Some theoretical aspects of verification (with a focus on bisimilarity)

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Electronic computer era In 1946, John Mauchly and J Presper Eckert developed ENIAC I Electrical Numerical Integrator And Calculator the world’s first electronic digital computer The fascinating era <strong>of</strong> electronic computers started ... Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 23 / 89
Automated theorem proving M. Davis in 1954 ... implementation <strong>of</strong> the decision procedure for Presburger arithmetic: the first success: computer proved that the sum <strong>of</strong> two even numbers is an even number Wang in 1958-1964 ... automated theorem prover (proved the simple laws <strong>of</strong> predicate calculus in Principia Mathematica) Davis, Putnam, Prawitz ... unification Robinson 1965 ... resolution principle Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 24 / 89
Page 1 and 2: Some theor
Page 3 and 4: Outline of the tal
Page 5 and 6: Propositional logic Augustus de Mor
Page 7 and 8: First order predicate calculus Alfr
Page 9 and 10: Axiomatization of
Page 11 and 12: Presburger arithmetic Example sente
Page 13 and 14: (Nondeterministic) finite automata;
Page 21 and 22: Finite automata - closure propertie
Page 23 and 24: Finite automata - closure propertie
Page 25 and 26: Finite automata - summary Nondeterm
Page 27 and 28: Decidability of Pr
Page 29 and 30: Decidability of Pr
Page 31 and 32: Addition and multiplication Theory
Page 33: Absolute limits (for automated <str
Page 37 and 38: Some available the
Page 39 and 40: Verification of a
Page 41 and 42: Verification of a
Page 43 and 44: Program-and-proof
Page 45 and 46: Denotational semantics, while-comma
Page 47 and 48: Fixpoints of monot
Page 53 and 54: Fixpoints for continuous functional
Page 55 and 56: Kripke structure (transition system
Page 57 and 58: First order logic of</stron
Page 59 and 60: Decidability of va
Page 61 and 62: Monadic second order logic
Page 63 and 64: Automata on infinite words (Nondete
Page 65 and 66: Linear Temporal Logic (LTL) In prac
Page 67 and 68: Vending machines V1 V3 def = 5k.5k.
Page 69 and 70: Branching time LTL does not make di
Page 71 and 72: Model checking CTL The ‘most comp
Page 81 and 82: More on tree unfoldings Unfolding <
Page 83 and 84: µ-calculus Kozen, Pratt (1980s) Br
Page 85 and 86:
Specification; process algebras Ope
Page 87 and 88:
Synchronisation Merge ✓ E a → E
Page 89 and 90:
Railway Components Road Rail down r
Page 91 and 92:
The Complete Railway System ✞ Cro
Page 93 and 94:
Bisimulation equivalence Milner, Pa
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Minsky counter machines A Minsky co
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Reduction of halti
Page 99 and 100:
Reduction of halti
Page 101 and 102:
Reduction of halti
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Reduction of halti
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Reduction - cont. • • . • •
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Bisimilarity over ‘context-free
Page 109 and 110:
Bisimulation game 2 Players: Attack
Page 111 and 112:
Type -1 systems; rules R a → w X
Page 113 and 114:
Our results Normed Processes Unnorm
Page 115 and 116:
Our results Normed Processes Unnorm
Page 117 and 118:
Inf-PCP (a version of</stro
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Implementation of
Page 129 and 130:
Implementation of
Page 131 and 132:
Checking rules CI7I15I3I8I1 ⊥ C
Page 133 and 134:
Formal methods (formal veri
Page 135 and 136:
Conferences Some s
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Some theoretical aspects of verification (with a focus on bisimilarity)

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