5,090 research outputs found
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
Fixpoint Games on Continuous Lattices
Many analysis and verifications tasks, such as static program analyses and
model-checking for temporal logics reduce to the solution of systems of
equations over suitable lattices. Inspired by recent work on lattice-theoretic
progress measures, we develop a game-theoretical approach to the solution of
systems of monotone equations over lattices, where for each single equation
either the least or greatest solution is taken. A simple parity game, referred
to as fixpoint game, is defined that provides a correct and complete
characterisation of the solution of equation systems over continuous lattices,
a quite general class of lattices widely used in semantics. For powerset
lattices the fixpoint game is intimately connected with classical parity games
for -calculus model-checking, whose solution can exploit as a key tool
Jurdzi\'nski's small progress measures. We show how the notion of progress
measure can be naturally generalised to fixpoint games over continuous lattices
and we prove the existence of small progress measures. Our results lead to a
constructive formulation of progress measures as (least) fixpoints. We refine
this characterisation by introducing the notion of selection that allows one to
constrain the plays in the parity game, enabling an effective (and possibly
efficient) solution of the game, and thus of the associated verification
problem. We also propose a logic for specifying the moves of the existential
player that can be used to systematically derive simplified equations for
efficiently computing progress measures. We discuss potential applications to
the model-checking of latticed -calculi and to the solution of fixpoint
equations systems over the reals
The Parma Polyhedra Library: Toward a Complete Set of Numerical Abstractions for the Analysis and Verification of Hardware and Software Systems
Since its inception as a student project in 2001, initially just for the
handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library
has been continuously improved and extended by joining scrupulous research on
the theoretical foundations of (possibly non-convex) numerical abstractions to
a total adherence to the best available practices in software development. Even
though it is still not fully mature and functionally complete, the Parma
Polyhedra Library already offers a combination of functionality, reliability,
usability and performance that is not matched by similar, freely available
libraries. In this paper, we present the main features of the current version
of the library, emphasizing those that distinguish it from other similar
libraries and those that are important for applications in the field of
analysis and verification of hardware and software systems.Comment: 38 pages, 2 figures, 3 listings, 3 table
Efficient algorithms for conditional independence inference
The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method
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