Contents

- 1 What is K-consistency?
- 2 What is strong K-consistency?
- 3 What type of constraints does arc consistency satisfy?
- 4 When a network of n variables is path consistent it implies that?
- 5 What is generalized arc consistency?
- 6 What is ARC consistency CSP?
- 7 How do you do arc consistency?
- 8 What does it mean for a network to be arc consistent?
- 9 What would be the effect of applying arc consistency?
- 10 How do you know if A heuristic is consistent?
- 11 When is a graph is strongly k-consistent?
- 12 What are the parameters of the consistency index?
- 13 What are the standard conditions for local consistency?
- 14 How is path consistency enforced in constraint propagation?

## What is K-consistency?

A consistency notion in constraint programming. Let. be a CSP. Given a set of variables with , a locally consistent instantiation on is k-consistent iff for any kth variable there exists a value such that. is locally consistent.

## What is strong K-consistency?

Consistency via Strong k-Consistency. Theorem Given: a CSP such that • all domains are non-empty, • it is strongly k-consistent, • the graph associated with it has width k−1. Then this CSP is consistent.

## What type of constraints does arc consistency satisfy?

(Arc Consistency) The pair (X, Y) of constraint variables is arc consistent if for each value x ∈ D X there exists a value y ∈ D y such that the assignments X = x and Y = y satisfy all binary constraints between X and Y. A CSP is arc consistent if all variable pairs are arc consistent.

## When a network of n variables is path consistent it implies that?

A CSP is path consistent, if every path is consistent. This definition is long but not difficult to decipher. On top of binary constraints between two variables, path consistency certifies binary consistency between the variables on a path. It is not difficult to see that path consistency implies arc consistency.

## What is generalized arc consistency?

A variable. is generalized arc consistent (GAC) with a constraint if every value of the variable can be extended to all the other variables of the constraint in such a way the constraint is satisfied. Generalized arc consistency is one of the most commonly enforced forms of consistency in constraint programming.

## What is ARC consistency CSP?

Arc consistency is a heuristic for pruning out possible values for the variables in a CSP which cannot possibly be part of a consistent solution. The AC3 procedure iteratively removes values until the graph is arc consistent.

## How do you do arc consistency?

Arc consistency eliminates values from domain of variable that can never be part of a consistent solution. We can achieve consistency on arc by deleting values form Di (domain of variable at tail of constraint arc) that fail this condition. Assume domains are size at most d and there are e binary constraints.

## What does it mean for a network to be arc consistent?

Answer: An arc < X,r(X, Y ) > is arc consistent if for each value x in dom(X) there is some value y in dom(y) such that r(x, y) is satisfied. What does it mean for a network to be arc consistent? Answer: All of its arcs are consistent.

## What would be the effect of applying arc consistency?

Arc consistency eliminates values from domain of variable that can never be part of a consistent solution. Each undirected constraint arc is really two directed constraint arcs, the effects shown above are from examining BOTH arcs.

## How do you know if A heuristic is consistent?

In the study of path-finding problems in artificial intelligence, a heuristic function is said to be consistent, or monotone, if its estimate is always less than or equal to the estimated distance from any neighbouring vertex to the goal, plus the cost of reaching that neighbour.

## When is a graph is strongly k-consistent?

A graph is strongly K-consistent if it is J-consistsent for all J<=K. Node consistency discussed earlier is equivalent to strong 1-consistency and arc-consistency is equivalent to strong 2-consistency (arc-consistency is usually assumed to include node-consistency as well).

## What are the parameters of the consistency index?

where τ is the shear stress, K is the consistency index, γ˙ is the shear rate, and n is the flow behaviour index. The parameters K and n characterise the rheology of power-law fluids.

## What are the standard conditions for local consistency?

The “standard” local consistency conditions all require that all consistent partial evaluations can be extended to another variable in such a way that the resulting assignment is consistent. A partial evaluation is consistent if it satisfies all constraints whose scope is a subset of the assigned variables.

## How is path consistency enforced in constraint propagation?

The form of constraint propagation that enforces path consistency works by removing some satisfying assignment from a constraint. Indeed, path consistency can be enforced by removing from a binary constraint all evaluations that cannot be extended to another variable.