Glushkov Automata - sbes - 2007

22nd Brazilian Symposium on Database 

SBBD 2007 

Assisting XML Schema Evolution that 

Preserves Validity 

Béatrice Bouchou 

bouchou@univ-tours.fr 

Laboratoire d'Informatique (LI) 

Denio Duarte 

denio@unochapeco.edu.br 

Centro Tecnológico (Cetec) 

bouchou@univ-tours.fr denio@unochapeco.edu.br

Agenda 

● Motivation 

● Theoretical Background 

● Approach 

● Final Considerations 


Motivation 

Document 

XML 


Motivation 

Documents are valid 

Schema 

Document 

XML 


Motivation 

Schema 

Document 

XML 

bouchou@univ-tours.fr denio@unochapeco.edu.br 

Constraint: 

Publications are grouped by: 

journal papers organized by 

subject and year of publication

Motivation 

Schema 

Document 

XML 


Publication : Subject (Year Journal + ) *

Motivation 

Labs decide to consider 

conference papers 

as publications Publication : Subject (Year Journal + ) * 

Schema 

Document 

XML 


Motivation 

Labs decide to consider 

conference papers 

as publications Publication : Subject (Year Journal + ) * 

Schema 

Document 

XML 


The schema must be updated

Motivation 

Publication : Subject (Year Journal + Conference) * 

Schema' 

Document 

XML 


Mandatory

Motivation 

Publication : Subject (Year Journal + Conference?) * 

Schema' 

Document 

XML 


Only one conference paper 

by year?

Motivation 

Publication : Subject (Year Journal + Conference + ) * 

Schema' 

Document 

XML 


Mandatory

Motivation 

Publication : Subject (Year Journal + Conference * ) * 

Schema' 

Document 

XML 


It's OK!

Motivation 


Schema' 

Document 

XML 


One of the laboratory sends 

several entries for conferences 

and journals.

Motivation 


Schema' 

Document 

XML 


The administrator must organize 

them for insertion since journals 

should appear before conference

Motivation 

Publication : Subject (Year (Journal|Conference) + ) * 

Schema' 

Document 

XML 


Motivation 

✔ It is difficult to evolve XML schemas 

mainly if the administrator is not a 

computer science expert. 

Schema' 

Document 

XML 


Motivation 

● The demand for tools designed for administrators 

not belonging to the computer science community 

● The cost (time and money) of revalidation process 

● Distributed XML databases following the same 

schema 


Theoretical Background 


Theoretical Background 

● Theoretical notions used in this work 

– Regular expressions (RE) to define the allowed subelements 

of an element. 

– Finite state automata (FSA) to verify whether or not 

the sub-elements respect the constraints imposed by 

the element. 

– Transformation of RE to FSA 

● Glushkov's Algorithm ⇒ 

Glushkov automaton 


Glushkov Automata 

● Given a RE, a Glushkov automaton is built as 

follows: 

– All symbols in RE are subscripted by their positions. 

+ * 

● Subject (Year Journal+)* Subject (Year Journal ) 

1 2 3 

– We add an end mark (#) to the RE: 

+ * 

● Subject (Year Journal ) #4 

1 2 3 

– Symbols and positions become transitions in the FSA 

– Each state represents a symbol (except the initial 

state) 

⇒ 



+ * 


1 2 3 

Year 

Subject Year 

0 1 2 3 

Journal 

� � 

Journal 

0 1 2 3 4 


# 

# 

4 

Glushkov Graph (homogeneous)


+ * 


1 2 3 

0 1 2 3 4 

Cycles are called orbits 



+ * 


1 2 3 

0 1 2 3 4 

The orbits represent the starred subexpression of 

the regular expression 



+ * 


1 2 3 

0 1 2 3 4 

The orbits represent the starred subexpression of 

the regular expression 



+ * 


1 2 3 

0 1 2 3 4 

● The hierarchy of orbits H is formed by the orbits in the graph 

and the set of all nodes (respecting the set inclusion property): 

● H={{3},{2,3},{0,1,2,3,4}} 



● The notion of orbit gives us another notion: 

– Context: the set of symbols that appear in an orbit. 

– A general context contains the symbols not 

belonging to any context. 

– Contexts are disjoint sets. 

● In our example: 

– Context for Journal: {Journal} corresponds to the 

orbit {3} 

– Context for Year: {Year} corresponds to the orbit {2,3} 

– The general one: {Subject} 



● We can transform a Glushkov automaton into a 

RE following Caron and Ziadi approach: (Caron & 

Ziadi, 2000 - TCS 1 ) 

– First, the orbits are removed: for each orbit, all arcs 

producing a cycle are deleted: 

0 1 2 3 4 

– The orbits are stored in the hierarchy of orbits H 

1 

Theoretical Computer Science 


Orbit {2,3}



RE: 

– First, the orbits are removed (cont.) 

0 1 2 3 4 


Orbit {3}



RE: 

– First, the orbits are removed (cont.) 

0 1 2 3 4 

● We have a graph without orbits 

● And the hierarchy of orbits H={{3},{2,3},{0,1,2,3,4}} 




RE: 

– Second, we start a reduction process over the graph 

without orbits by using H. 

– This process is applied according to H, respecting the 

set inclusion property. 




RE: 

– Applying three rules: 

Rule 1 

Rule 2 

Rule 3 

x y xy 

y 

x 


x|y 

x x?



