Con ict-driven clause learning is currently the most e cient complete algorithm for satis ability solving. However, a con ict-directed backtrack deletes potentially large portions of the current assignment that have no direct relation with the con ict. In this paper, we show that the CDCL algorithm can be generalized with a partial ordering on decision levels. This allows keeping levels that wo...

In this paper we tackle the problem of verifying whether a labeled partial order (LPO) is executable in a Petri net. In contrast to sequentially ordered runs an LPO includes both, information about dependencies and independencies of events. Consequently an LPO allows a precise and intuitive specification of the behavior of a concurrent or distributed system. In this paper we consider Petri nets...

The rank subtractivity partial ordering is defined on Cn×n (n ≥ 2) by A ≤− B⇔ rank(B−A) = rankB− rankA, and the star partial ordering by A ≤∗ B⇔ A∗A = A∗B ∧ AA∗ = BA∗. If A and B are normal, we characterize A ≤− B. We also show that then A ≤− B ∧ AB = BA⇔ A ≤∗ B⇔ A ≤− B ∧ A ≤− B. Finally, we remark that some of our results follow from well-known results on EP matrices.

In this note we answer a question raised by John Truss. He asked if every definable partial ordering in an o-minimal structure can be extended to a definable total order. His question is motivated by analogy with the Order Extension Principle, a weak choice-like axiom of interest to set theorists, which asserts that every partial ordering of a set can be extended to a total order of the set (se...

We propose a partial ordering that approximates a ranking of the items in a database according to their similarity to a query item. The partial ordering uses a single-link hierarchical clustering of the data items to rank them with respect to the query’s closest match. The technique avoids the O(kn) cost of calculating the similarity measure between the query and every item in the database. It ...