### Table 3 Linear algebra and max-plus algebra

"... In PAGE 23: ... (1992). Table3 illustrates some similarities between linear algebra and max-plus algebra. Here, we will not give an extensive treatment of the algebraic and system theoretic properties of the max-plus algebra but restrict to the modelling issues.... ..."

### Table 1. Logical and physical algebras.

1999

"... In PAGE 3: ... Such an algebra is system-specific, meaning that different systems may implement the same data model and the same logical algebra, but may use different physical algebras [12]. Table1 shows the logical and the physical operators used by the conventional optimizer. We describe the physical algebra operators in more detail in section 3.... ..."

Cited by 7

### Table 1: THE ALGEBRA OF BINARY FLOWNOMIALS .

1998

"... In PAGE 4: ... cation). In Table1 we use some particular cases of the rami cation and identi cation constants, namely ^0; ^2; _0; _2 denoted by ?; ^; gt;; _, respectively. In the standard version presented in [Ste94] there are three groups of algebraic equations (see Table 1): (A) a large group of algebraic equations for owgraphs modulo graph{isomorphism B1{B10, A1{A19, R1{R5 and F1{F5; (S) some critical algebraic equations S1{S4 for the data ow nodes for rami cation and identi cation; (Z) an axiom scheme ENZ, presented as a conditional equation.... In PAGE 5: ...Table1 are valid in the semantical models IRel(D). Suppose D is a set of value-vectors which represent the memory states of a computing device.... In PAGE 6: ... More details of the model(s) are presented in [BeS94, BrS96, BeS95]. Let us recall that not all the axioms in Table1 are valid in this model, but at least the BNA axioms hold. In the following we will use an extension of this setting to the many sorted case.... ..."

Cited by 9

### Table 1: The axioms for boolean algebras.

1999

"... In PAGE 8: ... 3. Data speci cations In the theory pCRL, the data must be given by means of a many-sorted equational speci cation D = h ; Ei that contains the axioms of boolean algebra (see Table1 ); such an equational speci cation is called a data speci cation. For easier explanation of our ideas we shall focuss on a certain kind of data speci cations that have a nice correspondence with theories of rst-order predicate logic.... In PAGE 8: ... We shall occasionally refer to the function declarations of the rst kind as relations, and to those of the second kind as functions. Let us x a data speci cation D = h ; Ei of this kind; we denote by Eb the set of axioms of sort b (it contains the axioms in Table1 ), and by Ed the set of axioms of sort d. We may regard as the rst-order language that has the relations of as relation symbols and the functions of as operation symbols.... ..."

### TABLE 1. Linear Algebra Kernel Descriptions

"... In PAGE 3: ... Sor improves more because it has a higher percentage of references removed. BLU Block LU BLUP Block LUP Chol Cholesky Decomposition Afold Adjoint Convolution Fold Convolution Seval Spline Evaluation Sor Successive Over Relaxation Linear Algebra Kernel Description TABLE1 . Linear Algebra Kernel Descriptions Linear Algebra Kernel Normalized Execution Time 92 93 61 69 90 95 85 90 VM MMk MMi LU LUP BLUBLUP Chol Afold Fold Seval Sor Mean 0 20 40 60 80 100 Original Optimized... ..."

### TABLE 1. Linear Algebra Kernel Descriptions

"... In PAGE 3: ... Sor improves more because it has a higher percentage of references removed. BLU Block LU BLUP Block LUP Chol Cholesky Decomposition Afold Adjoint Convolution Fold Convolution Seval Spline Evaluation Sor Successive Over Relaxation Linear Algebra Kernel Description TABLE1 . Linear Algebra Kernel Descriptions Linear Algebra Kernel Normalized Execution Time 92 93 61 69 90 95 85 90 VM MMk MMi LU LUP BLUBLUP Chol Afold Fold Seval Sor Mean 0 20 40 60 80 100 Original Optimized... ..."

### TABLE 1. Linear Algebra Kernel Descriptions

"... In PAGE 3: ... Sor improves more because it has a higher percentage of references removed. BLU Block LU BLUP Block LUP Chol Cholesky Decomposition Afold Adjoint Convolution Fold Convolution Seval Spline Evaluation Sor Successive Over Relaxation Linear Algebra Kernel Description TABLE1 . Linear Algebra Kernel Descriptions Linear Algebra Kernel Normalized Execution Time 92 93 61 69 90 95 85 90 VM MMk MMi LU LUP BLUBLUP Chol Afold Fold Seval Sor Mean 0 20 40 60 80 100 Original Optimized ... ..."

### Table 1. An algebraic specification of the object place.

1992

"... In PAGE 5: ...ig. 1. Highways, interchanges, and places shown at the Planning Level. A place at this level can be specified as demonstrated in Table1 . The object apos;s underlying figure is a vertex (which is a node in the graph model) and the vertex is assumed to be already specified.... ..."

Cited by 41

### Table 3. State space size and simulation time (sec) of the algebraic models.

"... In PAGE 23: ... As a simple example, we have proved that the mechanisms #1, #2, and #3 are deadlock free. To achieve this, we have generated with TwoTowers the state space of the EMPA specifications of the three mechanisms, whose size is reported in the upper part of Table3 , where Spec#i and Spec#is are the EMPA specifications for mechanism #i without or with the spike detection mechanism, respectively. Note that the state spaces are very compact because the semantic models are symbolic, as we have seen in Sect.... In PAGE 24: ... As an example, in the case of randomly generated traffic, the termination condi- tion in the auxiliary specification concerning mechanism #1, is as follows: elapse tick 60000 10 The simulation run stops after action elapse tick, representing the passage of time, has been executed 60000 times (one time unit is one ms); the experiment consists of 10 simulation runs. As far as the trace driven simulation is concerned, since the trace files are com- posed of 15000 transmission delays, which corresponds to a period of 5 min assuming a transmission rate of one packet every 20 ms, it has to be specified that the trace driven simulation terminates after 15000 executions of action prepare packet: prepare packet 15000 1 The duration of the experiments is reported in the lower part of Table3 . Exper- iments have been conducted on a personal computer with a 200 MHz Pentium II processor, 64 MB RAM, and Linux operating system.... ..."