[Show abstract][Hide abstract] ABSTRACT: This paper proposes a decomposition based algorithm for revision problems in classical propositional logic. A set of decomposing rules are presented to analyze the satisfiability of formulas. The satisfiability of a formula is equivalent to the satisfiability of a set of literal sets. A decomposing function is constructed to calculate all satisfiable literal sets of a given formula. When expressing the satisfiability of a formula, these literal sets are equivalent to all satisfied models of such formula. A revision algorithm based on this decomposing function is proposed, which can calculate maximal contractions of a given problem. In order to reduce the memory requirement, a filter function is introduced. The improved algorithm has a good performance in both time and space perspectives.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we propose a representative model based algorithm to calculate maximal contractions. For a formal theory Γ and a fact set Δ, the algorithm begins by accepting all models of refutation by facts of Γ with respect to Δ and filters these models to obtain the models of R-refutation. According to the completeness of R-calculus, the relevant maximal contraction is obtained simultaneously. In order to improve the efficiency, we divide the models into different classes according to the assignments of atomic propositions and only select relevant representative models to verify the satisfiability of each proposition. The algorithm is correct, and all maximal contractions of a given problem can be calculated by it. Users could make a selection according to their requirements. A benchmark algorithm is also provided. Experiments show that the algorithm has a good performance on normal revision problems.
[Show abstract][Hide abstract] ABSTRACT: We describe two formal proofs of the finite version of Hall's Marriage Theorem performed with the proof assistant Isabelle/HOL, one by Halmos and Vaughan and one by Rado. The distinctive feature of our formalisation is that instead of sequences (often found in statements of this theorem) we employ indexed families, thus avoiding tedious reindexing of sequences.
Certified Programs and Proofs - First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011. Proceedings; 01/2011
[Show abstract][Hide abstract] ABSTRACT: Problem of belief revision and specification evolution has been studied for years. Researchers have proposed ACM theory and R-calculus to solve the problem. This paper concerns with the revision of proposition logic and proposes a revision algorithm which can automatically find out a revision of given sets. The correctness of the algorithm is proved and concepts such as basic proposition, assignment equivalence relation and delegate model are introduced. Tactics are used to improve the efficiency of the revision algorithm. A revision system is realized based on the improved algorithm. And an example is run to illustrate the syntax and the property of the system.
Information Engineering and Computer Science, 2009. ICIECS 2009. International Conference on; 01/2010
[Show abstract][Hide abstract] ABSTRACT: The problem of belief revision and specification evolution has been studied for years. Different methods have been proposed to solve this problem. However, the problem of efficiency has not been solved well. Therefore, this paper proposes a revision algorithm based on assignment equivalence classes to improve the efficiency of the delegate model based algorithm. The new algorithm follows the same structure of the delegate model based algorithm but reduces the times of model checking. Concepts such as delegate models of a proposition set and sub-assignment equivalence classes are introduced, and relevant properties are also proved. The new algorithm is implemented, which has a better performance than before.
[Show abstract][Hide abstract] ABSTRACT: Packing problem has been proved to be an NP-hard problem. Many algorithms such as simulation annealing algorithm, genetic
algorithm and other heuristic algorithms have been proposed to solve two-dimensional and three-dimensional packing problem.
To solve the cube packing problem with time schedule, this paper first introduces some concepts such as packing level, space
distance and average neighbor birth order and then proposes a greedy algorithm. The algorithm tries every feasible corner
greedily to calculate the space utilization, packing level, space distance, average neighbor birth order of this placement,
and chooses the best placement according to these criteria. Theoretical analysis indicates that the time complexity of this
algorithm is O(A
2
B
2
C
2
T
2
n
5). The experiments show that the average space utilization of non-guillotine cutting test cases is 98.81%, and the average
space utilization of guillotine cutting test cases achieves 99.87%. Furthermore, optimal solutions of more than half cases
are achieved by this algorithm. The experimental results show that this algorithm can solve the problem of cube packing with
time schedule effectively and efficiently.
[Show abstract][Hide abstract] ABSTRACT: Mean-variance relationship (MVR), nowadays agreed in power law form, is an important function. It is currently used by traffic
matrix estimation as a basic statistical assumption. Because all the existing papers obtain MVR only through empirical ways,
they cannot provide theoretical support to power law MVR or the definition of its power exponent. Furthermore, because of
the lack of theoretical model, all traffic matrix estimation methods based on MVR have not been theoretically supported yet.
By observing both our laboratory and campus network for more than one year, we find that such an empirical MVR is not sufficient
to describe actual network traffic. In this paper, we derive a theoretical MVR from ON/OFF model. Then we prove that current
empirical power law MVR is generally reasonable by the fact that it is an approximate form of theoretical MVR under specific
precondition, which can theoretically support those traffic matrix estimation algorithms of using MVR. Through verifying our
MVR by actual observation and public DECPKT traces, we verify that our theoretical MVR is valid and more capable of describing
actual network traffic than power lawMVR.
Science in China Series F Information Sciences 04/2009; 52:645-655. DOI:10.1007/s11432-009-0084-y · 0.66 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: TM (Traffic Matrix) estimation is a hot research area recently. Current TM estimation methods are generally designed for backbone
and ISP networks. They estimate complete TM which is unnecessary for many IP networks in reality and especially unsuitable
for the networks that have many entries. In this paper, we propose an estimation algorithm that is designed for IP networks
on link layer. Our algorithm estimates the OD (Origin and Destination pair) count on the basis of link counts which are easy
to obtain. Our algorithm first builds a three-entry virtual network from actual network, and then achieves the final result
by multivariate linear regression. We verify our algorithm in the official network of our lab by comparing with exact OD count
data that are obtained by NetFlow.
Challenges for Next Generation Network Operations and Service Management, 11th Asia-Pacific Network Operations and Management Symposium, APNOMS 2008, Beijing, China, October 22-24, 2008. Proceedings; 01/2008