13,023 research outputs found
Towards Parameterized Regular Type Inference Using Set Constraints
We propose a method for inferring \emph{parameterized regular types} for
logic programs as solutions for systems of constraints over sets of finite
ground Herbrand terms (set constraint systems). Such parameterized regular
types generalize \emph{parametric} regular types by extending the scope of the
parameters in the type definitions so that such parameters can relate the types
of different predicates. We propose a number of enhancements to the procedure
for solving the constraint systems that improve the precision of the type
descriptions inferred. The resulting algorithm, together with a procedure to
establish a set constraint system from a logic program, yields a program
analysis that infers tighter safe approximations of the success types of the
program than previous comparable work, offering a new and useful efficiency vs.
precision trade-off. This is supported by experimental results, which show the
feasibility of our analysis
Towards Static Analysis of Functional Programs using Tree Automata Completion
This paper presents the first step of a wider research effort to apply tree
automata completion to the static analysis of functional programs. Tree
Automata Completion is a family of techniques for computing or approximating
the set of terms reachable by a rewriting relation. The completion algorithm we
focus on is parameterized by a set E of equations controlling the precision of
the approximation and influencing its termination. For completion to be used as
a static analysis, the first step is to guarantee its termination. In this
work, we thus give a sufficient condition on E and T(F) for completion
algorithm to always terminate. In the particular setting of functional
programs, this condition can be relaxed into a condition on E and T(C) (terms
built on the set of constructors) that is closer to what is done in the field
of static analysis, where abstractions are performed on data.Comment: Proceedings of WRLA'14. 201
A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
In this article we compare the mean-square stability properties of the
Theta-Maruyama and Theta-Milstein method that are used to solve stochastic
differential equations. For the linear stability analysis, we propose an
extension of the standard geometric Brownian motion as a test equation and
consider a scalar linear test equation with several multiplicative noise terms.
This test equation allows to begin investigating the influence of
multi-dimensional noise on the stability behaviour of the methods while the
analysis is still tractable. Our findings include: (i) the stability condition
for the Theta-Milstein method and thus, for some choices of Theta, the
conditions on the step-size, are much more restrictive than those for the
Theta-Maruyama method; (ii) the precise stability region of the Theta-Milstein
method explicitly depends on the noise terms. Further, we investigate the
effect of introducing partially implicitness in the diffusion approximation
terms of Milstein-type methods, thus obtaining the possibility to control the
stability properties of these methods with a further method parameter Sigma.
Numerical examples illustrate the results and provide a comparison of the
stability behaviour of the different methods.Comment: 19 pages, 10 figure
PURRS: Towards Computer Algebra Support for Fully Automatic Worst-Case Complexity Analysis
Fully automatic worst-case complexity analysis has a number of applications
in computer-assisted program manipulation. A classical and powerful approach to
complexity analysis consists in formally deriving, from the program syntax, a
set of constraints expressing bounds on the resources required by the program,
which are then solved, possibly applying safe approximations. In several
interesting cases, these constraints take the form of recurrence relations.
While techniques for solving recurrences are known and implemented in several
computer algebra systems, these do not completely fulfill the needs of fully
automatic complexity analysis: they only deal with a somewhat restricted class
of recurrence relations, or sometimes require user intervention, or they are
restricted to the computation of exact solutions that are often so complex to
be unmanageable, and thus useless in practice. In this paper we briefly
describe PURRS, a system and software library aimed at providing all the
computer algebra services needed by applications performing or exploiting the
results of worst-case complexity analyses. The capabilities of the system are
illustrated by means of examples derived from the analysis of programs written
in a domain-specific functional programming language for real-time embedded
systems.Comment: 6 page
The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges
In principle, the Luttinger-Ward Green's function formalism allows one to
compute simultaneously the total energy and the quasiparticle band structure of
a many-body electronic system from first principles. We present approximate and
exact expressions for the correlation energy within the GW-RPA approximation
that are more amenable to computation and allow for developing efficient
approximations to the self-energy operator and correlation energy. The exact
form is a sum over differences between plasmon and interband energies. The
approximate forms are based on summing over screened interband transitions. We
also demonstrate that blind extremization of such functionals leads to
unphysical results: imposing physical constraints on the allowed solutions
(Green's functions) is necessary. Finally, we present some relevant numerical
results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review
Confluence via strong normalisation in an algebraic \lambda-calculus with rewriting
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are
untyped lambda-calculi extended with arbitrary linear combinations of terms.
The former presents the axioms of linear algebra in the form of a rewrite
system, while the latter uses equalities. When given by rewrites, algebraic
lambda-calculi are not confluent unless further restrictions are added. We
provide a type system for the linear-algebraic lambda-calculus enforcing strong
normalisation, which gives back confluence. The type system allows an abstract
interpretation in System F.Comment: In Proceedings LSFA 2011, arXiv:1203.542
Coherent presentations of Artin monoids
We compute coherent presentations of Artin monoids, that is presentations by
generators, relations, and relations between the relations. For that, we use
methods of higher-dimensional rewriting that extend Squier's and Knuth-Bendix's
completions into a homotopical completion-reduction, applied to Artin's and
Garside's presentations. The main result of the paper states that the so-called
Tits-Zamolodchikov 3-cells extend Artin's presentation into a coherent
presentation. As a byproduct, we give a new constructive proof of a theorem of
Deligne on the actions of an Artin monoid on a category
Perturbative Calculation of Multi-Loop Feynman Diagrams. New Type of Expansions for Critical Exponents
We show that the calculation of L-loop Feynman integrals in D dimensions can
be reduced to a series of matrix multiplications in D times L dimensions. This
gives rise to a new type of expansions for the critical exponents in three
dimensions in which all coefficients can be calculated exactly.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Reachability Analysis of Innermost Rewriting
We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs and, several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of
terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. The proposed algorithm has been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy
- …