Queries on TreeStructured Data: Logical Languages

1
Queries on Tree-Structured Data(Logical)
Languages Complexity

• Christoph Koch
• Universität des Saarlandes
• Saarbrücken, Germany

2
Query Languages for Trees

• Languages that select (tuples of) nodes in
  unranked ordered node-labeled trees
• FO, MSO, conjunctive queries, (monadic) datalog,
  XPath
• Queries on trees with data values
• XPath with data values
• Tree transformation languages
• XSLT, tree transducers
• XQuery (functional programming language on trees)

3
XPath Examples
/descendanta/childb
/descendanta/childb descendantc and
not(following-siblingd)
c
a
/descendanta/childb following-siblingd
a
c
b
d
b
c
a
a
b
c
a
a
c
b
d
b
b
d
b
b
c
b
c
c
c
4
Queries on Trees
5
Complexity of XPath
XPath The Language
6
XPath Examples
/descendantbposition() 2
c
a
/descendant position() mod 2 1
a
/descendantb position() last()
c
1
b
d
b
c
a
1
3
2
a
b
c
a
2
3
a
c
4
8
b
d
b
b
d
b
7
b
c
(document order)
5
b
c
9
c
6
c
7
XPath Examples
/descendantc/ancestor position() 2
c
/descendant id(concat(text(),cd))/chil
dc
a
a
c
2
2
a
b
d
b
1
a
b
c
1
b
d
b
c
ltb idabcdgt
ltcgtablt/cgt
c
id(abcd)
8
Xpath and Fragments

• Core XPath Logically clean core of XPath
• All axes of Xpath (incl. ancestor, following, )
• Node tests label checks axislabel
• Conditions (predicates) existence of paths,
  boolean expressions (and, or, not).
• Wadler fragment Core Xpathposition
  arithmetics.
• Full Xpath id/idref, string manipulations,

9
Core XPath Example
/descendanta/childb
c
a
a
b
d
b
b
c
c
10
Complexity of XPath
XPath State-of- the-Art
11
XT vs. XALAN (Java implementations, UNIX)
Appending parenta/b to the query doubles its
running time (for branching factor 2 of document)
!!!
Queries a/b/parenta/b//parenta/b
Document (fixed) ltagt ltb/gt ltb/gt lt/agt
12
Observation

• THE SYSTEMS REQUIRE TIME EXPONENTIAL IN THE SIZE
  OF THE XPATH QUERY!!!
• Interpretation follows.
• (However, as we will show, it can be done in
  polynomial time (for full Xpath !!!))

13
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
14
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
15
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
a
a
b
b
b
b
16
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
a
a
b
b
b
b
17
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
a
a
b
b
b
b
a
a
a
a
b
b
b
b
b
b
b
b
18
Xpath Query /a/b/parenta/b/parenta/b
Document
ltagt ltb/gt ltb/gt lt/agt
a
a
b
b
b
b
a
a
b
b
b
b
a
a
a
a
b
b
b
b
b
b
b
b
Tree of nodes visited is of size
!!!
19
IE6 (native code, Windows)
MSXML4 constant-factor improvement as compared
to MSXML3/IE6.
Queries (below size 3) a/bcount(parenta/bcoun
t(parenta/b count(parenta/b) gt 1) gt 1) gt 1
20
Efficient Xpath Processing

• Theorem Full Xpath is in polynomial time w.r.t.
  combined complexity (both query and data assumed
  variable).
• Dynamic programming algorithm.
• Gottlob, K., Pichler, Efficient Algorithms for
  Processing XPath Queries, Proc. VLDB 2002

21
Documents and Contexts
Example document
ltagt ltb/gt ltb/gt ltb/gt ltb/gt lt/agt
Contexts
node
position in node set
size of node set
Context-value Tables (CVT)

• Four types of values in XPath (nset, num, str,
  bool)
• Defined for each Xpath expression .
• The CVT of is a relation

22
Query Trees
Query descendantb/following-siblingposition
() ! last()
Query Tree
Evaluation Idea Traverse query tree bottom-up
and compute CVT of each subexpression using the
CVTs of the constituent subexpressions.
23
Best Algorithms for XPath

