From LTL to Deterministic Parity Automata Javier Esparza 1 Jan K - - PowerPoint PPT Presentation

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From LTL to Deterministic Parity Automata Javier Esparza 1 Jan K - - PowerPoint PPT Presentation

Jan 18, 2023 437 likes •900 views

From LTL to Deterministic Parity Automata Javier Esparza 1 Jan K etnsk 1 Salomon Sickert 1 Jean-Franois Raskin 2 1. Technische Universitt Mnchen 2. Universit libre de Bruxelles 1 R EACTIVE S YNTHESIS Specification Controller

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SLIDE 1

From LTL to Deterministic Parity Automata

1

Jan Křetínský1 Salomon Sickert1 Javier Esparza1 Jean-François Raskin2

  • 2. Université libre de Bruxelles
  • 1. Technische Universität München
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SLIDE 2

REACTIVE SYNTHESIS

2

Specification Controller

LTL

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SLIDE 3

REACTIVE SYNTHESIS

2

Specification Controller

LTL NBA Nondeterministic Büchi

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SLIDE 4

REACTIVE SYNTHESIS

2

Specification Controller

LTL NBA DPA Nondeterministic Büchi Deterministic Parity

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SLIDE 5

REACTIVE SYNTHESIS

2

Specification Controller

LTL NBA DPA Parity Game Nondeterministic Büchi Deterministic Parity

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SLIDE 6

REACTIVE SYNTHESIS

2

Specification Controller

Controller LTL NBA DPA Parity Game Nondeterministic Büchi Deterministic Parity

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SLIDE 7

REACTIVE SYNTHESIS

  • SYNTCOMP 2016 / LTL Synthesis Track
  • Tools: Acacia(4Aiger), BoSy, PARTY, Unbeast
  • Techniques: Bounded Synthesis, Antichains, BDDs
  • No tool relied on parity games!

2

Specification Controller

Controller LTL NBA DPA Parity Game

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SLIDE 8

REACTIVE SYNTHESIS

  • SYNTCOMP 2016 / LTL Synthesis Track
  • Tools: Acacia(4Aiger), BoSy, PARTY, Unbeast
  • Techniques: Bounded Synthesis, Antichains, BDDs
  • No tool relied on parity games!

2

Specification Controller

Controller LTL NBA DPA Parity Game

LDBA Goal: Find a translation to make synthesis using Parity games competitive!

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SLIDE 9

LIMIT-DETERMINISTIC BÜCHI AUTOMATA

Initial Component Accepting Component

non-deterministic

deterministic

“Jumps”

3

Also known as: deterministic-in-the-limit or semi-deterministic

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SLIDE 10

LIMIT-DETERMINISTIC BÜCHI AUTOMATA

Initial Component Accepting Component

non-deterministic

deterministic

“Jumps”

3

Also known as: deterministic-in-the-limit or semi-deterministic

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SLIDE 11

LIMIT-DETERMINISTIC BÜCHI AUTOMATA

Initial Component Accepting Component

non-deterministic

deterministic

“Jumps”

3

Also known as: deterministic-in-the-limit or semi-deterministic

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SLIDE 12

Simple, optimal and practical translation from LTL to DPA (via LDBA)

4

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SLIDE 13

Simple, optimal and practical translation from LTL to DPA (via LDBA)

4

without Safra-trees (or similar approaches)

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SLIDE 14

Simple, optimal and practical translation from LTL to DPA (via LDBA)

4

without Safra-trees (or similar approaches) 2-Exp

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SLIDE 15

Simple, optimal and practical translation from LTL to DPA (via LDBA)

4

without Safra-trees (or similar approaches) 2-Exp yields small automata in practice

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SLIDE 16

LDBA RUN DAG

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× × Initial Component (non-deterministic) Accepting Component (deterministic) No branching on the right side!

