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Absolute continuity and summability of transport densities: simpler proofs
, 2008
"... and new estimates ..."
Proof:...
, 2006
"... • Proofs are highly structured texts. Be aware of their structure. • When constructing proofs, use the following schema: ..."
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• Proofs are highly structured texts. Be aware of their structure. • When constructing proofs, use the following schema:
Nonmonotonic Reasoning is Sometimes Simpler!
, 1993
"... We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4expansion for a given set A of premises is \Sigma P 2 complete. Similarly, we show that for a given formula ' and a set A of premises, it is \Sigm ..."
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Cited by 9 (2 self)
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We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4expansion for a given set A of premises is \Sigma P 2 complete. Similarly, we show that for a given formula ' and a set A of premises, it is \Sigma P 2  complete to decide whether ' belongs to at least one S4expansion for A, and it is \Pi P 2 complete to decide whether ' belongs to all S4expansions for A. This refutes a conjecture of Gottlob that these problems are PSPACEcomplete. An interesting aspect of these results is that reasoning (testing satisfiability and provability) in the monotonic modal logic S4 is PSPACEcomplete. To the best of our knowledge, the nonmonotonic logic S4 is the first example of a nonmonotonic formalism which is computationally easier than the monotonic logic that underlies it (assuming PSPACE does not collapse to \Sigma P 2 ). 1 Introduction First nonmonotonic logics were proposed in late 70s and e...
Proof
"... In the eld of formal methods, rewriting techniques and provers by consistency in particular appear as powerful tools for automating deduction. However, these provers su er limitations as they only give a (nonreadable) trace of their progress and a yes/no answer where the user would expect a detailed ..."
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detailed explicit proof. Therefore, we propose a general mechanism to build an explicit proof from the running of a generic class of inductionless induction provers. We then show howitapplies to Bouhoula's SPIKE prover, and give examples of proofs built by this method.
Proofs
"... “mcs ” — 2013/1/10 — 0:28 — page i — #1 Mathematics for Computer Science ..."
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Cited by 2 (0 self)
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“mcs ” — 2013/1/10 — 0:28 — page i — #1 Mathematics for Computer Science
IDENTIFICATION OF GENETIC NETWORKS FROM A SMALL NUMBER OF GENE EXPRESSION PATTERNS UNDER THE BOOLEAN NETWORK MODEL
 PACIFIC SYMPOSIUM ON BIOCOMPUTING 4:1728 (1999)
, 1999
"... ... for inferring genetic network architectures from state transition tables which correspond to time series of gene expression patterns, using the Boolean network model. Their results of computational experiments suggested that a small number of state transition (INPUT/OUTPUT) pairs are sufficient ..."
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Cited by 254 (17 self)
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in order to infer the original Boolean network correctly. This paper gives a mathematical proof for their observation. Precisely, this paper devises a much simpler algorithm for the same problem and proves that, if the indegree of each node (i.e., the number of input nodes to each node) is bounded by a
Simpler Projective Plane Embedding
, 2000
"... A projective plane is equivalent to a disk with antipodal points identified. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective planar embedding has been described by Mohar. We provide a new approach that takes O(n ..."
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Cited by 3 (0 self)
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A projective plane is equivalent to a disk with antipodal points identified. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective planar embedding has been described by Mohar. We provide a new approach that takes O(n 2 ) time but is much easier to implement. We programmed a variant of this algorithm and used it to computationally verify the known list of all the projective plane obstructions. Key words: graph algorithms, surface embedding, graph embedding, projective plane, forbidden minor, obstruction 1 Background A graph G consists of a set V of vertices and a set E of edges, each of which is associated with an unordered pair of vertices from V . Throughout this paper, n denotes the number of vertices of a graph, and m is the number of edges. A graph is embeddable on a surface M if it can be drawn on M without crossing edges. Archdeacon's survey [2] provides an excellent introduction to topologica...
Simpler Hybrid GMRES
, 2005
"... Abstract. Hybrid GMRES algorithms are effective for solving large nonsymmetric linear systems. GMRES is employed at the first phase to produce iterative polynomials, which will be used at the second phase to implement the Richardson iteration. In the process of GMRES, a least squares problem needs t ..."
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to be solved which involves an upper Hessenberg factorization. Instead of using GMRES, we may use simpler GMRES. Correspondingly, simpler hybrid GMRES algorithms are formulated. It is described how to construct the iterative polynomials from simpler GMRES. The new algorithms avoid the upper Hessenberg
Results 11  20
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