49,115 research outputs found
Pushdown Control-Flow Analysis of Higher-Order Programs
Context-free approaches to static analysis gain precision over classical
approaches by perfectly matching returns to call sites---a property that
eliminates spurious interprocedural paths. Vardoulakis and Shivers's recent
formulation of CFA2 showed that it is possible (if expensive) to apply
context-free methods to higher-order languages and gain the same boost in
precision achieved over first-order programs.
To this young body of work on context-free analysis of higher-order programs,
we contribute a pushdown control-flow analysis framework, which we derive as an
abstract interpretation of a CESK machine with an unbounded stack. One
instantiation of this framework marks the first polyvariant pushdown analysis
of higher-order programs; another marks the first polynomial-time analysis. In
the end, we arrive at a framework for control-flow analysis that can
efficiently compute pushdown generalizations of classical control-flow
analyses.Comment: The 2010 Workshop on Scheme and Functional Programmin
Deciding Conditional Termination
We address the problem of conditional termination, which is that of defining
the set of initial configurations from which a given program always terminates.
First we define the dual set, of initial configurations from which a
non-terminating execution exists, as the greatest fixpoint of the function that
maps a set of states into its pre-image with respect to the transition
relation. This definition allows to compute the weakest non-termination
precondition if at least one of the following holds: (i) the transition
relation is deterministic, (ii) the descending Kleene sequence
overapproximating the greatest fixpoint converges in finitely many steps, or
(iii) the transition relation is well founded. We show that this is the case
for two classes of relations, namely octagonal and finite monoid affine
relations. Moreover, since the closed forms of these relations can be defined
in Presburger arithmetic, we obtain the decidability of the termination problem
for such loops.Comment: 61 pages, 6 figures, 2 table
On Functions Weakly Computable by Pushdown Petri Nets and Related Systems
We consider numerical functions weakly computable by grammar-controlled
vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can
weakly compute all fast growing functions for
, hence they are computationally more powerful than
standard vector addition systems. On the other hand they cannot weakly compute
the inverses or indeed any sublinear function. The proof relies
on a pumping lemma for runs of GVASes that is of independent interest
The Role of Color Neutrality in Nuclear Physics--Modifications of Nucleonic Wave Functions
The influence of the nuclear medium upon the internal structure of a
composite nucleon is examined. The interaction with the medium is assumed to
depend on the relative distances between the quarks in the nucleon consistent
with the notion of color neutrality, and to be proportional to the nucleon
density. In the resulting description the nucleon in matter is a superposition
of the ground state (free nucleon) and radial excitations. The effects of the
nuclear medium on the electromagnetic and weak nucleon form factors, and the
nucleon structure function are computed using a light-front constituent quark
model. Further experimental consequences are examined by considering the
electromagnetic nuclear response functions. The effects of color neutrality
supply small but significant corrections to predictions of observables.Comment: 37 pages, postscript figures available on request to
[email protected]
Simple universal models capture all classical spin physics
Spin models are used in many studies of complex systems---be it condensed
matter physics, neural networks, or economics---as they exhibit rich
macroscopic behaviour despite their microscopic simplicity.
Here we prove that all the physics of every classical spin model is
reproduced in the low-energy sector of certain `universal models'.
This means that (i) the low energy spectrum of the universal model reproduces
the entire spectrum of the original model to any desired precision, (ii) the
corresponding spin configurations of the original model are also reproduced in
the universal model, (iii) the partition function is approximated to any
desired precision, and (iv) the overhead in terms of number of spins and
interactions is at most polynomial.
This holds for classical models with discrete or continuous degrees of
freedom.
We prove necessary and sufficient conditions for a spin model to be
universal, and show that one of the simplest and most widely studied spin
models, the 2D Ising model with fields, is universal.Comment: v1: 4 pages with 2 figures (main text) + 4 pages with 3 figures
(supplementary info). v2: 12 pages with 3 figures (main text) + 35 pages with
6 figures (supplementary info) (all single column). v2 contains new results
and major revisions (results for spin models with continuous degrees of
freedom, explicit constructions, examples...). Close to published version.
v3: minor typo correcte
- …