12,993 research outputs found
The First-Order Theory of Ground Tree Rewrite Graphs
We prove that the complexity of the uniform first-order theory of ground tree
rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower
bound, we show that there is some fixed ground tree rewrite graph whose
first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to
logspace reductions. Finally, we prove that there exists a fixed ground tree
rewrite graph together with a single unary predicate in form of a regular tree
language such that the resulting structure has a non-elementary first-order
theory.Comment: accepted for Logical Methods in Computer Scienc
The First-Order Theory of Ground Tree Rewrite Graphs
We prove that the complexity of the uniform first-order theory
of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n). Providing a matching lower bound, we show that there is some
fixed ground tree rewrite graph whose first-order theory is hard
for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory
Anomalous behavior in an effective model of graphene with Coulomb interactions
We analyze by exact Renormalization Group (RG) methods the infrared
properties of an effective model of graphene, in which two-dimensional massless
Dirac fermions propagating with a velocity smaller than the speed of light
interact with a three-dimensional quantum electromagnetic field. The fermionic
correlation functions are written as series in the running coupling constants,
with finite coefficients that admit explicit bounds at all orders. The
implementation of Ward Identities in the RG scheme implies that the effective
charges tend to a line of fixed points. At small momenta, the quasi-particle
weight tends to zero and the effective Fermi velocity tends to a finite value.
These limits are approached with a power law behavior characterized by
non-universal critical exponents.Comment: 42 pages, 7 figures; minor corrections, one appendix added (Appendix
A). To appear in Ann. Henri Poincar
Code Generation = A* + BURS
A system called BURS that is based on term rewrite systems and a search algorithm A* are combined to produce a code generator that generates optimal code. The theory underlying BURS is re-developed, formalised and explained in this work. The search algorithm uses a cost heuristic that is derived from the termrewrite system to direct the search. The advantage of using a search algorithm is that we need to compute only those costs that may be part of an optimal rewrite sequence
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
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