Branching Immediate Observation Petri Nets A strong class with - PowerPoint PPT Presentation

INFINITY Workshop July 7th, 2020 Branching Immediate Observation Petri Nets A strong class with simple reachability Chana Weil-Kennedy joint work with Javier Esparza and Mikhail Raskin The project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787367

INFINITY Workshop July 7th, 2020 Branching Immediate Observation Petri Nets A strong class with simple reachability non-semilinear PSPACE Chana Weil-Kennedy joint work with Javier Esparza and Mikhail Raskin The project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787367

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 2

Petri nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 3

Petri nets W R t 2 t 4 t 1 t 3 C S S C W R S C W R * (1,3,0,0) ⟶ (1,0,0,0) C. Weil-Kennedy, TUM 3

Petri nets W R t 2 t 4 t 1 t 3 C S S C W R S C W R * (1,3,0,0) ⟶ (1,0,0,0) C. Weil-Kennedy, TUM 3

Petri nets W R t 2 t 4 t 1 t 3 C S S C W R S C W R * (1,3,0,0) ⟶ (1,0,0,0) Reachability problem: Given a Petri net , and markings and 풩 M 0 M can marking reach marking in ? M 0 M 풩 C. Weil-Kennedy, TUM 3

Reachability Problem Reachability problem: Given a Petri net , and markings and 풩 M 0 M in can marking reach marking ? M 0 M 풩 • verification of systems modelled by Petri nets • many problems are interreducible with reachability in Petri nets in: • formal languages (e.g. shu ffl e closure of regular language) • logic (e.g. logics on data words) • process calculi (e.g. fragment of 휋 -calculus) [survey by S. Schmitz, ’16] C. Weil-Kennedy, TUM 4

Reachability Problem Reachability problem: Given a Petri net , and markings and 풩 M 0 M non-elementary complexity in can marking reach marking ? M 0 M 풩 [Czerwinzki, Lasota, Lazic, Leroux, Mazowiecki, ’19] • verification of systems modelled by Petri nets • many problems are interreducible with reachability in Petri nets in: • formal languages (e.g. shu ffl e closure of regular language) • logic (e.g. logics on data words) • process calculi (e.g. fragment of 휋 -calculus) [survey by S. Schmitz, ’16] C. Weil-Kennedy, TUM 4

Reachability Problem Reachability problem: Given a Petri net , and markings and 풩 M 0 M non-elementary complexity in can marking reach marking ? M 0 M 풩 [Czerwinzki, Lasota, Lazic, Leroux, Mazowiecki, ’19] • verification of systems modelled by Petri nets • many problems are interreducible with reachability in Petri nets in: • formal languages (e.g. shu ffl e closure of regular language) • logic (e.g. logics on data words) • process calculi (e.g. fragment of 휋 -calculus) [survey by S. Schmitz, ’16] Study subclasses of Petri nets C. Weil-Kennedy, TUM 4

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t 2 • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t 2 • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t 2 • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] Branching Parallel Processes (BPP) t 2 t • Token creation and destruction • Communication-free C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] [Esparza, Raskin, W.-K. , ’19] Branching Parallel Processes Immediate Observation nets (BPP) (IO) t t 2 t • Token creation and destruction • Conservative • Communication-free • Communication C. Weil-Kennedy, TUM 5

Branching immediate observation nets [Christensen et al., ’93] [Yen, ’97] [Lasota, ’09] [Mayr, Weihmann, ’15] [Esparza, Raskin, W.-K. , ’19] Branching Parallel Processes Immediate Observation nets (BPP) (IO) t t 2 t • Token creation and destruction • Conservative • Communication-free • Communication C. Weil-Kennedy, TUM 5

Definition Branching Immediate Observation nets (BIO) t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t t • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Definition Branching Immediate Observation nets (BIO) t 2 t t Card ( ∙ t − t ∙ ) ≤ 1 • Token creation and destruction • Communication C. Weil-Kennedy, TUM 6

Branching Immediate Observation nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 7

Branching Immediate Observation nets W R t 2 t 4 t 1 t 3 C S C. Weil-Kennedy, TUM 7

A strong class with simple reachability General Petri nets non-elementary [Czerwinzki, Lasota, Lazic, Leroux, Mazowiecki, ’19] Branching Immediate Observation (BIO) Conservative Branching Parallel Immediate PSPACE-complete Processes Observation [Esparza, Raskin, W.-K. , ’19] (BPP) (IO) NP-complete [Esparza, ’97] C. Weil-Kennedy, TUM 8

A strong class with simple reachability General Petri nets non-elementary [Czerwinzki, Lasota, Lazic, Leroux, Mazowiecki, ’19] Branching PSPACE-complete Immediate Observation (BIO) Conservative Branching Parallel Immediate PSPACE-complete Processes Observation [Esparza, Raskin, W.-K. , ’19] (BPP) (IO) NP-complete [Esparza, ’97] C. Weil-Kennedy, TUM 8

A strong class with simple reachability Unbounded Petri net classes with provably simpler reachability then the general case have semilinear reachability sets (e.g. BPP nets, reversible Petri nets…) C. Weil-Kennedy, TUM 9

A strong class with simple reachability Unbounded Petri net classes with provably simpler reachability then the general case have semilinear reachability sets (e.g. BPP nets, reversible Petri nets…) BIO nets may have non-semilinear reachability set BIO net c 2 p c 1 t 1 classic translation [Hopcroft, Pansiot, ’79] example t 2 t 4 of a 3-dimensional VASS VASS to Petri net t 3 q c 3 2 C. Weil-Kennedy, TUM 9

A strong class with simple reachability Unbounded Petri net classes with provably simpler reachability then the general case have semilinear reachability sets (e.g. BPP nets, reversible Petri nets…) BIO nets may have non-semilinear reachability set BIO net c 2 p c 1 t 1 classic translation [Hopcroft, Pansiot, ’79] example t 2 t 4 of a 3-dimensional VASS VASS to Petri net t 3 q c 3 2 C. Weil-Kennedy, TUM 10