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Groups and Constraints: Symmetry Breaking during Search
We present an interface between the ECLiPSe constraint logic programming system and the GAP computational abstract algebra system. The interface provides a method for efficiently dealing with large…
Generic SBDD Using Computational Group Theory
We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The essence of SBDD is to perform 'dominance checks' at each node in a search tree to ensure that no symmetrically…
Tractable Symmetry Breaking Using Restricted Search Trees
A new conceptual abstraction in symmetry breaking - the GE-tree is presented, and a polynomial-time algorithm for this construction in the case of CSPs with arbitrary value symmetries is given.
Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS
- A. Adams, Martin Dunstan, H. Gottliebsen, T. Kelsey, U. Martin, S. Owre
- Computer Science, MathematicsTPHOLs
- 3 September 2001
An interface between version 6 of the Maple computer algebra system with the PVS automated theorem prover is described, designed to allow Maple users access to the robust and checkable proof environment of PVS.
Conditional Symmetry Breaking
- Ian P. Gent, T. Kelsey, S. Linton, Iain McDonald, I. Miguel, Barbara M. Smith
- Computer ScienceCP
- 1 October 2005
It is demonstrated experimentally that three methods, well-known for breaking unconditional symmetries, can be applied to conditional symmetry breaking, and three methods are augmenting the search process to break the conditional symmetry dynamically through the use of a variant of Symmetry Breaking by Dominance Detection (SBDD).
New Developments in Symmetry Breaking in Search Using Computational Group Theory
This paper analyzes the structure of symmetry groups of constraint satisfaction problems, and implements several combinations of GE-trees and the classical SBDD method for breaking all symmetries.
Lightweight formal methods for computer algebra systems
The use of formal methods tools are demonstrated to provide a semantics for the type hierarchy of the AXIOM computer algebra system, and a methodology for Aldor program analysis and veri cation.
The Semigroups of Order 10
The use of mathematical results combined with distributed Constraint Satisfaction is described to show that the number of non-equivalent semigroups of order 10 is 12,418,001,077,381,302,684.
GAPLex: Generalized Static Symmetry Breaking
This work describes a novel algorithm that statically breaks symmetry in CSPs by using computational group theory during search, and believes this to be the first method that successfully combines the posting of symmetry breaking constraints before search, with symmetry breaking by analysis of search states.
The monoids of orders eight, nine & ten
We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our…