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SLIDE 17

LDBA RUN DAG

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1 2 3 Position:

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SLIDE 18

LDBA RUN DAG

6

1 2 3 Position:

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SLIDE 19

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

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SLIDE 20

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 21

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 22

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 23

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 24

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 25

LDBA RUN DAG

6

1 2 3 Position:

  • Facts:
  • No branching
  • All infinite branches

eventually stabilise at a specific position.

  • Idea:
  • Parity condition identifies

the oldest accepting run.

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SLIDE 26

LTL → DPA

  • Facts:
  • LTL → LDBA is exactly 2-Exp [S, Esparza, Jaax, Kretínský CAV’16]
  • LDBA → DPA is exactly Exp
  • Naive combination of with LDBA → DPA yields a 3-Exp construction.
  • However, the translation LTL → DPA should be 2-Exp!

7

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SLIDE 27

PRUNED RUN DAG

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× × Initial Component (non-deterministic) Accepting Component (deterministic)

L1 L2 L3

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SLIDE 28

PRUNED RUN DAG

8

× × Initial Component (non-deterministic) Accepting Component (deterministic)

L1 L2 L3

Oracle: L2 ⊆ L1

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SLIDE 29

PRUNED RUN DAG

8

× × Initial Component (non-deterministic) Accepting Component (deterministic)

L1 L2 L3

× × ×

Oracle: L2 ⊆ L1

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SLIDE 30

PRUNED RUN DAG

8

× × Initial Component (non-deterministic) Accepting Component (deterministic)

L1 L2 L3

Oracle: L3 ⊆ L2 ∪ L1

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SLIDE 31

PRUNED RUN DAG

8

× × Initial Component (non-deterministic) Accepting Component (deterministic)

L1 L2 L3

Oracle: L3 ⊆ L2 ∪ L1

× × ×

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SLIDE 32

CONCLUSION

  • Presented Construction:
  • Simpler Structure: rankings (lists) vs. Safra-trees
  • Optimal for LDBA → DPA and LTL → DPA (with pruning)
  • On-the-fly construction
  • Future Work:
  • Design a NBA → LDBA translation, which can be easily pruned.
  • Provide a complete synthesis toolchain combined with a parity game solver.
  • Publication:
  • From LTL and Limit-Deterministic Büchi Automata to Deterministic Parity
  • Automata. TACAS’17
  • Website: https://www7.in.tum.de/~sickert/projects/ltl2dpa

9

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SLIDE 33

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

2-EXP EXP 3-EXP

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SLIDE 34

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 35

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Safra-Piterman trees, Skeleton trees Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 36

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Safra-Piterman trees, Skeleton trees Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 37

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Focus on F and G, Rabinizer Safra-Piterman trees, Skeleton trees Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 38

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Focus on F and G, Rabinizer Safra-Piterman trees, Skeleton trees Focus on F and G, Kini, [CAV’16] Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 39

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Focus on F and G, Rabinizer Safra-Piterman trees, Skeleton trees Focus on F and G, Kini, [CAV’16] Appearance Records Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 40

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Focus on F and G, Rabinizer Safra-Piterman trees, Skeleton trees Focus on F and G, Kini, [CAV’16] Appearance Records Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 41

LANDSCAPE OF AUTOMATA

10

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

Focus on F and G, Rabinizer Safra-Piterman trees, Skeleton trees Focus on F and G, Kini, [CAV’16] Appearance Records Breakpoints Tableaux, Alternating Automata 2-EXP EXP 3-EXP

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SLIDE 42

LANDSCAPE OF AUTOMATA

11

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic Limit-Deterministic

DRA DPA DMA LDBA NBA LTL

2-EXP EXP 3-EXP

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SLIDE 43

LANDSCAPE OF AUTOMATA

12

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic

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SLIDE 44

LANDSCAPE OF AUTOMATA

12

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic Probabilistic MC

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SLIDE 45

LANDSCAPE OF AUTOMATA

12

Acceptance Conditions: Büchi Rabin Parity Muller Deterministic Nondeterministic

DRA DPA DMA LDBA NBA LTL

Limit-Deterministic Probabilistic MC Synthesis via Parity Games:

  • positional strategies
  • efficient solvers available