3,428 research outputs found
Branching: the Essence of Constraint Solving
This paper focuses on the branching process for solving any constraint
satisfaction problem (CSP). A parametrised schema is proposed that (with
suitable instantiations of the parameters) can solve CSP's on both finite and
infinite domains. The paper presents a formal specification of the schema and a
statement of a number of interesting properties that, subject to certain
conditions, are satisfied by any instances of the schema.
It is also shown that the operational procedures of many constraint systems
including cooperative systems) satisfy these conditions.
Moreover, the schema is also used to solve the same CSP in different ways by
means of different instantiations of its parameters.Comment: 18 pages, 2 figures, Proceedings ERCIM Workshop on Constraints
(Prague, June 2001
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
An Improved Tight Closure Algorithm for Integer Octagonal Constraints
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality''
or ``UTVPI integer constraints'') constitute an interesting class of
constraints for the representation and solution of integer problems in the
fields of constraint programming and formal analysis and verification of
software and hardware systems, since they couple algorithms having polynomial
complexity with a relatively good expressive power. The main algorithms
required for the manipulation of such constraints are the satisfiability check
and the computation of the inferential closure of a set of constraints. The
latter is called `tight' closure to mark the difference with the (incomplete)
closure algorithm that does not exploit the integrality of the variables. In
this paper we present and fully justify an O(n^3) algorithm to compute the
tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure
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Applications of Polyhedral Computations to the Analysis and Verification of Hardware and Software Systems
Convex polyhedra are the basis for several abstractions used in static
analysis and computer-aided verification of complex and sometimes mission
critical systems. For such applications, the identification of an appropriate
complexity-precision trade-off is a particularly acute problem, so that the
availability of a wide spectrum of alternative solutions is mandatory. We
survey the range of applications of polyhedral computations in this area; give
an overview of the different classes of polyhedra that may be adopted; outline
the main polyhedral operations required by automatic analyzers and verifiers;
and look at some possible combinations of polyhedra with other numerical
abstractions that have the potential to improve the precision of the analysis.
Areas where further theoretical investigations can result in important
contributions are highlighted.Comment: 51 pages, 11 figure
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