About: When reasoning about container data structures that can hold duplicate elements, multisets are the obvious choice for representing the data structure abstractly. However, the decidability and complexity of constraints on multisets has been much less studied and understood than for constraints on sets. In this presentation, we outline an efficient decision procedure for reasoning about multisets with cardinality constraints. We describe how to translate, in linear time, multisets constraints to constraints in an extension of quantifier-free linear integer arithmetic, which we call LIA*. LIA* extends linear integer arithmetic with unbounded sums over values satisfying a given linear arithmetic formula. We show how to reduce a LIA* formula to an equisatisfiable linear integer arithmetic formula. However, this approach requires an explicit computation of semilinear sets and in practice it scales poorly even on simple benchmarks. We then describe a recent more efficient approach for checking satisfiability of LIA*. The approach is based on the use of under- and over-approximations of LIA* formulas. This way we avoid the space overhead and explicitly computing semilinear sets. Finally, we report on our prototype tool which can efficiently reason about sets and multisets formulas with cardinality constraints.   Goto Sponge  NotDistinct  Permalink

An Entity of Type : fabio:Abstract, within Data Space : wasabi.inria.fr associated with source document(s)

AttributesValues
type
value
  • When reasoning about container data structures that can hold duplicate elements, multisets are the obvious choice for representing the data structure abstractly. However, the decidability and complexity of constraints on multisets has been much less studied and understood than for constraints on sets. In this presentation, we outline an efficient decision procedure for reasoning about multisets with cardinality constraints. We describe how to translate, in linear time, multisets constraints to constraints in an extension of quantifier-free linear integer arithmetic, which we call LIA*. LIA* extends linear integer arithmetic with unbounded sums over values satisfying a given linear arithmetic formula. We show how to reduce a LIA* formula to an equisatisfiable linear integer arithmetic formula. However, this approach requires an explicit computation of semilinear sets and in practice it scales poorly even on simple benchmarks. We then describe a recent more efficient approach for checking satisfiability of LIA*. The approach is based on the use of under- and over-approximations of LIA* formulas. This way we avoid the space overhead and explicitly computing semilinear sets. Finally, we report on our prototype tool which can efficiently reason about sets and multisets formulas with cardinality constraints.
Subject
  • Object-oriented programming
  • Basic concepts in set theory
  • Factorial and binomial topics
  • Integers
  • Logical expressions
  • Data structures
  • Elementary mathematics
  • Ring theory
  • Algebraic number theory
  • Abelian group theory
  • Elementary number theory
part of
is abstract of
is hasSource of
Faceted Search & Find service v1.13.91 as of Mar 24 2020


Alternative Linked Data Documents: Sponger | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data]
OpenLink Virtuoso version 07.20.3229 as of Jul 10 2020, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (94 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software