• Bottom-up algorithm time,
  space (memory consumption).
• Improved top-down algorithm
  time, space.
• Outside-in strategy minimization of contexts.
• Prototype implementation exists
  www.xmltaskforce.com
• Core Xpath position arithmetics (Wadler
  Fragment) time , space
  .
• Core Xpath time .
• n... size of data, q... size of query.
• Gottlob, K., Pichler, VLDB 2002 ICDE 2003

24
Core Xpath with data values
25
Core Xpath with data values
26
Core Xpath with data values
27
Combined Complexity
Core Xpath is P-hard!
P-hard not parallelizable (conj.)
In NC massively parallelizable
Xpath without negation, , concatenation,
multiplication is in LOGCFL!
Gottlob, K., Pichler, PODS 2003
28
Combined Complexity

• LOGCFL is in NC2 highly parallelizable
  solvable inO(log2 n) time with polynomially
  many processors.
• Core Xpath can be processed in time O(n).
  However, parallel algorithms for LOGCFL-hard
  problems do not run in linear time on a fixed
  number of processors!
• gtnot realistic

Gottlob, K., Pichler, PODS 2003
29
Combined Complexity
P-hardness highly unlikely that there are
algorithms for Xpath which do not take at least
polynomial memory gt Refutation of automata-based
techniques.
Gottlob, K., Pichler, PODS 2003
30
Combined Complexity

• Path queries with downward axes in LOGSPACE
  Current SDI algorithms (Xfilter, XTrie) are
  highly suboptimal!
• However, naive algorithm takes time O(n3) and
  will certainly not become linear!

Gottlob, K., Pichler, PODS 2003
31
Data and Query Complexity

• XPath is in L (data complexity).
• Also Segoufin, PODS 2003
• PF is L-hard under NC1-reductions (data
  complexity).
• XPath without multiplication, concatenation is in
  L w.r.t. query complexity.

XPath
PF
L-complete (NC1-red.)
Data complexity
Gottlob, K., Pichler, PODS 2003
32
Conjunctive Queries over Trees
Conjunctive Queries
33
Conjunctive Queries

• FO queries w/o disjunction, negation, universal
  quantification.
• Importance in database theory
• Great success story, very nice properties
• (e.g., containment is decidable).
• Well-studied (complexity, optimization, ...)

34
Data Model Tree Signatures

• Any unary relations (node labels)
• Binary relations Child, Child, Child,
  Nextsibling, Nextsibling, Nextsibling,
  Following
• Subsumes XPath axes
• Descendant Child
• Descendant-or-self Child
• Following-sibling Nextsibling.
• Reverse axes (e.g. Parent) redundant in CQs.

35
Conjunctive Query Example
36
Applications

• XML Queries XPath, XQuery
• Data Extraction and Integration
• Monadic datalog rules Lixto Baumgartner,
  Gottlob, Flesca 2001
• Internal Query language of MARS XQuery Rewriter
  Deutsch, Tannen 2003.
• Computational Linguistics
• Queries on Parse Trees lpath Bird et al., 2005
• Dominance Constraints Marcus, Hindle, Fleck,
  1983 incomplete specification of parse trees.
• Higher-order Unification Context Matching Problem

37
Cyclic Query Example (from Computational
Linguistics)
38
Complexity Results
(combined complexity)
(Partition of set of axes!)
39
Conjunctive Queries over Trees
Ptime Results
40
Hemichordal Relations
41
Special Case R µ
42
Examples of HC Relations

• Child is ltbflr-hemichordal

1
2
3
4
6
7
8
9
5
10
11
12
Never true!
43
Examples of HC Relations
44
Examples of non-HC Relations
45
PTime CQ Eval on HC Structures
46
PTime CQ Eval on HC Structures
47
Properties of HC-Relations
48
Properties of HC-Relations
49
Properties of HC-Relations

• For HC structures Global consistency
  arc-consistency !

