177,097 research outputs found
New neighborhood based rough sets
Neighborhood based rough sets are important generalizations of the classical rough sets of Pawlak, as neighborhood operators generalize equivalence classes. In this article, we introduce nine neighborhood based operators and we study the partial order relations between twenty-two different neighborhood operators obtained from one covering. Seven neighborhood operators result in new rough set approximation operators. We study how these operators are related to the other fifteen neighborhood based approximation operators in terms of partial order relations, as well as to seven non-neighborhood-based rough set approximation operators
A Reduced Semantics for Deciding Trace Equivalence
Many privacy-type properties of security protocols can be modelled using
trace equivalence properties in suitable process algebras. It has been shown
that such properties can be decided for interesting classes of finite processes
(i.e., without replication) by means of symbolic execution and constraint
solving. However, this does not suffice to obtain practical tools. Current
prototypes suffer from a classical combinatorial explosion problem caused by
the exploration of many interleavings in the behaviour of processes.
M\"odersheim et al. have tackled this problem for reachability properties using
partial order reduction techniques. We revisit their work, generalize it and
adapt it for equivalence checking. We obtain an optimisation in the form of a
reduced symbolic semantics that eliminates redundant interleavings on the fly.
The obtained partial order reduction technique has been integrated in a tool
called APTE. We conducted complete benchmarks showing dramatic improvements.Comment: Accepted for publication in LMC
More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints
In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain 2^O(k)* n^O(1), 2^O(k log(k))* n^O(1), 2^O(k^2) * n^O(1) and n^O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width. For this latter problem, we obtain n^O(k), n^O(k) and n^(2^O(k)) time algorithm parameterized by clique-width, Q-rank-width and rank-width
Quotient completion for the foundation of constructive mathematics
We apply some tools developed in categorical logic to give an abstract
description of constructions used to formalize constructive mathematics in
foundations based on intensional type theory. The key concept we employ is that
of a Lawvere hyperdoctrine for which we describe a notion of quotient
completion. That notion includes the exact completion on a category with weak
finite limits as an instance as well as examples from type theory that fall
apart from this.Comment: 32 page
Characterization of order-like dependencies with formal concept analysis
Functional Dependencies (FDs) play a key role in many fields
of the relational database model, one of the most widely used database
systems. FDs have also been applied in data analysis, data quality, knowl-
edge discovery and the like, but in a very limited scope, because of their
fixed semantics. To overcome this limitation, many generalizations have
been defined to relax the crisp definition of FDs. FDs and a few of their
generalizations have been characterized with Formal Concept Analysis
which reveals itself to be an interesting unified framework for charac-
terizing dependencies, that is, understanding and computing them in a
formal way. In this paper, we extend this work by taking into account
order-like dependencies. Such dependencies, well defined in the database
field, consider an ordering on the domain of each attribute, and not sim-
ply an equality relation as with standard FDs.Peer ReviewedPostprint (published version
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