... available for constraint programming.
2.1 Structure of document
The tutorial is structured in the following way. We start with a section on the motivation for
using constraints, discussing typical problems with conventional program development for
complex decision support systems. We then briefly re ...
Full Dynamic Substitutability by SAT Encoding
... However, computing fully interchangeable values is believed to be intractable [8,
13, 15, 34] so local forms such as neighbourhood interchangeability are much more
Definition. A value a for variable v is neighbourhood interchangeable with value
b if and only if for every constraint on ...
Simple Stochastic Temporal Constraint Networks
... said to be consistent if at least one solution exists. A value v is said to be a feasible value
for a variable X i if there exists a solution in which X i = v . The set of all feasible values
of a variable is called the minimal domain of the variable.
Major reasoning tasks with metric temporal const ...
A Partial Taxonomy of Substitutability and Interchangeability
... [Freuder, 1991]. At the end of the process, the leaves of the discrimination tree
are annotated with the equivalence NI values for the variable. The complexity of
this process is O(n2 d2 ), where n is the number of variables and d is the maximum
domain size. Alternatively, one can build a refutatio ...
Dynamic domain splitting for numeric CSPs
... are not allowed. Thus, for each domain only two values are to
be kept: its lower bound and its upper bound.
In this paper, we will only consider 2B-consistency 3 , which
is a kind of arc-consistency restricted to the bounds.
Constraint Based Reasoning over Mutex Relations in Graphplan
... Given a set of actions and a goal the task is to find out how to reach a state satisfying the given goal by using the allowed actions only. The whole process of finding of
how to satisfy the goal starts in a specified initial state of the planning world. This
notion is described in the following def ...
s 1 - UNL CSE
... Gottlob, G., Leone, N., Scarcello, F. : On Tractable Queries and Constraints. In: 10th International Conference
and Workshop on Database and Expert System Applications (DEXA 1999). (1999)
Decther, R.: Constraint Processing. Morgan Kaufmann (2003)
Freuder, E.C.: A Sufficient Condition for Backtrack-B ...
... point in the search. The current assignments of these variables may or may not
correspond to the assignments specified in the label.
Definition 3. A label, λ, is valid iff every variable assignment hx = ai ∈ λ is
the current assignment of the variable x.
During search we will induce nogoods, i.e. pa ...
PDF - Programming Systems Lab
... The constraint programming approach to solving combinatorial search problems
such as round robin scheduling problems works as follows. Encode the problem
as a constraint satisfaction problem , find a new problem #' that has the same
set of solutions by applying so-called consistency techniques. N ...
Calc/Cream - Related Web Pages
... Constraint programming is widely used to develop various applications including
constraint satisfaction problems and optimization problems, such as production
planning and scheduling, etc.
Constraint programming is originally studied as an extension of logic programming languages. However, after 199 ...
Exploiting Past and Future: Pruning by Inconsistent Partial State
... an unsatisfiable core by keeping track of all constraints involved in the proof of
unsatisfiability . Such constraints are the ones used during search to remove,
through their propagators, at least one value in the domain of one variable. We
adapt this “proof-based” approach to extract an unsatis ...
Automated Modelling and Solving in Constraint Programming
... set, which is given, for instance, as a set of examples of its
solutions and non-solutions. This kind of learning is called
constraint acquisition (Bessiere et al. 2005). The motivations for constraint acquisition are many. For example, in
order to solve partially defined constraints more efficient ...
Combining Linear Programming and Satisfiability Solving for
... The LPSAT architecture uses a systematic SAT solver as the controlling component of the engine and makes calls to an LP system. The LPSAT algorithm
is very similar to the DPLL algorithm for solving boolean satisfiability problems [Davis et al., 1962]. The key difference is in the definitions of “sat ...
Constraint Programming: In Pursuit of the Holy Grail
... can be found without any search. But the worstcase complexity of the algorithm for obtaining Nconsistency in an N-node constraint graph is
exponential. Unfortunately, if a graph is (strongly)
K-consistent for K
GQR: A Fast Solver for Binary Qualitative Constraint Networks
... A (binary) constraint network is defined by a set of variables taking values in a given domain and a family of binary constraint relations between pairs of variables (on this
domain). The constraint satisfaction problem is to determine for a given constraint network, whether there exists
an assignme ...
ECAI Paper PDF - MIT Computer Science and Artificial Intelligence
... In this section we investigate how optimization over lattices, as defined in Sec. 2, and in particular diagnosis, can be framed as a
semiring-CSP. Since the mathematical properties of semiring-CSPs
ensure that local constraint propagation is applicable, this will be the
basis for efficient solution ...
av -bv -c - IDA.LiU.se
... The pruning operation removes unsupported values from the
domains of variables. Each constraint can be made arc
consistent in this way.
Constraint Programming - What is behind?
... a node consistency (NC). It removes values from
variables’ domains that are inconsistent with unary
constraints on respective variable.
The most widely used consistency technique is
called arc consistency (AC). This technique
removes values from variables’ domains that are
inconsistent with binary c ...
Getting More Out of the Exposed Structure in Constraint
... the dark cells represent the pairs of values that satisfy the
constraint (its solutions). On the left of and below a grid
are depicted the marginal distributions over the first and second variable respectively (i.e. the projection of the set of
solutions onto each axis). The core concept of support ...
Disjunctive Temporal Planning with Uncertainty
... (SC) if there exists a decision that, combined with any realisation, satisfies the constraints. In other words, there is a
way to assign values to the decision variables such that, given
any values for the parameters, at least one disjunct on each
constraint is satisfied. Note this means that a DTPU ...
Optimal 2-constraint satisfaction via sum
... exact algorithms for MAX-2-SAT. One of the best results is due to Gramm et
al.  who give an algorithm that runs in time Õ(2m/5 ), where m is the number
of clauses. 1 This is better than the trivial bound Õ(2n ), when the number of
clauses m is less than 5n. But note that m may well grow quadrat ...
Lecture notes for week 5
... As constraint propagation techniques get more involved (in order to more
effectively prune variable domains), CPU time increases.
In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints. Several such conditions exist, the most known being node consistency, arc consistency, and path consistency. Local consistency can be enforced via transformations of the problem called constraint propagation.Local consistency conditions can be grouped into various classes. The original local consistency conditions require that every consistent assignment can be consistently extended to another variable. Directional consistency only requires this condition to be satisfied when the other variable is higher than the ones in the assignment, according to a given order. Relational consistency includes extensions to more than one variable, but this extension is only required to satisfy a given constraint or set of constraints.Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions. Such a transformation is called constraint propagation. Constraint propagation works by reducing domains of variables, strengthening constraints, or creating new ones. This leads to a reduction of the search space, making the problem easier to solve by some algorithms. Constraint propagation can also be used as an unsatisfiability checker, incomplete in general but complete in some particular cases.