Information Technology Reference
In-Depth Information
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- Concatenation
of two constraint vectors is performed by summing the o
sets and
performing a union of modulo sets for every basic constraint. The result will thus
consume at least the same amount of input events as the constituent vectors would
in isolation.
- Distributing
preserves truth due to the design of the eval() procedure, as
each disjunct will also include the concatenated outer disjunct.
- Bounded Repetition
of a constraint vector
·
over
∨
C
raised to a power
k
is equivalent to
concatenating a sequence of
k
consecutive
C
vectors. The modulo sets thus remains
unchanged, whilst the o
sets of each basic constraint are multiplied by a factor
k
.
Bounded repetition of a disjunction of constraint is performed by expanding the
disjunction as a
multinomial
, discarding the coe
ff
cients. This produces a disjunc-
tion of sequences with every combination of the terms, essentially unravelling the
loop.
- Unbounded Repetition
resolves to a concatenation of zero or more constraint ex-
pressions. If a single constraint vector is being raised to a power, then its o
set is
added to its modulo set, thus matching when the original expression is taken one
or more times. In the case of an unbounded repetition of a DCE, each disjunct
can be taken an unbounded number of times, forming a sequence of constraint ex-
pressions. Equivalent sequences can be formed by changing the disjunctions into
concatenations, whilst simultaneously placing each concatenated expression in an
unbounded loop.
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