3,229 research outputs found
Termination Proofs in the Dependency Pair Framework May Induce Multiple Recursive Derivational Complexity
We study the derivational complexity of rewrite systems whose termination is
provable in the dependency pair framework using the processors for reduction
pairs, dependency graphs, or the subterm criterion. We show that the
derivational complexity of such systems is bounded by a multiple recursive
function, provided the derivational complexity induced by the employed base
techniques is at most multiple recursive. Moreover we show that this upper
bound is tight.Comment: 22 pages, extended conference versio
On Sharing, Memoization, and Polynomial Time (Long Version)
We study how the adoption of an evaluation mechanism with sharing and
memoization impacts the class of functions which can be computed in polynomial
time. We first show how a natural cost model in which lookup for an already
computed value has no cost is indeed invariant. As a corollary, we then prove
that the most general notion of ramified recurrence is sound for polynomial
time, this way settling an open problem in implicit computational complexity
On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image
We explore the conjectured duality between the critical O(N) vector model and
minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free
theory, the conformal partial wave expansion (CPWE) of the four-point function
of the scalar singlet bilinear is reorganized to make it explicitly
crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge
fields. We are able to analytically establish the factorized form of the fusion
coefficients as well as the two-point function coefficient of the HS currents.
We insist in directly computing the free correlators from bulk graphs with the
unconventional branch. The three-point function of the scalar bilinear turns
out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be
precisely related to the CPWs of the boundary dual scalar and its shadow. The
flow in the IR by Legendre transforming at leading 1/N, following the pattern
of double-trace deformations, and the assumption of degeneracy of the hologram
lead to the CPWE of the scalar four-point function at IR. Here we confirm some
previous results, obtained from more involved computations of skeleton graphs,
as well as extend some of them from d=3 to generic dimension 2<d<4.Comment: 22 pages, 5 figure
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
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