Transducer-Based Rewriting Games for Active XML Martin Schuster TU - - PowerPoint PPT Presentation

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transducer based rewriting games for active xml

Transducer-Based Rewriting Games for Active XML Martin Schuster TU - - PowerPoint PPT Presentation

Aug 14, 2023 124 likes •728 views

Transducer-Based Rewriting Games for Active XML Martin Schuster TU Dortmund Highlights 2016 1/8 Active XML 2/8 Active XML City Name, Meteo, Events City Name S TRING Meteo @meteo_svc Name Meteo Events Events @event_svc

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Transducer-Based Rewriting Games for Active XML

Martin Schuster

TU Dortmund

Highlights 2016

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Active XML

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Active XML

City → Name, Meteo, Events Name → STRING Meteo → @meteo_svc Events → @event_svc event_svc: → (Sports|Concert)*@event_svc meteo_svc: → STRING

. . .

City Name Brussels Meteo @meteo_svc centigrade Events @event_svc Brussels

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Active XML

City → Name, Meteo, Events Name → STRING Meteo → @meteo_svc Events → @event_svc event_svc: → (Sports|Concert)*@event_svc meteo_svc: → STRING

. . .

City Name Brussels Meteo 24◦/sunny Events Sports football @event_svc Brussels

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The Schema Rewriting Problem

Server Client City → Name, Meteo, Events Events → @event_svc City → Name, Meteo, Events Events → (Sports|Concert)* event_svc: → (Sports|Concert)*

Server (CC-BY-SA 3.0) RRZE Icons, Client (LGPL) Everaldo Coelho

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The Schema Rewriting Problem

Server Client City → Name, Meteo, Events Events → @event_svc City → Name, Meteo, Events Events → (Sports|Concert)* event_svc: → (Sports|Concert)*

Server (CC-BY-SA 3.0) RRZE Icons, Client (LGPL) Everaldo Coelho

Goal: Rewrite source document into target schema using function calls

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The Schema Rewriting Problem

Server Client City → Name, Meteo, Events Events → @event_svc City → Name, Meteo, Events Events → (Sports|Concert)* event_svc: → (Sports|Concert)*

Server (CC-BY-SA 3.0) RRZE Icons, Client (LGPL) Everaldo Coelho

Goal: Rewrite source document into target schema using function calls Only schemas for remote services known in advance

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The Schema Rewriting Problem

Server Client City → Name, Meteo, Events Events → @event_svc City → Name, Meteo, Events Events → (Sports|Concert)* event_svc: → (Sports|Concert)*

Server (CC-BY-SA 3.0) RRZE Icons, Client (LGPL) Everaldo Coelho

Goal: Rewrite source document into target schema using function calls Only schemas for remote services known in advance find a safe rewriting strategy

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The Schema Rewriting Problem

Server Client City → Name, Meteo, Events Events → @event_svc City → Name, Meteo, Events Events → (Sports|Concert)* event_svc: → (Sports|Concert)*

Server (CC-BY-SA 3.0) RRZE Icons, Client (LGPL) Everaldo Coelho

Goal: Rewrite source document into target schema using function calls Only schemas for remote services known in advance find a safe rewriting strategy Context-free game on nested words

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Nested Words

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Nested Words

Idea: Correct nesting of tags over label alphabet Σ Example a/aabc/c/ba/a/a

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Nested Words

Idea: Correct nesting of tags over label alphabet Σ Linearisations of Σ-labelled forests Example a/aabc/c/ba/a/a a a b c a

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Context-Free Games on Nested Words: Example

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a}

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} |f/ff/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f|/ff/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/f|f/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/f|ag/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fa|g/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fag|/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fag|/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fag|/g/a ↓

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fag|/g/a ↓ f/faa/a/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fag|/g/a ↓ f/faa/a/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fagg/g/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fagg/g|/g/a

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Context-Free Games on Nested Words: Example

Intuition: JULIET picks function node to call, ROMEO chooses replacement JULIET wins once a target language string is reached

Example T = {f/fan/an | n ≥ 0}, f → {angm/gm/an | n, m ≥ 0}, g → {a/a} f/ff|/f ↓ f/fagg/g|/g/a ↓ ???

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Dealing with function parameters

In previous work:

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

Events @event_svc Brussels

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

Events @event_svc Brussels

Events

Sports football @event_svc Brussels

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

Events @event_svc Brussels

Events

Sports football @event_svc Brussels

How to model dependencies between input and output?

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

Events @event_svc Brussels

Events

Sports football @event_svc Brussels

How to model dependencies between input and output?

Nested Word Transducers

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Dealing with function parameters

In previous work: Basic setting: Ignore and overwrite Validation games: Overwrite if valid w.r.t. input schema

Events @event_svc Brussels

Events

Sports football @event_svc Brussels

How to model dependencies between input and output?

Nested Word Transducers Closely related to (variants of) visibly pushdown transducers

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Research goals and restrictions

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness:

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion Relabelling NWT: No insertion

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion Relabelling NWT: No insertion . . .

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion Relabelling NWT: No insertion . . . Restrictions to strategies for JULIET:

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion Relabelling NWT: No insertion . . . Restrictions to strategies for JULIET: Unbounded/bounded/no recursion

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Research goals and restrictions

Algorithmic problem: Determine if JULIET has a winning strategy Main goal: Find tractable case Restrictions to transducer expressiveness: General NWT ǫ-free NWT: Limited insertion Relabelling NWT: No insertion . . . Restrictions to strategies for JULIET: Unbounded/bounded/no recursion . . .

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

No recursion Bounded Unbounded NWT 2-EXPTIME undecidable undecidable

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

No recursion Bounded Unbounded NWT 2-EXPTIME undecidable undecidable ǫ-free NWT

CO-NEXPTIME

non-elementary undecidable

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

No recursion Bounded Unbounded NWT 2-EXPTIME undecidable undecidable ǫ-free NWT

CO-NEXPTIME

non-elementary undecidable Relabelling PSPACE PSPACE EXPTIME

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

No recursion Bounded Unbounded NWT 2-EXPTIME undecidable undecidable ǫ-free NWT

CO-NEXPTIME

non-elementary undecidable Relabelling PSPACE PSPACE EXPTIME

Tractable cases (not shown here) of little practical interest.

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(Some) Results

Complexity of deciding if JULIET has a winning strategy: (Completeness results)

No recursion Bounded Unbounded NWT 2-EXPTIME undecidable undecidable ǫ-free NWT

CO-NEXPTIME

non-elementary undecidable Relabelling PSPACE PSPACE EXPTIME

Tractable cases (not shown here) of little practical interest. Next step: Transducers that express practical schema languages (DTDs/XML Schema).

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Literature I

R. Alur, P

. Madhusudan. Adding nesting structure to words.

J. ACM, 56.3, 2009
E. Filiot, J. Raskin, P

. Reynier, F. Servais, J. Talbot. Properties of Visibly Pushdown Transducers. MFCS, 355–367, 2010.

T. Milo, S. Abiteboul, B. Amann, O. Benjelloun, F. Dang Ngoc.

Exchanging intensional XML data. ACM Trans. Database Syst.,30(1):1–40, 2005

A. Muscholl, T. Schwentick, L. Segoufin.

Active Context-Free Games. Theory Comput. Syst., 39(1):237–276, 2006

J. Raskin, F. Servais.

Visibly Pushdown Transducers. ICALP, (2)386–397, 2008.

A. Thomo, S. Venkatesh, Y. Ye.

Visibly Pushdown Transducers for Approximate Validation of Streaming XML. FoIKS, 219–238, 2008.