Related papers: Symmetries in Integer Programs
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
We represent planning as a set of loosely coupled network flow problems, where each network corresponds to one of the state variables in the planning domain. The network nodes correspond to the state variable values and the network arcs…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
Software platforms often act as structure preserving systems. They provide consistent interfaces and behaviors that remain stable under specific transformations that we denote as symmetries. This paper explores the idea that architectural…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible…
The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
Program synthesis is the process of automatically translating a specification into computer code. Traditional synthesis settings require a formal, precise specification. Motivated by computer education applications where a student learns to…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…