242,363 research outputs found

    Extensional Collapse Situations I: non-termination and unrecoverable errors

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    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

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    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

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    For any finite path vv on the square grid consisting of north and east unit steps, starting at (0,0), we construct a poset Tam(v)(v) that consists of all the paths weakly above vv with the same number of north and east steps as vv. For particular choices of vv, we recover the traditional Tamari lattice and the mm-Tamari lattice. Let v\overleftarrow{v} be the path obtained from vv by reading the unit steps of vv in reverse order, replacing the east steps by north steps and vice versa. We show that the poset Tam(v)(v) is isomorphic to the dual of the poset Tam(v)(\overleftarrow{v}). We do so by showing bijectively that the poset Tam(v)(v) is isomorphic to the poset based on rotation of full binary trees with the fixed canopy vv, from which the duality follows easily. This also shows that Tam(v)(v) is a lattice for any path vv. We also obtain as a corollary of this bijection that the usual Tamari lattice, based on Dyck paths of height nn, is a partition of the (smaller) lattices Tam(v)(v), where the vv are all the paths on the square grid that consist of n1n-1 unit steps. We explain possible connections between the poset Tam(v)(v) 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

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    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 k2elk_2^\text{el} and k2magk_2^\text{mag} measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers fo\mathfrak{f}^\text{o} and ko\mathfrak{k}^\text{o} 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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