Sentence examples for free instances from inspiring English sources

As before, Ω x) is an open formula with x as its only free variable; Ω(m) is the result of replacing the free instances of x with a name for m.

For example a free instance that has already been purchased may have used only 50% of its purchased time.

Customers who have a free instance of Yammer with more than 100 users can switch to Socialtext Signals, and get a hosted or on-premise microblogging appliance to suit their needs.

The Generalized Horn Flat patterns have the following form: (a1 > b1), …, (an > bn) ⊢ (a > b); where negations are allowed in the left hand side of the pattern and where the letters ai, a, etc only admit conditional-free instances.

Now, we devise a dynamic-programming-based algorithm solving W-MTO in quadratic time on cross-pair-free instances.

Cross-pair-free instances of W-MTO are of special interest since they constitute our "trivial instances".

Next, we show that W-MTO is fixed-parameter tractable with respect to the parameter q v by extending the dynamic programming algorithm for cross-pair-free instances.

To this end, we introduce the concept of "cross pairs" and show that for cross-pair-free instances MTO can be solved in O(n) time.

Theorem 2. On n-vertex trees, W EIGHTED M AXIMUM T REE O RIENTATION for cross-pair-free instances with given root can be solved in O(n) time.

We introduce the concept of cross pairs and show that cross-pair-free instances of W-MTO can be solved in quadratic time, as a corollary also improving the cubic-time algorithm of Medvedovsky et al. [ 3] for MTO on paths to quadratic time.

By refining the solving strategy for cross-pair-free instances, we show that M AXIMUM T REE O RIENTATION can be solved in O (2 q v ⋅ n 2 ⋅ q v ) time, where q v denotes the maximum number of cross pairs passing through a vertex.