Constraints.jl: Streamlining Constraint Definition and Integration in Julia

Constraints defined from Languages

# Constraints.xcsp_regular — Function.

xcsp_regular(; list, automaton)

Ensures that a sequence `x` (interpreted as a word) is accepted by the regular language represented by a given automaton. This constraint verifies the compliance of `x` with the language rules encoded within the `automaton` parameter, which must be an instance of `<:AbstractAutomaton`.

Arguments

• list::Vector{Int}: A list of variables

• automaton<:AbstractAutomaton: An automaton representing the regular language

Variants

• :regular: Ensures that a sequence x (interpreted as a word) is accepted by the regular language represented by a given automaton. This constraint verifies the compliance of x with the language rules encoded within the automaton parameter, which must be an instance of <:AbstractAutomaton.

concept(:regular, x; language)
concept(:regular)(x; language)

Examples

c = concept(:regular)

states = Dict(
    (:a, 0) => :a,
    (:a, 1) => :b,
    (:b, 1) => :c,
    (:c, 0) => :d,
    (:d, 0) => :d,
    (:d, 1) => :e,
    (:e, 0) => :e,
)
start = :a
finish = :e

a = Automaton(states, start, finish)

c([0,0,1,1,0,0,1,0,0]; language = a)
c([1,1,1,0,1]; language = a)

source

# Constraints.xcsp_mdd — Function.

xcsp_mdd(; list, diagram)

Return a function that checks if the list of values list satisfies the MDD diagram.

Arguments

• list::Vector{Int}: list of values to check.

• diagram::MDD: MDD to check.

Variants

• :mdd: Multi-valued Decision Diagram (MDD) constraint. The MDD constraint is a constraint that can be used to model a wide range of problems. It is a directed graph where each node is labeled with a value and each edge is labeled with a value. The constraint is satisfied if there is a path from the first node to the last node such that the sequence of edge labels is a valid sequence of the value labels.

concept(:mdd, x; language)
concept(:mdd)(x; language)

Examples

c = concept(:mdd)

states = [
    Dict( # level x1
        (:r, 0) => :n1,
        (:r, 1) => :n2,
        (:r, 2) => :n3,
    ),
    Dict( # level x2
        (:n1, 2) => :n4,
        (:n2, 2) => :n4,
        (:n3, 0) => :n5,
    ),
    Dict( # level x3
        (:n4, 0) => :t,
        (:n5, 0) => :t,
    ),
]

a = MDD(states)

c([0,2,0]; language = a)
c([1,2,0]; language = a)
c([2,0,0]; language = a)
c([2,1,2]; language = a)
c([1,0,2]; language = a)
c([0,1,2]; language = a)

source