108,648 research outputs found
A General Framework for Automatic Termination Analysis of Logic Programs
This paper describes a general framework for automatic termination analysis
of logic programs, where we understand by ``termination'' the finitenes s of
the LD-tree constructed for the program and a given query. A general property
of mappings from a certain subset of the branches of an infinite LD-tree into a
finite set is proved. From this result several termination theorems are
derived, by using different finite sets. The first two are formulated for the
predicate dependency and atom dependency graphs. Then a general result for the
case of the query-mapping pairs relevant to a program is proved (cf.
\cite{Sagiv,Lindenstrauss:Sagiv}). The correctness of the {\em TermiLog} system
described in \cite{Lindenstrauss:Sagiv:Serebrenik} follows from it. In this
system it is not possible to prove termination for programs involving
arithmetic predicates, since the usual order for the integers is not
well-founded. A new method, which can be easily incorporated in {\em TermiLog}
or similar systems, is presented, which makes it possible to prove termination
for programs involving arithmetic predicates. It is based on combining a finite
abstraction of the integers with the technique of the query-mapping pairs, and
is essentially capable of dividing a termination proof into several cases, such
that a simple termination function suffices for each case. Finally several
possible extensions are outlined
On van der Corput property of shifted primes
We prove that the upper bound for the van der Corput property of the set of
shifted primes is O((log n)^{-1+o(1)}), giving an answer to a problem
considered by Ruzsa and Montgomery for the set of shifted primes p-1. We
construct normed non-negative valued cosine polynomials with the spectrum in
the set p-1, p<=n, and a small free coefficient a_0=O((log n)^{-1+o(1)}). This
implies the same bound for the Poincar\'e property of the set p-1, and also
bounds for several properties related to uniform distribution of related sets
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