CHAPTER 8
DYNAMIC PROGRAMMING
Many valuation algebras have an associated notion of a solution, best or preferred value with respect to some criteria. Most typical are solutions to linear equations or inequalities. In logic, solutions may correspond to the truth value assignments under which a sentence evaluates to true. Likewise, the solutions of a constraint system are the variable assignments that satisfy the constraints and in optimization problems, solutions lead to either maximum or minimum values. Given a set r or variables, we again write Ωx for the frame of each variable 
and Ωs for the set of all possible tuples or configurations of a subset 
, see Section 1.2. If 
denotes a valuation algebra defined over the subset lattice 
, a solution for some valuation 
with domain d(
) = s always corresponds to some element × . We know from Instance 1.2 that such tuple systems form a relational ...
