On the Step Explosion Problem

On the Step Explosion Problem Stephan Roch Humboldt-Universität zu Berlin Karsten Wolf (= Karsten Schmidt) Universität Rostock

Steps in Petri nets … irrelevant for set of reachable markings: m m‘  m m1 ….. m‘ {t1,…,tn} t1 t2 tn  State space tools do not consider steps

Steps in Petri nets with read arcs a b p1 p2 (1,1) (0,1) (1,0) (0,0) a b {a,b}

Steps in Petri nets with inhibitory arcs a b p1 p2 (0,0,1,1) (0,1,0,1) (1,0,1,0) (1,1,0,0) a b {a,b} p3 p4

Steps in Petri nets with reset arcs a b p1 p2 (1,1,0,0) (0,0,1,0) (0,0,0,1) (0,0,1,1) a b {a,b} p3 p4

Steps in Petri nets with capacities a b p1 p2 (1,1,0,0) (0,0,1,1) {a,b} p3 p4 - first consume then produce -

Steps in Petri nets with priorities a b p1 p2 (1,1,0,0) (0,1,1,0) (1,0,0,1) (0,0,0,0) (0,0,0,0) (0,0,1,1) {a,b} p3 p4 t1 t2 a t2 b t1

Steps in Petri nets with signal arcs a t1 p (1) (1) (1) (2) {a,t1} {b,t2} {a,b,t2} b t2 {a,b,t1}

How to deal with the additional markings? ,[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],s s1 s2

An irreducible step a b p1 p2 (1,1) (0,1) (1,0) (0,0) a b {a,b}

A reducible step a b p1 p2 (1,1) (0,1) (1,0) (0,0) a b {a,b} b

Main result: An easily computable over-approximation of the irreducuble steps ,[object Object],[object Object],[object Object],[object Object]

Relation  for nets with read arcs ,[object Object],a b a b p1 p2 a  rd b b  rd a b  rd a a  rd b a b p1 p2 {a,b}  {a} {b}

Proof of reducibility ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],b a

Computation of a reduced step list ,[object Object],[object Object],[object Object],[object Object],Plenty of time No time

Computation of all strongly connected sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Compute all SCS in Fac  Comp which include Comp

Computation of all strongly connected sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Compute all SCS in Fac  Comp which include Comp Every SCS is included in one SCC

Computation of all strongly connected sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Compute all SCS in Fac  Comp which include Comp Those SCS that do not contain x

Computation of all strongly connected sets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Compute all SCS in Fac  Comp which include Comp Those SCS that contain x

Steps and stubborn sets ,[object Object],[object Object],a b c {a}  {ab}, {ac}, {abc}  {bc}, {b}, {c} Situation with Irreducible steps: Much better

Steps and CTL ,[object Object],a b c d EX (p3  p4) true (full), false (reduced) EG ((p1  p2)  (p3  p4)) true (full), false (reduced) E((p1  p2)U(p3  p4)) true (full), false (reduced)

Some numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

On the Step Explosion Problem

Recommended

Recommended

More Related Content

What's hot

What's hot (17)

Viewers also liked

Viewers also liked (20)

Similar to On the Step Explosion Problem

Similar to On the Step Explosion Problem (20)

More from Universität Rostock

More from Universität Rostock (20)

Recently uploaded

Recently uploaded (20)

On the Step Explosion Problem