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Pragmatic model checking: from theory to implementations

Universität Rostock, profile picture
Universität Rostock

The document discusses pragmatic model checking, including theoretical foundations, practical implementations, and optimization techniques to develop effective model checkers. It emphasizes the challenges of state explosion in complex systems, illustrated by an example involving IBM's business process modeling, and introduces concepts such as partial order reduction, symmetry reduction, and state compression as strategies to manage this complexity. Furthermore, it highlights the importance of pragmatism in achieving results amidst the inherent complexity of model checking.

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Pragmatic model checking:
 from theory to implementations Niels Lohmann
1 2 3 How does a model checker work? How to build an effective model checker? How to use a model checker pragmatically?
1 2 3 How does a model checker work? How to build an effective model checker? How to use a model checker pragmatically?
Model checking in a nutshell model ' specification model checker yes ( witness path) no ( counterexample) 4
Model checking in a nutshell model ' model checker yes ( witness path) no ( counterexample) specification memory overflow 4
State explosion business process* with 66 parallel branches * modeled by IBM customers using the IBM Websphere business modeler 5
State explosion business process* with 66 parallel branches * modeled by IBM state space:
 66 19 2 ≈ 2.37 ∙ 10 markings customers using the IBM Websphere business modeler 5
State explosion business process* with 66 parallel branches * modeled by IBM state space:
 66 19 2 ≈ 2.37 ∙ 10 markings memory for state space:
 608 exabytes** (66 bit per marking) customers using the IBM Websphere business modeler ** mega, giga, peta,
 tera, exa… 5
State explosion business process* with 66 parallel branches * modeled by IBM customers using the IBM Websphere business modeler state space:
 66 19 2 ≈ 2.37 ∙ 10 markings memory for state space:
 608 exabytes** (66 bit per marking) ** mega, giga, peta,
 tera, exa… time for state space generation
 7799 years (10 CPU cycles/marking at 3 GHz) 5
State explosion business process* with 66 parallel branches * modeled by IBM customers using the IBM Websphere business modeler state space:
 66 19 2 ≈ 2.37 ∙ 10 markings memory for state space:
 608 exabytes** (66 bit per marking) ** mega, giga, peta,
 tera, exa… time for state space generation
 7799 years (10 CPU cycles/marking at 3 GHz) energy consumption for state space generation
 2,9 megatons of TNT (at 50 watts) 5
State explosion business process* with 66 parallel branches * modeled by IBM customers using the IBM Websphere business modeler state space:
 66 19 2 ≈ 2.37 ∙ 10 markings memory for state space:
 608 exabytes** (66 bit per marking) ** mega, giga, peta,
 tera, exa… time for state space generation
 7799 years (10 CPU cycles/marking at 3 GHz) energy consumption for state space generation
 2,9 megatons of TNT (at 50 watts) 5
The core algorithm ! ! markings = [] search(m0,φ) ! ! ! 1 2 3 4 5 6 def search(m,φ): check(m,φ) markings.add(m) for t in enabled(m): m' = fire(m,t) if not m' in markings: search(m',φ) • search is a simple depth first search (+ SCC detection) • check depends on the nature of the property and may terminate search • enabled and fire implement the Petri net firing rule 6
Reduction techniques apply theoretic results to 1. store fewer markings 2. fire fewer transitions /
 generate fewer markings 
 
