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

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<strong>Some</strong> specialized tools for deductive program <strong>verification</strong>s The Stanford Temporal Prover, STeP http://www-step.stanford.edu/ Stanford university, USA TLV - Temporal Logic Verifier http://www.wisdom.weizmann.ac.il/ verify/tlv/ Weizmann Institute <strong>of</strong> Science, Israel ———————————– A comprehensive survey <strong>of</strong> <strong>verification</strong> tools at Faculty <strong>of</strong> Informatics, Masaryk University Brno, Czech Rep. http://anna.fi.muni.cz/yahoda/ Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 31 / 89
Denotational semantics, while-command for command c ... semantics C[[c]] : Σ → Σ⊥ C[[while b do c]] ... (σ, σ ′ ) s.t. σ if B[[b]]σ = false then σ if B[[b]]σ = true and σ c then σ while b do c −→ σ ′ while b do c −→ σ ′ while b do c −→ σ −→ σ ′ −→ σ ′′ and σ ′′ while b do c I.e., we apply a functional Γ : (Σ → Σ⊥) → (Σ → Σ⊥): ⊥ ⊆ Γ(⊥) ⊆ Γ(Γ(⊥)) ⊆ Γ(Γ(Γ(⊥))) ⊆ . . . Petr Jančar (TU Ostrava) <strong>Some</strong> <strong>aspects</strong> <strong>of</strong> <strong>verification</strong> Kolloquium Jena, 14 May 2007 32 / 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 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: Program-and-proof
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
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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
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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