91,553 research outputs found
Adapting Real Quantifier Elimination Methods for Conflict Set Computation
The satisfiability problem in real closed fields is decidable. In the context
of satisfiability modulo theories, the problem restricted to conjunctive sets
of literals, that is, sets of polynomial constraints, is of particular
importance. One of the central problems is the computation of good explanations
of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the
input constraints whose conjunction is already unsatisfiable. We adapt two
commonly used real quantifier elimination methods, cylindrical algebraic
decomposition and virtual substitution, to provide such conflict sets and
demonstrate the performance of our method in practice
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries
Lie group theory states that knowledge of a -parameters solvable group of
symmetries of a system of ordinary differential equations allows to reduce by
the number of equations. We apply this principle by finding some
\emph{affine derivations} that induces \emph{expanded} Lie point symmetries of
considered system. By rewriting original problem in an invariant coordinates
set for these symmetries, we \emph{reduce} the number of involved parameters.
We present an algorithm based on this standpoint whose arithmetic complexity is
\emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can
generally reduce the number of parameters defining the system behavior by
studying the system's Lie symmetrie
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