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Arity hierarchy for temporal logics

2008
*
Theoretical Computer Science
*

which uses modalities of

doi:10.1016/j.tcs.2008.06.006
fatcat:4qy6yzt6orb3tbamywitzlian4
*arity*less than n. ... The main result states that in contrast to Kamp's Theorem, for every n there is a modality of*arity*n definable by a monadic logic formula, which is not equivalent over trees to any temporal logic formula ...*Arity**Hierarchy*over ω: Is TLAR r less expressive than TLAR r+1 over the class of ω-chains? ...##
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The Arity Hierarchy in the Polyadic μ-Calculus

2015
*
Electronic Proceedings in Theoretical Computer Science
*

In this paper we show a

doi:10.4204/eptcs.191.10
fatcat:oi5irp6ef5fd3getjjvgiiit2m
*hierarchy*result with respect to expressive power inside the polyadic mu-calculus: for every level of fixpoint alternation, greater*arity*of relations gives rise to higher expressive ... Consequently, we obtain an*arity**hierarchy*relative to the alternation*hierarchy*. ... The*Arity**Hierarchy*The Principle Construction The aim of this section is to show that L 1 µ , L 2 µ , . . . forms a strict*hierarchy*with respect to expressive power. ...##
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A double arity hierarchy theorem for transitive closure logic

1996
*
Archive for Mathematical Logic
*

As a consequence, the

doi:10.1007/bf01268616
fatcat:jzilabwfofcytdi33oab7uvm5i
*arity**hierarchies*of all the familiar forms of fixed point logic are strict simultaneously with respect to the*arity*of the induction predicates and the*arity*of generalized quantifiers ... The*arity**hierarchies*of the corresponding quantifiers are strict by our theorem. • The*arity**hierarchy*of the Hamiltonian path quantifier Q HP is strict. ... Consequently, in this case we say that the*arity**hierarchy*of Q C is strong. Note that we actually proved that the*arity**hierarchies*of Q T C and Q DT C * are strong. ...##
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SEPARATING AUXILIARY ARITY HIERARCHY OF FIRST-ORDER INCREMENTAL EVALUATION SYSTEMS USING (3K+1)-ary INPUT RELATIONS

2000
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International Journal of Foundations of Computer Science
*

In fact, there is a query, over input relations of

doi:10.1142/s0129054100000302
fatcat:oruvnxpdmnawvhbxdcdeyypqlq
*arity*3k + 1, in FOIES k ? FOIES k?1 . ... However, that separation was achieved using queries having input relations of*arity*at least 6k. ...##
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Page 8497 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
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Mathematical Reviews
*

We show that the

*arity**hierarchy*in this case is also strict. ... The positions of queries in the two*arity*-based*hierarchies*can differ; we give the positions in this*hierarchy*of the queries considered for the other*arity**hierarchy*.” © 1998 Academic Press {For the ...##
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Arity and alternation in second-order logic

1996
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Annals of Pure and Applied Logic
*

We show that this imposes a proper

doi:10.1016/0168-0072(95)00013-5
fatcat:b3iwj3l4sze6plwzp7jw2nmvsu
*hierarchy*on second-order logic, i.e. for every k, n there are problems not definable in AA(k, n) but definable in AA(k + cl, n + d,) for some cl, d,. ... Let SAA@, n)(AA(k, n)) be the set of second-order formulas such that the*arity*of the relation variables is bounded by k and the number of alternations of (both first-order and) second-order quantification ... We define now*hierarchies*AAZ(k, n) , AAII(k, n) , AA(k, n) , the strict AA-*Hierarchy*(alternation-*arity**hierarchy*) and SAAC(k, n) , SAAII(k, n) , SAA(k, n) , the second-order AA-*Hierarchy*(alternation-urity ...##
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Incremental recomputation of recursive queries with nested sets and aggregate functions
[chapter]

1998
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Lecture Notes in Computer Science
*

This is again in sharp contrast to maintenance in relational calculus, which admits a strict

doi:10.1007/3-540-64823-2_13
fatcat:h55jvl63t5c5xftwxdxcscckae
*arity*-based*hierarchy*. ... We also show that one does not need auxiliary relations of*arity*more than 2. ... Since the*arity**hierarchy*collapses in the presence of simple extensions such as aggregate functions as in IES(SQL) k , we feel that a*hierarchy*based on*arities*is not robust and not natural for incremental ...##
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About the relation between spatial subdivisions and object hierarchies used in ray tracing

2007
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Proceedings of the 23rd Spring Conference on Computer Graphics - SCCG '07
*