 while preserving the property 3. store markings more efficiently 7
1. Partial order reduction observation: concurrent transitions can be fired in any order, yielding the same final state idea: fix one ordering by postponing the firing of some transitions implementation: search on Petri net structure 8
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
1. Partial order reduction algorithm (sketch): • choose one activated transition • until fixed point is reached: add all conflicting transitions only fire these transitions 9
2. Symmetry reduction observation: symmetric models (e.g. due to copies of components) have symmetric behavior i1 c1 idea: do not store markings if a symmetric copy is already stored implementation: Petri net graph automorphisms i2 r1 s c2 r2 10
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 r2 11
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] symmetric markings c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] symmetric markings c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] symmetric markings c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction i1 [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] i2 [r2,c2] symmetric markings c1 [i1,c2] r1 s c2 graph automorphisms r2 12
2. Symmetry reduction [i1,s,i2] [r1,s,i2] [i1,s,r2] [r1,s,r2] [c1,i2] [c1,r2] [i1,c2] [r2,c2] complete state space reduced state space 13
3. State compression observation: the value of some places depend on the value of others i1 r1 c1 s i2 r2 c2 m = [1,0,0,0,0,0,1] i1 c1 idea: do not store markings of “implicit places” implementation: Petri net place invariants i2 r1 s c2 r2 14
3. State compression place invariants: for all reachable markings m: i1 r1 c1 s i2 r2 c2 m = [1,0,0,0,0,0,1] i1 m(c1) + m(c2) + m(s) = 1
 m(i1) + m(c1) + m(r1) = 1
 m(i2) + m(c2) + m(r2) = 1 i2 c1 r1 s c2 r2 15
3. State compression place invariants: for all reachable markings m: i1 r1 c1 s i2 r2 c2 m = [1,0,0,0,0,0,1] i1 m(c1) + m(c2) + m(s) = 1
 m(i1) + m(c1) + m(r1) = 1
 m(i2) + m(c2) + m(r2) = 1 c1 therefore: m(s) = 1 − m(c1) − m(c2)
 m(i1) = 1 − m(c1) − m(r1)
 m(i2) = 1 − m(c2) − m(r2) i2 s c2 r1 i1, i2, and s are implicit r2 16
Reduction techniques: implementation ! ! ! ! markings = [] c = compressor() s = symmetries() search(m0,φ) ! ! ! 1 2 3 4 5 6 def search(m,φ): check(m,φ) markings.add(c.compress(m)) for t in selection(enabled(m)): m' = fire(m,t) if not s.symm(m') in markings: search(m',φ) • compressor and symmetries preprocess the net • compress creates shorter marking vectors • selection chooses some enabled transitions • symm checks if symmetric marking is already stored 17
Reduction techniques: summary • can be combined • a lot of them work on the
 Petri net structure • preprocessing pays off • some are Petri net exclusive • decades of research 18
1 2 3 How does a model checker work? How to build an effective model checker? How to use a model checker pragmatically?
Key: Pragmatism good news model checking is decidable bad news at a devastating complexity • in the end: we only optimize a small depth-first search…
 … that is run billions of times • we need to understand every aspect • pragmatism is key: we want a result at all costs 20
The programming language: C++ manual memory
 management type system low-level
 optimization portability preprocessor optional
 object orientation threading 21
Used anti-patterns • heavy use of preprocessor (conditional compilation, compile-time decisions, architecture-dependent constants) • god objects • a lot of global variables • no standard libraries/
 generic algorithms (STL, Boost) • remember: performance, not reusability 22
Data structures frontend (parser) backend (verification) syntactic sugar canonic representation class hierarchies flat C-style arrays generated code/
 standard libraries simple and user-specified
 data types focus on simplicity focus on performance 23
A remark on complexity • While solving an EXPSPACE-complete problems,
 don’t be afraid of complexity! • Preprocessing and optimizations
 can have dramatic impact. • NP-complete (SAT-solving) or
 NP-hard (integer linear programming)
 problems can be “feasible”. 24
Formalism compilers modeling formalisms verification formalism WS-BPEL low-level Petri nets AI planning - varying feature set
 - domain dependent
 - moving target, short lifespan - no structural restrictions
 - domain independent
 - sound, mature theory 25
Petri net model checking • exploit domain knowledge to optimize core functions • firing transitions • storing markings • know lifecycle of concepts • often contradicts object orientation 26
Checking enabledness orange transition
 is disabled 27
Checking enabledness orange transition
 is disabled scapegoat
 place 27
Checking enabledness orange transition
 is disabled blue
 transition
 fires scapegoat
 place 27
Checking enabledness orange transition
 is disabled scapegoat
 place blue
 transition
 fires scapegoat place still unmarked 27
Checking enabledness orange transition
 is disabled scapegoat
 place blue
 transition
 fires scapegoat place still unmarked orange transition
 is still disabled 27
Storing markings markings bit vectors bin tree [0,1,3,3,1] 00 01 11 11 01 00 01 11 11 01 [0,1,3,2,0] 00 01 11 10 00 00 01 11 10 00 [0,1,3,2,1] 00 01 11 10 01 00 01 11 10 01 28
