Enumerating homomorphisms

Enumerating Homomorphisms

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensiv...

Lattice Homomorphisms Induced by Group Homomorphisms

Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...

Enumerating Molecules

This report is a comprehensive review of the field of molecular enumeration from early isomer counting theories to evolutionary algorithms that design molecules in silico. The core of the review is a detail account on how molecules are counted, enumerated, and sampled. The practical applications of molecular enumeration are also reviewed for chemical information, structure elucidation, molecula...

POMDP Homomorphisms

The problem of finding hidden state in a POMDP and the problem of finding abstractions for MDPs are closely related. In this paper, we analyze the connection between existing Predictive State Representation methods [3] and homomorphic reductions of Markov Processes [5, 6]. We formally define a POMDP homomorphism, then extend PSR reduction methods to find POMDP homomorphisms when the original PO...

n-Homomorphisms