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Verification of distributed algorithms with algebraic Petri Nets
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Verification of distributed algorithms with algebraic Petri Nets
Ekkart Kindler1 and Wolfgang Reisig1
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Institut für Informatik, Humboldt-Universität zu Berlin, D-10099, Berlin, Germany |
Abstract
This paper demonstrates by help of an example how algebraic Petri nets can be used for modelling and verification of distributed
algorithms. For lack of space we could only sketch the used proof techniques; still the proof should provide a flavour of
our method. In essence the basic technique for deriving simple temporal properties is to verify the validity of some state
formulas which are derived from the structure of the net and the verified formula: equations for place invariants, simple
implications for siphons and traps, and some more complex implications for assertions. Though not completely explained here,
even the pick up rule for leadsto properties can be reduced to checking the validity of some state formulas. For combining
temporal formulas in order to verify more complex properties we mainly use standard rules: weakening of invariants, PSP-rule
and proof graphs for liveness properties.
A formal presentation of this method is beyond the scope of this paper. A formal presentation of algebraic nets as used in
this paper can be found in [3]; more information about the verification techniques and some more interesting examples can
be found in [4, 8].
This work was supported by the DFG (Project ‘Distributed Algorithms’).
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