C ategorical A utomata L earning F ramework calf-project.org Gerco - - PowerPoint PPT Presentation

Categorical Automata Learning Framework

Gerco van Heerdt Matteo Sammartino Alexandra Silva LiVe @ ETAPS 2017 calf-project.org

Our team

Alexandra Silva UCL Gerco van Heerdt UCL

Joshua Moerman Radboud University Maverick Chardet ENS Lyon

Collaborators:

Bartek Klin Warsaw University Michal Szynwelski Warsaw University Matteo Sammartino UCL

Automata learning

Learner queries answers builds System black-box

S

automaton model of

S

Automata learning

Learner queries answers builds System black-box

S

automaton model of

S

No formal specification available? Learn it!

set of system behaviors is a regular language Finite alphabet of system’s actions A

L ⊆ A

L* algorithm (D.Angluin ’87)

set of system behaviors is a regular language Finite alphabet of system’s actions A

L ⊆ A

L* algorithm (D.Angluin ’87)

Learner Teacher

L

set of system behaviors is a regular language Finite alphabet of system’s actions A

L ⊆ A

L* algorithm (D.Angluin ’87)

Learner Teacher

L

Q:w ∈ L? A: Y/N

set of system behaviors is a regular language Finite alphabet of system’s actions A

L ⊆ A

L* algorithm (D.Angluin ’87)

Learner Teacher

L

Q:w ∈ L? A: Y/N

L(H) = L?

Q: A: Y / N + counterexample H = hypothesis automaton

H

set of system behaviors is a regular language Finite alphabet of system’s actions A

L ⊆ A

L* algorithm (D.Angluin ’87)

Learner Teacher

L

Q:w ∈ L? A: Y/N Minimal DFA accepting L

L

builds L(H) = L?

Q: A: Y / N + counterexample H = hypothesis automaton

H

Non-deterministic Weighted Register Mealy Machines

A zoo of automata

Alternating Universal Probabilistic

Non-deterministic Weighted Register Mealy Machines

Algorithms Correctness proofs

involved and hard to check

A zoo of automata

Alternating Universal Probabilistic

Non-deterministic Weighted Register Mealy Machines

Algorithms Correctness proofs

involved and hard to check

A zoo of automata

Alternating Universal Probabilistic

Category theory comes to the rescue!

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

DFAs

F = (−) × A

C = Set

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Q × A

DFAs

F = (−) × A

C = Set

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Q × A

1

DFAs

F = (−) × A

C = Set

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Q × A

1

q0 ∈ Q

DFAs

F = (−) × A

C = Set

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Q × A

1

q0 ∈ Q

2

DFAs

F = (−) × A

C = Set

Abstract automata

DFAs

FQ Q

”Q

I

initQ Q

Y

• utQ

Endofunctor = automaton type

F : C → C

Category = universe of state-spaces

C

Q × A

1

q0 ∈ Q F ⊆ Q

2

DFAs

F = (−) × A

C = Set

Abstract learning

Abstract observation data structure

Abstract learning

Abstract observation data structure approximates

FQ Q

”Q

I

initQ Q

Y

• utQ

Target minimal automaton

Abstract learning

Abstract observation data structure approximates

FQ Q

”Q

I

initQ Q

Y

• utQ

Target minimal automaton Hypothesis automaton

FH H I Y

”H

• utH

initH

abstract closedness and consistency

Abstract learning

Abstract observation data structure

General correctness theorem

=

Guidelines for implementation

approximates

FQ Q

”Q

I

initQ Q

Y

• utQ

Target minimal automaton Hypothesis automaton

FH H I Y

”H

• utH

initH

abstract closedness and consistency

Abstract learning

Abstract observation data structure

General correctness theorem

=

Guidelines for implementation

approximates

FQ Q

”Q

I

initQ Q

Y

• utQ

Target minimal automaton Hypothesis automaton

FH H I Y

”H

• utH

initH

abstract closedness and consistency

CALF: Categorical Automata Learning Framework

Gerco van Heerdt, Matteo Sammartino, Alexandra Silva

(arXiv:1704.05676)

Other automata & optimizations

Nom Vect Set DFAs Nominal automata Weighted automata

Change base category

Other automata & optimizations

Nom Vect Set DFAs Nominal automata Weighted automata

Change base category

Other automata & optimizations

Side-effects (via monads)

NFAs Partial automata Universal automata Alternating automata Powerset Powerset with intersection Double powerset Maybe monad

Nom Vect Set DFAs Nominal automata Weighted automata

Change base category

Observation tables Discrimination trees

Change main data structure

Other automata & optimizations

Side-effects (via monads)

NFAs Partial automata Universal automata Alternating automata Powerset Powerset with intersection Double powerset Maybe monad

Nom Vect Set DFAs Nominal automata Weighted automata

Change base category

Observation tables Discrimination trees

Change main data structure

Learning Nominal Automata (POPL ’17)

Joshua Moerman, Matteo Sammartino, Alexandra Silva, Bartek Klin, Michal Szynwelski

Other automata & optimizations

Side-effects (via monads)

NFAs Partial automata Universal automata Alternating automata Powerset Powerset with intersection Double powerset Maybe monad

Nom Vect Set DFAs Nominal automata Weighted automata

Change base category

Observation tables Discrimination trees

Change main data structure

Learning Nominal Automata (POPL ’17)

Joshua Moerman, Matteo Sammartino, Alexandra Silva, Bartek Klin, Michal Szynwelski

Other automata & optimizations

Side-effects (via monads)

NFAs Partial automata Universal automata Alternating automata Powerset Powerset with intersection Double powerset Maybe monad

Learning Automata with Side-effects

Gerco van Heerdt, Matteo Sammartino, Alexandra Silva

(arXiv:1704.08055)

Automaton type Optimizations

Minimization algorithms Testing algorithms

Automata Learning algorithms

Connections with other algorithms

Ongoing and future work

• Library & tool to learn control + data-flow models

(as nominal automata)

• Applications:
• Specification mining
• Network verification, with
• Verification of cryptographic protocols
• Ransomware detection