Summary and Future Work

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT

Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

Thanks for your attention!

Summary and Future Work Summary:

•

^Problem:given a textT and a patternP, enumerate efficiently all matches ofPonT

•

^Result:we can do this withreasonable complexityinP and withlinearpreprocessing andconstantdelay inT Extensions and future work:

•

Extending the results from text totrees

•

^{Supportingupdates}on the input data

•

Understanding the connections withcircuit classes

•

Enumerating results in a relevantorder?

•

Testing how well our methods perform inpractice

References i

Amarilli, A., Bourhis, P., and Mengel, S. (2018).

Enumeration on trees under relabelings.

InICDT.

Bagan, G. (2006).

MSO queries on tree decomposable structures are computable with linear delay.

InCSL.

Florenzano, F., Riveros, C., Ugarte, M., Vansummeren, S., and Vrgoc, D. (2018).

Constant delay algorithms for regular document spanners.

InPODS.

References ii

Kazana, W. and Segoufin, L. (2013).

Enumeration of monadic second-order queries on trees.

TOCL, 14(4).

Losemann, K. and Martens, W. (2014).

MSO queries on trees: Enumerating answers under updates.

InCSL-LICS.

Niewerth, M. and Segoufin, L. (2018).

Enumeration of MSO queries on strings with constant delay and logarithmic updates.

InPODS. To appear.

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: set circuit construction (details)

•

^Automaton:“Select all node pairs(α,β)”

•

^{States:{∅,α,β,αβ}}

n

α:n

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

∪ ∪ ∪ ∪

∅ α β αβ

×

×

Proof idea for trees: general enumeration approach

→ Enumerate the setT(g)captured by each gateg

→ Do it bytop-down inductionon the circuit

Base case: variable α:n : enumeratehα:niand stop

∪-gate

∪

g₁ g₂

Concatenation:enumerateT(g₁) and then enumerateT(g₂)

×-gate

×

g1 g2

Lexicographic product: for everyt₁inT(g₁):

for everyt2 inT(g2): outputt₁+t₂

Proof idea for trees: general enumeration approach

→ Enumerate the setT(g)captured by each gateg

→ Do it bytop-down inductionon the circuit

Base case: variable α:n :

enumeratehα:niand stop

∪-gate

∪

g₁ g₂

Concatenation:enumerateT(g₁) and then enumerateT(g₂)

×-gate

×

g1 g2

Lexicographic product: for everyt₁inT(g₁):

for everyt2 inT(g2): outputt₁+t₂

Proof idea for trees: general enumeration approach

→ Enumerate the setT(g)captured by each gateg

→ Do it bytop-down inductionon the circuit

Base case: variable α:n : enumeratehα:niand stop

∪-gate

∪

g₁ g₂

Concatenation:enumerateT(g₁) and then enumerateT(g₂)

×-gate

×

g1 g2

Lexicographic product: for everyt₁inT(g₁):

for everyt2 inT(g2): outputt₁+t₂

Dans le document Enumerating Pattern Matches in Texts and Trees (Page 180-200)