### Table 1. Basic notions from time scales calculus.

Cited by 1

### Table 1 below recalls in brief the basic notions around taxonomies, faceted tax- onomies and materialized faceted taxonomies (for more please refer to [13]).

2004

"... In PAGE 4: ... Table1 . Notations CTCA was proposed for defining the meaningful compound terms over a faceted taxonomy in a flexible and efficient manner.... ..."

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### Table 1: Basic conditions on I 16Remark that the notion of constraint satisfaction refers to an arbitrary set of literals I, be it contradictory or otherwise.

1995

Cited by 88

### Table 1: Basic conditions on I 16Remark that the notion of constraint satisfaction refers to an arbitrary set of literals I, be it contradictory or otherwise.

1995

Cited by 88

### Table 1 presents the rules of a generic free variable semantic tableau calculus. Starting from the initial tableau for a given closed formula of L+ , such rules allow to prolongate tableau branches in the standard way, as described for instance in [9]. We also refer the reader to [9] for all related basic notions, such as those of closed branch, closed tableau, satis able tableau, etc. The -, -, and -rules are the standard ones, so they deserve no further explanation. Concerning the -rule, we will characterize its proviso in such a way as to enforce soundness and encompass the -rule variants present in literature that de ne Skolem terms in a syntactical way.

"... In PAGE 32: ...47 10.81 Table1 . Complexity of the Case Studies... In PAGE 33: ... The last two examples contain mutually recursive operators. Table1 illustrates the complexity of the examples. It contains the number of lemmas (constant for all heuristics), and, for our novel heuristics with mandatory and obligatory literals, the number of manual interactions (manually applied inference rules + manually chosen induction order), the number of automatically applied inference rules (including the later deleted ones), the number of deleted inference rules due to a failed relief test and the runtime in seconds measured by a CMU Common Lisp system on a machine with a 1330 MHz AMD processor and 512 MB RAM.... In PAGE 60: ... - The term f( !S ) in the -rule is computed by a given function S (T ;m;n), where T is the current tableau, m is the index of the branch to be expanded, and n is the position of the -formula to be instantiated. Table1 . Tableau rules for a generic calculus.... In PAGE 61: ... We indicate with sko = (P; F [ sko) the augmented signature and with L sko the language over sko. The Skolem term f( !S ) in the -rule in Table1 consists of a function symbol f 2 sko of arity n 0 and an n-tuple !S of terms in L+ sko, whose variables belong to Var+. In general, the constraints that f( !S ) must satisfy may depend on the current tableau T , on the branch which is about to be expanded, and on the -formula on that is about to be instantiated.... In PAGE 62: ... Then we put: S (T ; m; n) =Def f( !H ) : (1) Section 4 illustrates how to apply our generic -rule to show the correctness of some -rules in literature. But before doing that, we will show that the tableau calculus described in Table1 is sound, provided that its associated Skolem terms construction rule satis es the above conditions C1-C8. It will be enough to show that tableau satis ability is preserved by the ex- pansion rules in Table 1 and substitution applications.... In PAGE 62: ... But before doing that, we will show that the tableau calculus described in Table 1 is sound, provided that its associated Skolem terms construction rule satis es the above conditions C1-C8. It will be enough to show that tableau satis ability is preserved by the ex- pansion rules in Table1 and substitution applications. To this purpose, it is convenient to stratify the language L+ sko, and then show how we can expand a given structure for L+ to a canonical structure for L+ sko.... In PAGE 64: ...Soundness of the generic -rule We are now ready to show that the tableau calculus in Table1 is sound, provided that the Skolem terms construction rule is de ned as in (1) and conditions C1- C8 hold. This will plainly be entailed by the following theorem.... In PAGE 64: ...t. Let A be an assignment in Msko. By the inductive hypothesis there exists a branch on T such that (Msko; A) j= . Let T 0 be the tableau resulting from an application of one of the expansion rules in Table1 or from an application of a substitution to T . If T 0 = T , then it can be shown that Msko satis es T 0 (cf.... In PAGE 84: ... f:(memb(C, A)), :(memb(C, B)), memb(C, intersect(A, B))g. Table1 . Timing and clauses of OSHL, Otter, Vampire, E-SETHEO and DCTP on set of theorems [-1-left for various values of n.... ..."

### Table 1. Basic stereological formulas.

"... In PAGE 2: ...1 Stereology Measurements follow stereological formulas, which connect the measurements obtained using different probes with the sought properties. Table1 contains basic stereological formulas using standard notion of stereology (see, e.g.... ..."

### Table 1: Lower and upper bounds for routing under various assumptions on the available knowledge, and for various values of k. left side of every entry the lower bound is given, on the right side the number of steps taken by an algorithm. In all results a factor n is omited, and lower order terms are neglected. In Table 1 the three main columns correspond to fully-local-knowledge routing, local-knowledge routing and global-knowledge routing, respectively. In Table 2 we distinguish sorting without making copies and sorting in which it is allowed to make copies. Contents. The remainder of this paper is organized as follows: we start with general notions and basic 3

1993

"... In PAGE 3: ...Table1... ..."

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### Table 1. Dynamic basic block size.

2000

"... In PAGE 1: ... Basic blocks are the most familiar notion of atomic regions. The data in Table1 shows that dynamic basic block size for a majority of the SPEC2000 integer benchmarks is below 9 instructions. The benchmarks were compiled using the Compaq Alpha compiler with a high level (-O4) of opti- mization including function in-lining and loop unrolling.... ..."

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### Table 1. Dynamic basic block size.

2000

"... In PAGE 1: ... Basic blocks are the most familiar notion of atomic regions. The data in Table1 shows that dynamic basic block size for a majority of the SPEC2000 integer benchmarks is below 9 instructions. The benchmarks were compiled using the Compaq Alpha compiler with a high level (-O4) of opti- mization including function in-lining and loop unrolling.... ..."

Cited by 26

### Table 1. Dynamic basic block size.

"... In PAGE 1: ... Basic blocks are the most familiar notion of atomic regions. The data in Table1 shows that dynamic basic block size for a majority of the SPEC2000 integer benchmarks is below 9 instructions. The benchmarks were compiled using the Compaq Alpha compiler with a high level (-O4) of opti- mization including function in-lining and loop unrolling.... ..."