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For a given partial solution,
the partial inverse problem is to modify the coefficients
such that there is a full solution containing the partial solution,
while the full solution becomes optimal under new coefficients, and
the total modification is minimum.
In this paper, we show that the partial inverse
assignment problem and the partial inverse minimum cut problem are NP-hard if
there are bound constraints on the changes of coefficients.
We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement...
The standard procedure to transform a regular expression of size n
to an ϵ-free nondeterministic finite automaton yields automata
with O(n) states and O(n2) transitions. For a long time this
was supposed to be also the lower bound, but a result by
Hromkovic et al. showed how to build an ϵ-free NFA with
only O(n log2(n)) transitions. The current lower bound on the
number of transitions is Ω(n log(n)). A rough running time estimation for the common
follow sets (CFS) construction proposed...
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