50
Complexity Results
(combined complexity)
(Partition of set of axes!)
51
Conjunctive Queries over Trees
Expressive Power CQ APQ
52
CQ µ APQ

• Acyclic positive query (APQ) union of acyclic
  conjunctive queries.
• Each APQ can be rewritten (in linear time) into
  Xpath.
• Theorem Gottlob, K., Schulz, PODS 2004.Each CQ
  can be expressed as an APQ.

53
Conjunctive Queries over Trees
Exponential Blowup CQ gt APQ
54
Succinctnes of Conj. Queries
Dn
Theorem Gottlob, K., Schulz, PODS 2004. There
is no polynomial mapping of the Dn to equivalent
APQs.
55
Summary Conjunctive Queries

• Complete characterization of tractability
  frontier (P/NP) of CQs over trees (in terms of
  axis relations).
• Machinery for proving Ptime-Results
• lt-hemichordality property
• Expressive power of CQs over trees
• Each CQ is equivalent to an acyclic positive
  query (APQ)
• Blow-up from CQs to APQs is exponential and
  necessarily so.

56
Queries on Trees
Monadic Datalog
57
Relevance Web Wrapping

• Extract structured data from unstructured Web
  pages.
• Numerous applications e.g., extract current list
  of book prices from amazon.com Web site.
• Commercial wrapping system Lixto Baumgartner,
  Flesca, Gottlob, VLDB 2001 uses monadic datalog
  as kernel language.

58
Scope of Wrapping
root

• Assign new labels to some nodes of the tree.
• Drop others as irrelevant.
• No need for arbitrary data transformations.
• Labeling unary information extraction
  functions over domain of nodes.
• Navigate recursively in trees.

59
Monadic Datalog on Trees

• Unary IDB predicates.
• Over unranked ordered trees Signature ?U
  predicates firstchild, lastchild, nextsibling,
  labell, root, leaf.
• Shortcuts, e.g. subelem ancestor accessible
  via a given path, rewrite using firstchild and
  nextsibling.

lastchild
firstchild
nextsibling
nextsibling
firstchild
lastchild
nextsibling
nextsibling
60
How complex is Monadic Datalog?

• Previously known facts on full Datalog over
  Graphs
• Data complexity of datalog P-complete (impl. in
  Vardi 88)
• Combined complexity EXPTIME-complete (impl. in
  Vardi 88)
• Comb. compl. of sirups EXPTIME-cplt.
  (Gottlob,Papadimitriou 99)
• Comb. compl. of monadic datalog NP-complete
  (folklore?)

Theorem Gottlob K. 2002
Monadic Datalog over ?U has combined complexity
O(dataquery)
Query Complexity P-complete and linear-time.
61
Proof idea
1.) Transform datalog program input tree in
linear time into a ground
propositional logic program

• Exploit functional dependencies
• nextsibling(X,Y) each connected rule
  has only a
• linear number of ground instances.
• Decouple independent atoms of rule bodies

p(X) ?q(X) r(Y) nextsibling(X,Z) s(Z).
p(X) ?q(X) r nextsibling(X,Z) s(Z). r
? r(Y).
2.) Execute ground program in linear time by
using well-known algorithms
DowlingGallier Minoux
62
Expressiveness Result

• Theorem. Given a unary query Q over ltfirstchild,
  lastchild, nextsibling, labelagt,
• Q is definable in MSO iff Q is definable as a
  monadic datalog program.

63
Monadic Datalog and TMNF

• Example
• D0(x) - Root(x).
• D1(x) - D0(x0), First-Child(x0, x).
• D0(x) - D1(x0), First-Child(x0, x).
• D0(x) - D0(x0), Next-Sibling(x0, x).
• D1(x) - D1(x0), Next-Sibling(x0, x).
• TMNF (tree-marking normal form) - restricted
  syntax
• P(x) - P1(x), P2(x). P(x) - P0(x0), R(x0, x).
  P(x) - P0(x0), R(x, x0).

• D0 nodes at even depth in tree.
• D1 nodes at odd depth in tree.