In this paper we study the relation between object

doi:10.1145/2614348.2614355
dblp:conf/sccg/Havran07
fatcat:msqa5an4zbg23owsc56z6p3kku
*hierarchies*(such as bounding volume*hierarchies*) and spatial subdivisions (such as kd-trees and octrees) in the context of ray tracing for static scenes ... Second, we show how kd-trees can be emulated via bounding volume*hierarchies*. More importantly we show how bounding volume*hierarchies*can be emulated via kd-trees in six-dimensional space. ... Relation between Object*Hierarchies*and Spatial Subdivisions In Section 3 we have discussed the properties of spatial subdivisions in dependence on their*arity*. ...##
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Towards Design Formalization to Support Reuse in ECAD Frameworks
[chapter]

1995
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Electronic Design Automation Frameworks
*

For instance, a feature '

doi:10.1007/978-0-387-34880-3_23
fatcat:5r6aubgapbgkzdlzlnk6ruitsa
*Arity*is 4' is a specialization of a feature '*Arity*is Even', i.e. '*Arity*is 4' < '*Arity*is Even'. ... Example 1 (design*hierarchy*) In figure 4 , the design*hierarchy*is illustrated by an example using the PLAYOUT design system [Zim89] . ...##
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Horn tables-an efficient tool for handling incomplete information in databases

1989
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Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '89
*

The representation

doi:10.1145/73721.73728
dblp:conf/pods/Grahne89
fatcat:l4xv6tkynbgg3mnzvuldyffrji
*hierarchy*. THE COMPLEXITY OF QUERY EVALUATION A query q of*arity*(ai, . . . . a,,) + (bt, . . . . b,,,) is a mapping from instances to instances of the appropriate*arities*. ... An instance I of*arity*(n) satisjies a dependency c of*arity*(n) if I is a model (in the sence of mathematical logic) of the sentence. ...##
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Multi-Method Dispatch Using Multiple Row Displacement
[chapter]

1999
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Lecture Notes in Computer Science
*

The first example uses the type

doi:10.1007/3-540-48743-3_14
fatcat:iqfkazfo45embkvdlknthhtrhe
*hierarchy*and 2-*arity*method definitions from Figure 5 (a). ... Figure 2 presents a sample inheritance*hierarchy*H and its induced 2-*arity*product-type graph, H 2 . ...##
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Modeling hierarchy using symbolic regression

2013
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2013 IEEE Congress on Evolutionary Computation
*

Here we present a symbolic regression method that detects and captures hidden

doi:10.1109/cec.2013.6557932
dblp:conf/cec/IckeB13a
fatcat:qk5l3ka4mndxddjeyowhbt5kju
*hierarchy*in a given system. ... Accordingly, the h1 and h2 algorithms start to lose their advantage in faithfully modeling the*hierarchy*as the*arity*increases. ... 5000 randomly generated stimuli creating a 5000x((*arity*layers − 1)/(*arity*− 1)) dataset. ...##
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Arity Bounds in First-Order Incremental Evaluation and Definition of Polynomial Time Database Queries

1998
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Journal of computer and system sciences (Print)
*

The positions of queries in the two

doi:10.1006/jcss.1998.1565
fatcat:52nhopb6wfajnhtcl4zcfws6ci
*arity*-based*hierarchies*can differ; we give the positions in this*hierarchy*of the queries considered for the other*arity**hierarchy*. ] ... We show that the*arity**hierarchy*in this case is also strict. ... It should be pointed out that for the small*arities*the*hierarchies*are separated using graph queries, whereas for large*arities*the*hierarchies*are separated using queries over relations with large*arities*...##
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Hierarchies in inclusion logic with lax semantics
[article]

2014
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arXiv
*
pre-print

*Arity*

*hierarchy*is shown to be strict by relating the question to the study of

*arity*

*hierarchies*in fixed point logics. ... In case of universal quantifiers, the corresponding

*hierarchy*collapses at the first level. ... ⊓ ⊔ Strictness of the

*Arity*

*Hierarchy*In this section we will show that the following strict

*arity*

*hierarchy*holds (already in finite models). Theorem 6. ...

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Polish Notation

2015
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Formalized Mathematics
*

We present some mathematical folklore about representing formulas in "Polish notation", that is, with operators of fixed

doi:10.1515/forma-2015-0014
fatcat:m25fzpr3mjcshd4o7tnm56jiqy
*arity*prepended to their arguments. ... The Polish*arity*from list B yielding a Polish*arity*-function of T is defined by the term (Def. 30) the*arity*from list B. ... The Polish*arity*ϕ yielding a natural number is defined by the term (Def. 35) α(Polish-WFF-head ϕ). Let us consider n. Let ϕ be an element of the Polish-expression*hierarchy*(T , α, n). ...
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