242,363 research outputs found
Extensional Collapse Situations I: non-termination and unrecoverable errors
We consider a simple model of higher order, functional computation over the
booleans. Then, we enrich the model in order to encompass non-termination and
unrecoverable errors, taken separately or jointly. We show that the models so
defined form a lattice when ordered by the extensional collapse situation
relation, introduced in order to compare models with respect to the amount of
"intensional information" that they provide on computation. The proofs are
carried out by exhibiting suitable applied {\lambda}-calculi, and by exploiting
the fundamental lemma of logical relations
Model-Checking Process Equivalences
Process equivalences are formal methods that relate programs and system
which, informally, behave in the same way. Since there is no unique notion of
what it means for two dynamic systems to display the same behaviour there are a
multitude of formal process equivalences, ranging from bisimulation to trace
equivalence, categorised in the linear-time branching-time spectrum.
We present a logical framework based on an expressive modal fixpoint logic
which is capable of defining many process equivalence relations: for each such
equivalence there is a fixed formula which is satisfied by a pair of processes
if and only if they are equivalent with respect to this relation. We explain
how to do model checking, even symbolically, for a significant fragment of this
logic that captures many process equivalences. This allows model checking
technology to be used for process equivalence checking. We show how partial
evaluation can be used to obtain decision procedures for process equivalences
from the generic model checking scheme.Comment: In Proceedings GandALF 2012, arXiv:1210.202
An extension of Tamari lattices
For any finite path on the square grid consisting of north and east unit
steps, starting at (0,0), we construct a poset Tam that consists of all
the paths weakly above with the same number of north and east steps as .
For particular choices of , we recover the traditional Tamari lattice and
the -Tamari lattice.
Let be the path obtained from by reading the unit
steps of in reverse order, replacing the east steps by north steps and vice
versa. We show that the poset Tam is isomorphic to the dual of the poset
Tam. We do so by showing bijectively that the poset
Tam is isomorphic to the poset based on rotation of full binary trees with
the fixed canopy , from which the duality follows easily. This also shows
that Tam is a lattice for any path . We also obtain as a corollary of
this bijection that the usual Tamari lattice, based on Dyck paths of height
, is a partition of the (smaller) lattices Tam, where the are all
the paths on the square grid that consist of unit steps.
We explain possible connections between the poset Tam and (the
combinatorics of) the generalized diagonal coinvariant spaces of the symmetric
group.Comment: 18 page
Extended I-Love relations for slowly rotating neutron stars
Observations of gravitational waves from inspiralling neutron star
binaries---such as GW170817---can be used to constrain the nuclear equation of
state by placing bounds on stellar tidal deformability. For slowly rotating
neutron stars, the response to a weak quadrupolar tidal field is characterized
by four internal-structure-dependent constants called "Love numbers." The tidal
Love numbers and measure the tides raised by
the gravitoelectric and gravitomagnetic components of the applied field, and
the rotational-tidal Love numbers and
measure those raised by couplings between the applied
field and the neutron star spin. In this work we compute these four Love
numbers for perfect fluid neutron stars with realistic equations of state. We
discover (nearly) equation-of-state independent relations between the
rotational-tidal Love numbers and the moment of inertia, thereby extending the
scope of I-Love-Q universality. We find that similar relations hold among the
tidal and rotational-tidal Love numbers. These relations extend the
applications of I-Love universality in gravitational-wave astronomy. As our
findings differ from those reported in the literature, we derive general
formulas for the rotational-tidal Love numbers in post-Newtonian theory and
confirm numerically that they agree with our general-relativistic computations
in the weak-field limit.Comment: 31 pages, 6 figures, 9 tables; v2: updated to match published versio
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