Storing markings markings bit vectors bin tree [0,1,3,3,1] 00 01 11 11 01 00 01 11 11 01 [0,1,3,2,0] 00 01 11 10 00 00 01 11 10 00 [0,1,3,2,1] 00 01 11 10 01 00 01 11 10 01 28
Storing markings markings bit vectors bin tree [0,1,3,3,1] 00 01 11 11 01 1 01 [0,1,3,2,0] 00 01 11 10 00 00 01 11 10 00 [0,1,3,2,1] 00 01 11 10 01 00 01 11 10 01 28
Storing markings markings bit vectors bin tree [0,1,3,3,1] 00 01 11 11 01 1 01 [0,1,3,2,0] 00 01 11 10 00 00 01 11 10 00 [0,1,3,2,1] 00 01 11 10 01 00 01 11 10 01 28
Storing markings markings bit vectors bin tree [0,1,3,3,1] 00 01 11 11 01 1 01 [0,1,3,2,0] 00 01 11 10 00 00 01 11 10 00 [0,1,3,2,1] 00 01 11 10 01 01 28
Know what you need • sometimes, only a special case is needed: • • • Tarjan algorithm where only TSCCs are needed linear algebra (sparse matrix, only carrier is needed) no library can offer this 29
Optimizations • profiling, low-level optimizations (caching) • know your limits: (in LoLA: malloc) 30
Academic software design hardly any tenure programmers seldom seen as important coding is never top priority your thesis is! there is no (paying) customer no agreed feature set definitely no coding professionals university cannot teach experience very fast
 scientific progress maintenance is not enforced moving targets once the paper is out, nobody cares hard to collect/ keep knowledge people leave frequently and for good frequently changing staff 2-5 year contracts 31
Lessons learned • prototyping and check on real data • KISS; few dependencies • split large tools to smaller
 “brain-sized” units • test coverage to avoid the fear of breaking everything • goal orientation:
 no UI, integration via streams 32
1 2 3 How does a model checker work? How to build an effective model checker? How to use a model checker pragmatically?
Verification questions: the don’ts Don’t ask for global states. Usually, only a few aspects (marking of a few places) are relevant. Don’t ask two things at once. If the properties affect different parts of the model, ask separately. Don’t use the X operator. In distributed systems, it makes no sense to ask for “the” next state. Don’t order unordered things. Usually, all components should be correct, not just component #1. 34
Verification questions: the dos Ask simple questions. Sometimes, you don’t need temporal logics at all. Make a verification model. Manipulating the original model may help to ask simpler questions. Use domain knowledge. Exploit implicit assumptions about the model and the property. 35
Simple properties complex simple reason EF φ reachability of φ trivial check function AG φ ¬EF ¬φ again reachability AGEF φ check for φ in all TSCC reachability +
 TSCC detection lesson: (hardly) no need
 for complex CTL* formulae compilers will help to find best match SCC TSCC 36
Checking relaxed soundness Definition: A workflow net is relaxed sound iff for all transitions exists a terminating firing sequence. o i if choices are not synchronized, the net deadlocks but every transition can fire in a terminating sequence net is relaxed sound 37
Net manipulation: algorithm 1. for all transitions t: create a net with test place pt: pt t i o 2. check for EF (pt > 0 ⋀ o = 1) 38
Net manipulation: summary − check 8 nets instead of 1 + checking reachability is simpler than extended CTL + each state space is smaller than the original + one counterexample for each failure + parallelizable 39
Checking soundness Definition: A workflow net is sound iff (1) the final marking [o] is always reachable (2) [o] is the only marking with tokens on place o, and (3) no transition is dead. + domain knowledge: nets are free-choice Definition: A free-choice workflow net is sound iff
 (1) AGEF [o] holds,
 (2) the net is 1-safe, and
 (3) no transition is dead. 40
Checking soundness Definition: A free-choice workflow net is sound iff (1) AGEF [o] holds, (2) the net is 1-safe, and (3) no transition is dead. (1) check if the marking [o] is reachable in all TSCCs. (2) for every join-place p, check if m with m(p)>1 is reachable. (3) for every transition t, check if reachable •t is X = t p 41
Pragmatic use: summary • help the model checker help you • reformulate your question • many small state spaces are better than one large 42
1 2 3 How does a model checker work? How to build an effective model checker? How to use a model checker pragmatically? Conclusions
Take home points • model checking = theory + practice + pragmatism • academic software design is a discipline on its own • asking the right question(s) is crucial 44
Pragmatic model checking:
 from theory to implementations Niels Lohmann
Copyrights Atombombentest Romeo, public domain United States Department of Energy
 http://commons.wikimedia.org/wiki/File:Castle_Romeo.jpg Raspberry Pi, CC-BY-SA Jwrodgers
 http://commons.wikimedia.org/wiki/File:RaspberryPi.jpg apoptosis inducing factor, GPL
 http://en.wikipedia.org/wiki/File:Apoptosis_inducing_factor.png Tux, by lewing@isc.tamu.edu
 http://en.wikipedia.org/wiki/File:Tux.png Integrated Circuit, public domain
 http://commons.wikimedia.org/wiki/File:Chip.jpg Websphere software logo, public domain
 http://commons.wikimedia.org/wiki/File:Websphere_logo.png BPMN logo, copyright Object Management Group (OMG) 46

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