2,367 research outputs found
The Algebraic Intersection Type Unification Problem
The algebraic intersection type unification problem is an important component
in proof search related to several natural decision problems in intersection
type systems. It is unknown and remains open whether the algebraic intersection
type unification problem is decidable. We give the first nontrivial lower bound
for the problem by showing (our main result) that it is exponential time hard.
Furthermore, we show that this holds even under rank 1 solutions (substitutions
whose codomains are restricted to contain rank 1 types). In addition, we
provide a fixed-parameter intractability result for intersection type matching
(one-sided unification), which is known to be NP-complete.
We place the algebraic intersection type unification problem in the context
of unification theory. The equational theory of intersection types can be
presented as an algebraic theory with an ACI (associative, commutative, and
idempotent) operator (intersection type) combined with distributivity
properties with respect to a second operator (function type). Although the
problem is algebraically natural and interesting, it appears to occupy a
hitherto unstudied place in the theory of unification, and our investigation of
the problem suggests that new methods are required to understand the problem.
Thus, for the lower bound proof, we were not able to reduce from known results
in ACI-unification theory and use game-theoretic methods for two-player tiling
games
On preferences over subsets and the lattice structure of stable matchings
This paper studies the structure of stable multipartner matchings in
two-sided markets where choice functions are quotafilling in the sense that they
satisfy the substitutability axiom and, in addition, fill a quota whenever possible.
It is shown that (i) the set of stable matchings is a lattice under the common
revealed preference orderings of all agents on the same side, (ii) the supremum
(infimum) operation of the lattice for each side consists componentwise of the
join (meet) operation in the revealed preference ordering of the agents on that
side, and (iii) the lattice has the polarity, distributivity, complementariness and full-quota properties
On the homomorphism order of labeled posets
Partially ordered sets labeled with k labels (k-posets) and their
homomorphisms are examined. We give a representation of directed graphs by
k-posets; this provides a new proof of the universality of the homomorphism
order of k-posets. This universal order is a distributive lattice. We
investigate some other properties, namely the infinite distributivity, the
computation of infinite suprema and infima, and the complexity of certain
decision problems involving the homomorphism order of k-posets. Sublattices are
also examined.Comment: 14 page
General relativistic dynamics of compact binaries at the third post-Newtonian order
The general relativistic corrections in the equations of motion and
associated energy of a binary system of point-like masses are derived at the
third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian
expansion of the metric in harmonic coordinates at the 3PN approximation. The
metric is parametrized by appropriate non-linear potentials, which are
evaluated in the case of two point-particles using a Lorentzian version of an
Hadamard regularization which has been defined in previous works.
Distributional forms and distributional derivatives constructed from this
regularization are employed systematically. The equations of motion of the
particles are geodesic-like with respect to the regularized metric. Crucial
contributions to the acceleration are associated with the non-distributivity of
the Hadamard regularization and the violation of the Leibniz rule by the
distributional derivative. The final equations of motion at the 3PN order are
invariant under global Lorentz transformations, and admit a conserved energy
(neglecting the radiation reaction force at the 2.5PN order). However, they are
not fully determined, as they depend on one arbitrary constant, which reflects
probably a physical incompleteness of the point-mass regularization. The
results of this paper should be useful when comparing theory to the
observations of gravitational waves from binary systems in future detectors
VIRGO and LIGO.Comment: 78 pages, submitted to Phys. Rev. D, with minor modification
Mod-two cohomology of symmetric groups as a Hopf ring
We compute the mod-2 cohomology of the collection of all symmetric groups as
a Hopf ring, where the second product is the transfer product of Strickland and
Turner. We first give examples of related Hopf rings from invariant theory and
representation theory. In addition to a Hopf ring presentation, we give
geometric cocycle representatives and explicitly determine the structure as an
algebra over the Steenrod algebra. All calculations are explicit, with an
additive basis which has a clean graphical representation. We also briefly
develop related Hopf ring structures on rings of symmetric invariants and end
with a generating set consisting of Stiefel-Whitney classes of regular
representations v2. Added new results on varieties which represent the
cocycles, a graphical representation of the additive basis, and on the Steenrod
algebra action. v3. Included a full treatment of invariant theoretic Hopf
rings, refined the definition of representing varieties, and corrected and
clarified references.Comment: 31 pages, 6 figure
A new look at the conditions for the synthesis of speed-independent circuits
This paper presents a set of sufficient conditions for the gate-level synthesis of speed-independent circuits when constrained to a given class of gate library. Existing synthesis methodologies are restricted to architectures that use simple AND-gates, and do not exploit the advantages offered by the existence of complex gates. The use of complex gates increases the speed and reduces the area of the circuits. These improvements are achieved because of (1) the elimination of the distributivity, signal persistency and unique minimal state requirements imposed by other techniques; (2) the reduction in the number of internal signals necessary to guarantee the synthesis; and finally (3) the utilization of optimization techniques to reduce the fan-in of the involved gates and the number of required memory elements.Peer ReviewedPostprint (published version
An Inflationary Fixed Point Operator in XQuery
We introduce a controlled form of recursion in XQuery, inflationary fixed
points, familiar in the context of relational databases. This imposes
restrictions on the expressible types of recursion, but we show that
inflationary fixed points nevertheless are sufficiently versatile to capture a
wide range of interesting use cases, including the semantics of Regular XPath
and its core transitive closure construct.
While the optimization of general user-defined recursive functions in XQuery
appears elusive, we will describe how inflationary fixed points can be
efficiently evaluated, provided that the recursive XQuery expressions exhibit a
distributivity property. We show how distributivity can be assessed both,
syntactically and algebraically, and provide experimental evidence that XQuery
processors can substantially benefit during inflationary fixed point
evaluation.Comment: 11 pages, 10 figures, 2 table
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