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

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Logical basis for mathematics Gottlob Frege (1848-1925) in 1879, Begriffschrift (boolean connectives ... but also quantifiers, relations, functions) beginnings <strong>of</strong> first order logic Frege the first to distinguish between syntax and semantics. David Hilbert (1862-1943) ... wanted logical basis for mathematics Alfred Whitehead (1861-1947), Bertrand Russell (1872-1970): Principia mathematica (1910-1913) Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 6 / 89
First order predicate calculus Alfred Tarski (1902-1983) (till 1923 Alfred Teitelbaum): end <strong>of</strong> 1920s ... interpretation (semantics) e.g., ∀x.∀y.∃z.(x + y < z) is true in (N, +,
Page 1 and 2: Some theor
Page 3 and 4: Outline of the tal
Page 5: Propositional logic Augustus de Mor
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 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
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Decidability of va
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Monadic second order logic
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Automata on infinite words (Nondete
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Linear Temporal Logic (LTL) In prac
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Vending machines V1 V3 def = 5k.5k.
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Branching time LTL does not make di
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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
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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
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Implementation of
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Checking rules CI7I15I3I8I1 ⊥ C
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Formal methods (formal veri
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Conferences Some s
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Some theoretical aspects of verification (with a focus on bisimilarity)

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