RE: 

– Moreover, if a node represents a whole orbit, it is 

decorated with a + (positive closure) 



● Reduction process: 

0 - 

1 - 

2 - 

3 - 

4 - 

0 

0 

0 

0 

0 

1 2 3 4 

1 2 3 + 4 

R 1 

1 (2 3 + ) + 4 

R 3 

1 (2 3 + ) + 4 

R 1 

1 (2 3 + ) * 4 

R 1 

0 1 (2 3 + ) * 5 - 4 Result: 

R 1 


H={{3},{2,3},{0,1,2,3,4}} 

H={{2,3},{0,1,2,3,4}} 

H={{2,3},{0,1,2,3,4}} 

H={{0,1,2,3,4}} 

H={{0,1,2,3,4}} 

0 1 (2 3 + ) * 4


● Reduction process: 

0 - 

1 - 

2 - 

3 - 

4 - 

0 

0 

0 

0 

0 

1 2 3 4 

1 2 3 + 4 

R 1 

1 (2 3 + ) + 4 

R 3 

1 (2 3 + ) + 4 

R 1 

1 (2 3 + ) * 4 

R 1 

R 1 


H={{3},{2,3},{0,1,2,3,4}} 

H={{2,3},{0,1,2,3,4}} 

H={{2,3},{0,1,2,3,4}} 

H={{0,1,2,3,4}} 

H={{0,1,2,3,4}} 

0 1 (2 3 + ) * 5 - 4 Result: Subject (Year Journal+)*

Schema Update Primitives 

● Primitives: 

– Insertion, replacing, deletion, creation 

● Attributes, elements, content models 

– Cardinality changes 

– Constraints 

● Functional dependencies, types 



● Guerrini et al in [WIDM 1 , 2005] have shown the 

impact of schema update primitives over XML 

documents: 

– We can propose primitives that may be 

consistency-preserving 

1 

Workshop on Web Information and Data Management 



● They are: 

– Insertion as optional: 

● Attributes, elements 

– Creation 

● Content model 

– Element's cardinality changes 

● 1 to 0 

● 1 or 0 to 0:n 


Approach 


Proposed Conservative Primitives 

● Insertion of a sub-element in an element content 

model 

– ins 

● Making an element to be optional: 

– makeOpt 

● Extending the cardinality 

– ExtendCard 

● Create a new content model 

– createCM 


Insertion 

● User tool (prototype): 

You have chosen to insert Conference into the content model of Publication 

Select an element that has a semantic close to that of Conference: 

Subject (Year Journal + )* 

Select if you want to insert Conference: 

relatively to Journal 

relatively to (Journal+) 

Select if you want to insert Conference: 

as a choice: Journal | Conference 

before: Conference Journal 

after: Journal Conference 

Do you want Conference to be repeated: 

Yes 

No 


Insertion 

● To insert a new sub-element e' into an element e 

content model E 

– A node n (representing e' to be inserted into E) is 

inserted into the corresponding Glushkov graph 

without orbits G w (in a given position τ and context ζ): 

ins (e,e',τ,context,mode, times) 

● context= true (e' is inserted relatively to ζ) or false (relatively 

to τ) 

● mode can be choice, sequence-after or sequence-before 

● times = true, e' is decorated with + 

ins (Publication, Conference,3,false, choice, false) 


Insertion 

Publication : Subject (Year Journal+)* 

ins (Publication, Conference,3, false, choice, false) 

G 

G w 

G' w 

0 1 2 3 4 

0 1 2 3 4 

0 1 2 3 4 


5 

H={{3},{2,3},{0,1,2,3,4}} 

H'={{5,3},{2,3,5},{0,1,2,3,4,5}}

Insertion 

Publication : Subject (Year Journal+)* 

ins (Publication, Conference,3, false, choice, false) 

G' w 

G' w 

0 1 2 3 4 

0 1 2 3|5 4 

+ 

G' w 0 1 (2 (3|5))*4 


5 

H'={{5,3},{2,3,5},{0,1,2,3,4,5}} 

H'={{5,3},{2,3,5},{0,1,2,3,4,5}} 

H'={{5,3},{2,3,5},{0,1,2,3,4,5}} 

H'={} 

Subject (Year (Journal|Conference)+)*

Other Primitives (Syntax) 

● Making an element to be optional: 

– makeOpt(e,τ) 


– ExtendCard(e,τ) 

● Create a new content model 

– createCM(e,E) 


High Level Primitives 

● Express complex updates in a more compact way: 

– insSubExp(e,β,τ,context,mode,times) 

● Making a sub-expression optional 

– makeSubExpOpt(e,β) 


– extendSubExp(e,β) 


Final Considerations 


Conclusions 

● Glushkov automata (and graphs) allow us to 

identify starred sub-expressions of a regular 

expression. 

● The updates are performed in a intuitive way. 

● The proposed framework is consistencypreserving: 

– The documents valid wrt the old schema are 

valid wrt to the new one. 


Conclusions 

● Evolving XML schema is still a challenge: 

– Revalidation costs 

– Access to the documents to be revalidated 

– Data loss (to transform an invalid document into 

a valid one) 

– If the documents to be revalidated are stored in 

different sites: transfer costs. 


Directions 

● The proposed primitives are not complete 

● Using our approach together with nonconservative 

primitives in a general framework 

● Apply this method for document integration 

● Consider other types of schema representation 

● Extend this approach to treat facet updates 


22nd Brazilian Symposium on Data Base 

SBBD 2007 

Assisting XML Schema Evolution that 

Preserves Validity 

Thank You!

Glushkov Automata - sbes - 2007

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