64
Summary Monadic Datalog

• Gottlob K., JACM 2004
• M.dl.o.t. can be evaluated in time O(Program
  Data).
• M.dl.o.t. captures the unary MSO queries over
  trees.
• Gottlob K., LICS 2002, Frick, Grohe, K.,
  LICS 2003
• Linear-time reduction to TMNF.
• Linear-time reduction also from Core Xpath to
  TMNF (negation!)
• Grohe and Schweikardt, CSL 2003
• But M.dl. much less succinct than MSO, monadic
  fixpoint logic. (nonelementarily less succinct
  unless FPTW1)
• However, no problems observed in practice yet.
• Wrapping Killer Application for Datalog?
• Also known Containment for monadic datalog (on
  arbitrary finite structures) is decidable!
  Cosmadakis, Gaifman, Kannellakis, Vardi, 1988

65
Monadic Datalog with Xpath Axes

• It would be desirable to support Xpath axes
  (child, descendant, ...) in monadic datalog
  queries.
• But how difficult is it to evaluate such queries?
• Proposition. Monadic datalog is in NP w.r.t.
  combined complexity (arbitrary finite
  structures).
• Observation Monadic datalog over some signature
  ? is in P (resp., NP-complete) iff the
  conjunctive queries over ? are.

66
Queries on Trees
Summary
67
Expressiveness
68
Complexity
69
End
70
State of the Art XPath

• XT, XALAN, IE, SAXON exponential time w.r.t.
  size of queries.
• XQuery algebra motivates Exptime implementation.
• Queries tend to be small, but
• Not small enough in practice (some queries with m
  location steps require time ).
• Xpath as a tree pattern matching language
  Queries are not that short.

71
Complexity of XPath
P-Time Bottom-up XPath Evaluation
72
PTime Evaluation Example
Document Tree
Query Tree
(In fact, this is only a relevant subset of the
full tables.)
73
PTime Evaluation Example
Document Tree
Query Tree
74
PTime Evaluation Example
Document Tree
Query Tree
75
PTime Evaluation Example
Document Tree
Query Tree
76
PTime Evaluation Example
Document Tree
Query Tree
77
PTime Evaluation Example
Document Tree
Query Tree
78
PTime Evaluation Example
Document Tree
Query Tree
Query result b2, b3
79
Context-Value Table Principle
if
CVT for each operation can
be computed in polynomial time given the CVTs for
sub-expressions
then
CVT of overall query can be computed (bottom-up)
in polynomial time.
80
Queries on Trees
Proof PF is NL-complete
81
(No Transcript)
82
Where can we go from v2 in one step?
83
Where can we go from v2 in one step?
84
Where can we go from v2 in one step?
85
Where can we go from v2 in one step?
86
Where can we go from v2 in one step?
87
Where can we go from v2 in one step?
88
Where can we go from v2 in one step?

• Reachable from v2 in one step v1, v3!

89
PF is NL-hard.

• Reachability in precisely m steps
• Add loop at each node to graph
• Set m E.

90
Conjunctive Queries over Trees
various
91
Conjunctive Queries in MARS

• Example from DeutschTannen, VLDB 2003
• XQueryltresultgt for a in distinct(//author/t
  ext()) return ltitemgt ltwritergt a
  lt/writergt for b in //book, a1 in
  b/author/text(), t in b/title
  where aa1 return t
  lt/itemgtlt/resultgt
• Conjunctive QueryQ(a,b,a1,t) -
  //author/text()(a), //book(b),
  ./author/text()(b,a1), ./title(b,t),
  aa1.

92
Contributions Conjunctive Queries

• Complete characterization of tractability
  frontier (P/NP) of CQs over trees (in terms of
  axis relations).
• Machinery for proving Ptime-Results
• lt-hemichordality property
• Expressive power of CQs over trees
• Each CQ is equivalent to an acyclic positive
  query (APQ)
• Blow-up from CQs to APQs is exponential and
  necessarily so.

93
Hemichordal Relations
94
Hemichordata

• half the propertiesof chordata.
• Hemichordality sw.reminiscent of chordality.

