Functions

A deadline miss – representated as UInt8(0)

A deadline hit – representated as UInt8(1)

A deadline miss – representated as UInt8(0) (equivalent to Miss)

A deadline hit – representated as UInt8(1) (equivalent to Hit)

A struct keep track of the current node and its direct children (if some exist).

Abstract representation of an automaton type

Automaton()

Automaton struct containing a dict to represent the vertices (including head) and transitions of the automaton.

• Key = Word (represented by integer).
• Value = WordVertex (containing current vertex and its direct children vertices)

Abstract representation of a constraint type

RowHitConstraint(x, k)

Constructor for RowHitConstraint.

RowMissConstraint(x)

Constructor for RowMissConstraint.

AnyHitConstraint(x, k)

Constructor for AnyHitConstraint.

AnyMissConstraint(x, k)

Constructor for AnyMissConstraint.

build_automaton(Lambda::T) where {T <: Union{Constraint, Set{Constraint}}}

Creates a minimal weakly-hard automaton according to the (set of) weakly-hard constraint(s) Lambda.

NOTE: The function handles both single constraints and sets of constraints.

Examples

julia> build_automaton(AnyHitConstraint(1, 3))
Automaton{Int64} with 3 vertices:
{
	WordVertex{Int64}(100 => ---, 001)
	WordVertex{Int64}(010 => 100, 001)
	WordVertex{Int64}(001 => 010, 001)
} with head: WordVertex{Int64}(1 => 10, 1)

julia> build_automaton(Set([AnyHitConstraint(1, 3), RowHitConstraint(2, 6)]))
Automaton{Int64} with 7 vertices:
{
	WordVertex{Int64}(001101 => 011010, 000011)
	WordVertex{Int64}(000110 => 001100, 001101)
	WordVertex{Int64}(011001 => ------, 000011)
	WordVertex{Int64}(011010 => ------, 110101)
	WordVertex{Int64}(001100 => ------, 011001)
	WordVertex{Int64}(000011 => 000110, 000011)
	WordVertex{Int64}(110101 => ------, 000011)
} with head: WordVertex{Int64}(11 => 110, 11)

transitions(automaton::Automaton)

Returns all the transitions in automaton in the form of a set of pairs where each pair consists of (v1, v2, c12), i.e., the tail of the transition v1, the head of the transition v2, and the label of the transition c12.

vertices(automaton::Automaton)

Returns all the vertices in automaton.

is_dominant(l1, l2)

Returns whether the weakly-hard constraint l1 dominates l2 or not.

Examples

julia> is_dominant(AnyHitConstraint(1, 3), RowMissConstraint(1))
false

julia> is_dominant(AnyHitConstraint(1, 3), RowMissConstraint(2))
true

is_equivalent(l1, l2)

Returns whether the weakly-hard constraint l1 is equivalent to l2 or not.

Examples

julia> is_equivalent(AnyHitConstraint(1, 3), RowMissConstraint(1))
false

julia> is_equivalent(AnyHitConstraint(1, 3), RowMissConstraint(2))
true

is_satisfied(L, w)

Returns whether the word w satisfies the constraint L or not; here, L can be either a single constraint or a constraint set.

Examples

julia> is_satisfied(AnyHitConstraint(1, 3), 595) # bitstring(595) = ...1001010011
true

julia> is_satisfied(AnyHitConstraint(1, 3), 600) # bitstring(600) = ...1001011000
false

random_sequence(automaton::Automaton, N::Integer)

The function takes an arbitrary walk of length N in automaton. Returns a sequence that satisfy all weakly-hard constraints used to build the automaton.

all_sequences(automaton::Automaton, N::Integer)

The function returns a set containing all sequences of length N satisfying the constraints used to build the automaton. In other words, the function generates the satisfaction set of length N sequences.

Example

julia> all_sequences(build_automaton(AnyHitConstraint(2, 3)), 5)
Set{Int8} with 9 elements:
  22
  13
  15
  29
  27
  31
  30
  14
  23

dominant_set(Lambda::Set{Constraint})

Calculates the dominant constraint set given a set of weakly-hard constraints, Lambda.

Examples

julia> dominant_set(Set([RowMissConstraint(1), 
                         AnyMissConstraint(3, 5), 
                         AnyMissConstraint(1, 7)]))
Set{Constraint} with 1 element:
  AnyMissConstraint(1, 7)

minimize_automaton!(automaton::Automaton)

Minimises the automaton representation of a set of weakly-hard constraints.

bitstring(w::BigInt [, n::Integer])

A String giving the literal bit representation of a big integer w. If n is specified, it pads the bit representation to contain at least n characters.

Examples

julia> bitstring(BigInt(4))
"100"

julia> bitstring(BigInt(4), 5)
"00100"