64 research outputs found
Interacting Dark Sector and Precision Cosmology
We consider a recently proposed model in which dark matter interacts with a
thermal background of dark radiation. Dark radiation consists of relativistic
degrees of freedom which allow larger values of the expansion rate of the
universe today to be consistent with CMB data (-problem). Scattering
between dark matter and radiation suppresses the matter power spectrum at small
scales and can explain the apparent discrepancies between CDM
predictions of the matter power spectrum and direct measurements of Large Scale
Structure LSS (-problem). We go beyond previous work in two ways: 1.
we enlarge the parameter space of our previous model and allow for an arbitrary
fraction of the dark matter to be interacting and 2. we update the data sets
used in our fits, most importantly we include LSS data with full -dependence
to explore the sensitivity of current data to the shape of the matter power
spectrum. We find that LSS data prefer models with overall suppressed matter
clustering due to dark matter - dark radiation interactions over CDM
at 3-4 . However recent weak lensing measurements of the power spectrum
are not yet precise enough to clearly distinguish two limits of the model with
different predicted shapes for the linear matter power spectrum. In two
Appendices we give a derivation of the coupled dark matter and dark radiation
perturbation equations from the Boltzmann equation in order to clarify a
confusion in the recent literature, and we derive analytic approximations to
the solutions of the perturbation equations in the two physically interesting
limits of all dark matter weakly interacting or a small fraction of dark matter
strongly interacting.Comment: 29 pages + 2 Appendices; published versio
Implementing an Automatic Differentiator in ACL2
The foundational theory of differentiation was developed as part of the
original release of ACL2(r). In work reported at the last ACL2 Workshop, we
presented theorems justifying the usual differentiation rules, including the
chain rule and the derivative of inverse functions. However, the process of
applying these theorems to formalize the derivative of a particular function is
completely manual. More recently, we developed a macro and supporting functions
that can automate this process. This macro uses the ACL2 table facility to keep
track of functions and their derivatives, and it also interacts with the macro
that introduces inverse functions in ACL2(r), so that their derivatives can
also be automated. In this paper, we present the implementation of this macro
and related functions.Comment: In Proceedings ACL2 2011, arXiv:1110.447
ACL2(ml):machine-learning for ACL2
ACL2(ml) is an extension for the Emacs interface of ACL2. This tool uses
machine-learning to help the ACL2 user during the proof-development. Namely,
ACL2(ml) gives hints to the user in the form of families of similar theorems,
and generates auxiliary lemmas automatically. In this paper, we present the two
most recent extensions for ACL2(ml). First, ACL2(ml) can suggest now families
of similar function definitions, in addition to the families of similar
theorems. Second, the lemma generation tool implemented in ACL2(ml) has been
improved with a method to generate preconditions using the guard mechanism of
ACL2. The user of ACL2(ml) can also invoke directly the latter extension to
obtain preconditions for his own conjectures.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Verifying Sierpi\'nski and Riesel Numbers in ACL2
A Sierpinski number is an odd positive integer, k, such that no positive
integer of the form k * 2^n + 1 is prime. Similar to a Sierpinski number, a
Riesel number is an odd positive integer, k, such that no positive integer of
the form k * 2^n + 1 is prime. A cover for such a k is a finite list of
positive integers such that each integer j of the appropriate form has a
factor, d, in the cover, with 1 < d < j. Given a k and its cover, ACL2 is used
to systematically verify that each integer of the given form has a non-trivial
factor in the cover.Comment: In Proceedings ACL2 2011, arXiv:1110.447
Formal Verification of an Iterative Low-Power x86 Floating-Point Multiplier with Redundant Feedback
We present the formal verification of a low-power x86 floating-point
multiplier. The multiplier operates iteratively and feeds back intermediate
results in redundant representation. It supports x87 and SSE instructions in
various precisions and can block the issuing of new instructions. The design
has been optimized for low-power operation and has not been constrained by the
formal verification effort. Additional improvements for the implementation were
identified through formal verification. The formal verification of the design
also incorporates the implementation of clock-gating and control logic. The
core of the verification effort was based on ACL2 theorem proving.
Additionally, model checking has been used to verify some properties of the
floating-point scheduler that are relevant for the correct operation of the
unit.Comment: In Proceedings ACL2 2011, arXiv:1110.447
Towards a formally verified network-on-chip
Contains fulltext :
75650.pdf (publisher's version ) (Open Access)9th International Conference 2009 Formal Methods in Computer-Aided Design FMCAD 2009, 15 november 200
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