby string scale unification is facilitated via exotic matter with
intermediate scale mass. This mechanism guarantees that a virtual MSSM
unification below the string scale is extrapolated from the running of gauge
couplings upward from M_Z^o when an intermediate scale desert is assumed. In
this letter we explore the possibility of optical unification within the
context of weakly coupled heterotic strings. In particular, we investigate this
for models of free fermionic construction containing the NAHE set of basis
vectors. This class is of particular interest for optical unification, because
it provides a standard hypercharge embedding within SO(10), giving the standard
k_Y = 5/3 hypercharge level, which was shown necessary for optical unification.
We present a NAHE model for which the set of exotic SU(3)_C
triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with
hypercharge offers the possibility of optical unification. Whether this model
can realize optical unification is conditional upon these exotics not receiving
Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum
expectation values is non-perturbatively chosen to cancel the FI D-term, xi,
generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten
mechanism. A study of perturbative flat directions and their phenomenological
implications for this model is underway.
This paper is a product of the NFS Research Experiences for Undergraduates
and the NSF High School Summer Science Research programs at Baylor University.Comment: 16 pages. Standard Late
Unification in the Description Logic EL
The Description Logic EL has recently drawn considerable attention since, on
the one hand, important inference problems such as the subsumption problem are
polynomial. On the other hand, EL is used to define large biomedical
ontologies. Unification in Description Logics has been proposed as a novel
inference service that can, for example, be used to detect redundancies in
ontologies. The main result of this paper is that unification in EL is
decidable. More precisely, EL-unification is NP-complete, and thus has the same
complexity as EL-matching. We also show that, w.r.t. the unification type, EL
is less well-behaved: it is of type zero, which in particular implies that
there are unification problems that have no finite complete set of unifiers.Comment: 31page
Stringent Phenomenological Investigation into Heterotic String Optical Unification
For the weakly coupled heterotic string (WCHS) there is a well-known factor
of twenty conflict between the minimum string coupling unification scale,
Lambda_H ~5x10^(17) GeV, and the projected MSSM unification scale, Lambda_U ~
2.5x10^(16) GeV, assuming an intermediate scale desert (ISD). Renormalization
effects of intermediate scale MSSM-charged exotics (ISME) (endemic to
quasi-realistic string models) can resolve this issue, pushing the MSSM scale
up to the string scale. However, for a generic string model, this implies that
the projected Lambda_U unification under ISD is accidental. If the true
unification scale is 5.0x10^(17) GeV, is it possible that illusionary
unification at 2.5x10^(17) GeV in the ISD scenario is not accidental? If it is
not, then under what conditions would the assumption of ISME in a WCHS model
imply apparent unification at Lambda_U when ISD is falsely assumed? Geidt's
"optical unification" suggests that Lambda_U is not accidental, by offering a
mechanism whereby a generic MSSM scale Lambda_U < Lambda_H is guaranteed. A
WCHS model was constructed that offers the possibility of optical unification,
depending on the availability of anomaly-cancelling flat directions meeting
certain requirements. This paper reports on the systematic investigation of the
optical unification properties of the set of stringent flat directions of this
model. Stringent flat directions can be guaranteed to be F-flat to all finite
order (or to at least a given finite order consistent with electroweak scale
supersymmetry breaking) and can be viewed as the likely roots of more general
flat directions. Analysis of the phenomenology of stringent flat directions
gives an indication of the remaining optical unification phenomenology that
must be garnered by flat directions developed from them.Comment: standard latex, 18 pages of tex
Multiple Scales in Pati-Salam Unification Models
We investigate models where gauge unification (GUT) proceeds in steps that
include Pati-Salam symmetry. Beyond the Standard Model, we allow for a
well-defined set of small representations of the GUT gauge group. We show that
all possible chains of Pati-Salam symmetry breaking can be realized in
accordance with gauge-coupling unification. We identify, in particular, models
with unification near the Planck scale, with intermediate left-right or SU(4)
quark-lepton symmetries that are relevant for flavor physics, with new colored
particles at accessible energies, and with an enlarged electroweak Higgs
sector. We look both at supersymmetric and non-supersymmetric scenarios.Comment: 48 pages, 11 figures, version accepted for publication in JHE
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