Tremblay, J. P., and R. P. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw-Hill 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and CDA transformation, we now proceed to define a formal model for a sequence of transformations on a model. Figure 4(b) defines an algebra for a sequence of transformations on a model. As shown in Figure 4(b) a sequence of transformations forms a well understood algebraic system called a Group [12] that has its foundations in discrete mathematics. Having shown that the sequence of transforms constitute a Group, we can further utilize operations and tools based on discrete mathematics to reason and verify different characteristics and attributes of the transformations. The algebraic model of ....

....the algebraic system T; 1. 8 i ; j; k 2 T, i ( j k ) i j ) k (Associativity) 2. 9 2 Tsuch that 8 i 2 T i = i = i (Identity) 3. 8 i 2 T;9 2 Tsuch that i = i = Inverse) the algebraic system T; is a Group [12] Figure 4. Algebra for CA and CDA not present in sequential simulations) It must be noted that the modeling and simulation costs are independent of each other. In other words, although the number of components may decrease (and consequently the cost of modeling may decrease) the time taken to ....

TREMBLAY, J. P., AND MANHOHAR, R. Discrete Mathematical Structures With Applications to Computer Science. McGraw-Hill Computer Science Series, USA, 1975.

....cannot be ignored Corresponding author. Email: chen bit.csc.lsu.edu 0169 023X 96 15.00 1996 Elsevier Science B.V. All rights reserved SDI: 0169 023X(96)00006 7 incompatibility between subsets and their instances by the operations V (join) and A (meet) derived from an ordinary lattice [2, 13]. In this paper we propose to use the Boolean lattice concept to represent the structure of an entity set and its subsets. We studied the Boolean Entity lattice structure [8] about the same time as other researchers [10, 12] Their research emphasises the application of Boolean lattice to language ....

J.P. Trimblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science

....lastname can be obtained using only the values bound to the label mmdoc. author. Thus, mmdoc. author. lastname mmdoc. author. Note that imposes a partial ordering on the ePath expression, and it is transitive. We shall talk about the relationships of label expression as forming a lattice [15]. In order to be a lattice, any two elements (i.e. tagged elements or label) must have a least upper bound and a greatest lower bound according to the ordering. However, in practice, we only need the assumptions that 1. is a partial order, and 2. There is a top 0 element, a label upon ....

J.P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw Hill, New York, 1975.

....R is not an equivalence relation, it is a compatibility relation (i.e. it is reflexive and symmetric) While a compatibility relation does not necessarily define a partition of a set, it does define a covering of a set, by the maximal compatibility classes of the relation. Recall that (as in [19]) a subset C is called a maximal compatibility class if every element of C is related to every other element of C and no element of C is related to all the elements of C. Each maximal compatibility class contains stable steps that correspond to a single set of activity choices. More ....

J. P. Tremblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw-Hill, New York, 1975.

....can be obtained using only the values bound to the label mmdoc.author. Thus mmdoc.author.lastname mmdoc.author. Note that imposes a partial ordering on the label expression, and it is transitive. We shall talk about the relationships of label expression as forming a lattice [17]. In order to be a lattice, any two elements (i.e. tagged elements or label) must have a least upper bound and a least lower bound according to the ordering. However, in practice, we only need the assumptions that 1. is a partial order, and 2. The is a top ( element, a label upon which ....

J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw Hill, New York, 1975. 8

....in the above definition) 2. The equality predicate = has the standard interpretation of syntactic identity. 3. The predicate is interpreted as a binary relation over VH such that for every x; y 2 L; x y ( x y x 6= y. the graph G over the nodes of VH can be depicted as a Hasse diagram [TM75] Such a diagram is an undirected graph were all edges are considered as arrows from bottom to top, i.e. smaller elements are placed lower. 4. The predicate is interpreted as the transitive closure of . 5. For any two elements u; v 2 VH , u v holds iff either u v or u = v. Respectively ....

J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw-Hill, New York, 1975.