95
Conjunctive Queries over Trees
NP-Hardness Results
96
NP-Hardness Proofs

• All by reduction from 1-in-3 3SAT
• In each clause, precisely one variable must be
  true.
• No negative literals.
• Problem NP-Complete.

97
Clause Gadget, ChildFollowing
98
NP-Hardness, ChildFollowing
...
Clause 1 (P1, Q1, R1)
Clause 2 (P2, Q2, R2)
Clause n (Pn, Qn, Rn)
Following...
A
B
C
B
D
E
Clause i (A,B,C)
Clause j (B,D,E)
99
Clause Gadget, NextsiblingFollowing
100
Clause Gadget, ChildChild
101
Conjunctive Queries over Trees
Expressive Power CQ µ APQ
102
CQ µ APQ

• Theorem Gottlob, K., Schulz, PODS 2004. Each CQ
  can be expressed as an APQ.
• Proof Idea Bottom-up rewriting of query
• polynomially many steps
• At most 2 (3) alternatives in each step.
• In each step, move a v up in the query graph.
• Takes exponential time, query may be of exp. size.

103
CQ µ APQ
104
CQ µ APQ
105
CQ µ APQ
106
CQ µ APQ
107
CQ µ APQ
108
CQ µ APQ
109
Conjunctive Queries over Trees
Exponential Blowup CQ gt APQ
110
n-Diamond Query, Models
Dn
111
Step 1
112
Step 2
113
Step 3
114
Step 4

• There are only polynomially many paths in Qi, but
  there are exponentially many in Dn.
• gt There is (much more than) one path of Dn which
  is not in Qi.
• We construct a model M from Qi and Dn s.t. Qi is
  true on M but Dn is false on M (because that path
  is not satisfied.)

115
Step 4
116
Step 4
Bottommost X2
M
Topmost X1
117
Step 4
Bottommost X2
M satisfies (b) but not (a) !!!
M
Topmost X1
118
Queries on Trees
Monadic Datalog
119
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
120
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
121
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
122
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
123
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
124
HTML Example
lt!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01
Transitional//EN"gt lthtmlgt ltbodygt lth1gtPeople _at_
DBAIlt/h1gt lttable border"1" cellpadding"3"
cellspacing"1"gt lttrgt lttdgtGeorg Gottloblt/tdgt
lttdgtgottlob_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18420lt/tdgt lt/trgt lttrgt
lttdgtChristoph Kochlt/tdgt
lttdgtkoch_at_dbai.tuwien.ac.atlt/tdgt
lttdgt18449lt/tdgt lt/trgt lt/tablegt lt/bodygt lt/htmlgt
People _at_ DBAI
125
Monadic Datalog as a Wrapping Language
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).
126
Monadic Datalog as a Wrapping Language
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).

• Rules simple -gt visual specification
• Select root as start pattern.
• Define destination pattern entry by selecting a
  document region.
• Selection is interpreted relative to start
  pattern.
• Add further constraints.

127
Monadic Datalog as a Wrapping Language
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).
128
Monadic Datalog as a Wrapping Language
root
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).
html
body
table
tr
tr
td
td
td
td
td
td
129
Monadic Datalog as a Wrapping Language
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).
130
Monadic Datalog as a Wrapping Language
entry(X) - root(R), subelemhtml.body.table.tr(R
, X). name(X) - entry(E), firstchild(E, X),
labeltd(X). email(X) - name(N),
nextsibling(N, X), labeltd(X). phone(X) -
email(M), nextsibling(M, X), labeltd(X).
lt?xml version"1.0"?gt ltpeopledbgt ltentrygt
ltnamegtGeorg Gottloblt/namegt
ltemailgtgottlob_at_dbai.tuwien.ac.atlt/emailgt
ltphonegt18420lt/phonegt lt/entrygt ltentrygt
ltnamegtChristoph Kochlt/namegt
ltemailgtkoch_at_dbai.tuwien.ac.atlt/emailgt
ltphonegt18449lt/phonegt lt/entrygt lt/peopledbgt
131
Queries on Trees
XQuery
132
Expressiveness 2