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

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Finite automaton - an outside view a b b a b q0 Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 15 / 89
Decidability <strong>of</strong> Presburger arithmetic (by automata) ∀x.∀y.∀x1.∀y1.∃z.∃z1. ¬(x1 + x1 = x) ∨ ¬(y1 + y1 = y) ∨ ((x + y = z1) ∧ (z + z = z1)) An automaton accepting all (binary codes <strong>of</strong>) (i, j, k) which satisfy i + j = k i 0 0 1 0 1 j 0 1 1 0 0 k 1 0 0 0 1 q0 Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 16 / 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: Finite automata - summary Nondeterm
Page 29 and 30: Decidability of Pr
Page 31 and 32: Addition and multiplication Theory
Page 33 and 34: Absolute limits (for automated <str
Page 35 and 36: Automated theorem proving M. Davis
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 77 and 78:
Model checking CTL The ‘most comp
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Model checking CTL The ‘most comp
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More on tree unfoldings Unfolding <
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µ-calculus Kozen, Pratt (1980s) Br
Page 85 and 86:
Specification; process algebras Ope
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Synchronisation Merge ✓ E a → E
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Railway Components Road Rail down r
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The Complete Railway System ✞ Cro
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Bisimulation equivalence Milner, Pa
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Minsky counter machines A Minsky co
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Reduction of halti
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Reduction of halti
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Reduction of halti
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Reduction of halti
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Reduction - cont. • • . • •
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Bisimilarity over ‘context-free
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Bisimulation game 2 Players: Attack
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Type -1 systems; rules R a → w X
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Our results Normed Processes Unnorm
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Our results Normed Processes Unnorm
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Inf-PCP (a version of</stro
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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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