....is calculated by adding the materialized results for A 1 and A 2 , i.e. 6 plus 4. Assuming that the many to one property didn t hold, such operations wouldn t be possible because some object could be counted multiple times. Lemma 1: The aR tree defines a hierarchy among MBRs that forms a lattice [TM75]. Proof: sketch) Let E l be the set of materialized results for all entries of all nodes of the aR tree at level l, i.e. E l = X i,j .agr, X i in level l, j [1, C i ] Following the notation of [HRU96] we say that E i E j if E i can be answered by E j . From the previous discussion it ....

Tremblay J.P., Manohar R. Discrete Mathematical Structures with Applications to Computer Science. McGraw Hill Book Company, New York, 1975.

....replacing each with , and vice versa. And, if f contains the constants 0 or 1 , each 0 is replaced with 1 , and vice versa. Thus, the dual of a CNF is a DNF, and the dual of a DNF is a CNF. Moreover, the dual of a read k CNF is a read k DNF, and vice versa. By the duality law (e.g. [43]) any identity or theorem about formulas remains true when the formulas are replaced by their duals. Because of this duality, it is easily seen that an algorithm that solves the monotone CNF conversion problem can be modified in a straightforward way to solve the monotone DNF conversion problem. ....

J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw-Hill, 1961.

....can be obtained using only the values bound to the label Paper:author. Thus Paper:author:lastname Paper:author. Note that imposes a partial ordering on the label expression, and it is transitive. We shall talk about the relationships of label expression as forming a lattice [13]. In order to be a lattice, any two elements (i.e. tagged elements or label) must have a least upper bound and a least lower bound according to the ordering. However, in practice, we only need the assumptions that 1. is a partial order, and 2. The is a top ( element, a label upon which ....

J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw Hill, New York, 1975.

....being considered, including a separate case for each value of a predicate of the form foo = a b b a r S ( 6 . If some of the predicates are equalities for continuous values (i.e. foo is an integer or a float) then this set is infinite. Being a power set, it is a lattice [30]. The bottom of the lattice is the case where none of the predicates are known to hold, and top is the case where all of the predicates hold. An implementation that can function in the bottom case is trivial, but likely uninteresting: the null function. An implementation that functions in the ....

....each other, and thus can be trivially composed. If there is overlap, then we compose the adaptation spaces by computing the direct product of the two lattices representing the respective complete adaptation spaces, say S and T. Since S and T are both lattices, the direct product is a lattice [30]. Once the spaces are composed, they can be pruned of impossible and uninteresting cases, grouped into implementations, and transformed into transition graphs as described in Section 3.1 and Section 3.2. 4 Experimental Implementation of Adaptation Spaces This section illustrates our use of ....

Jean-Paul Tremblay. Discrete Mathematical Structures with Applications to Computer Science, chapter Lattices and Boolean Algebra, pages 378--397. McGraw-Hill, 1975.

....(part, customer) There are certain queries that are not comparable with each other using the operator. For example: part) 6 (customer) and (customer) 6 (part) The operator imposes a partial ordering on the queries. We shall talk about the views of a data cube problem as forming a lattice [TM75]. In order to be a lattice, any two elements (views or queries) must have a least upper bound and a greatest lower bound according to the ordering. However, in practice, we only need the assumptions that 2 The analysis in [GBLP95] assumes that every possible cell of the data cube exists. ....

....that independently group by any or no member of the hierarchy for each of n dimensions, then we can represent each view by an n tuple (a 1 ; a 2 ; a n ) where each a i is a point in the hierarchy for the ith dimension. This lattice is called the direct product of the dimensional lattices [TM75]. We directly get a operator for these views by the rule (a 1 ; a 2 ; a n ) b 1 ; b 2 ; b n ) if and only if a i b i for all i We illustrate the building of this direct product lattice in the presence of hierarchies using an example based on the TPC D benchmark. EXAMPLE ....

J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. . McGraw Hill Book Company, New York, 1975.

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Tremblay, J. P., and R. P. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw-Hill 1975.

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J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw-Hill International Editions. ISBN 0-07-100322-3.

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J. P. Tremblay and R. Manohar. Discrete Mathematical Structures with Applications to Computer Science. McGraw-Hill Book Company, 1975.

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