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Name

caesar.bdd - structural and behavioural analysis of Nested-Unit Petri Nets

Synopsis

caesar.bdd option [ filename.nupn ]

Description

Taking as input filename.nupn (or by default the standard input), which contains a Nested-Unit Petri Net (NUPN) encoded in the nupn format, caesar.bdd performs various structural or behavioural analyses, depending on the option specified on the command-line, and writes the corresponding results to the standard output. Error messages, if any, are displayed on the standard error.

Options

-check
Perform syntactic, structural and behavioural analysis of the Nested-Unit Petri Net to verify whether the stated constraints of the NUPN format are satisfied. The -check option performs additional checks and warns about redundant units, places that are never marked, and transitions that may never fire, etc.; these checks rely upon sufficient conditions, so that there is no guarantee that all never-marked places and never-fired transitions are reported. In addition to these static checks, the -check option also explores the marking graph using BDDs (Binary Decision Diagrams), prints the number of states reached at each iteration, and checks whether all reachable markings are one safe and unit safe; such checks are inconclusive if the marking graph is too large for being generated.

Important:
For performance reasons, the other options of caesar.bdd assume that the contents of filename.nupn are correct; these options often perform less stringent verifications than -check, or even no verification at all. In particular, options -dead-transitions, -concurrent-units, and -exclusive-places do not perform dynamic checks but rely on an optimized encoding of markings: such options may produce invalid results if some markings are not one safe or not unit safe. When dealing with an unknown Nested-Unit Petri Net, it is therefore advisable to first analyze its contents with -check before using any other option than -check.

-arcs
Display the number of arcs in the Nested-Unit Petri Net.

-bits
Display the number of bits needed to encode (using the best encoding) the markings of the Nested-Unit Petri Net.

-concurrent-units (or -unit)
Explore the set of reachable markings and determine the pairs of "concurrent" units, i.e., pairs of units Ui and Uj that satisfy the predicate Disjoint (Ui, Uj) specified in the nupn format definition, and such that there exists at least one reachable marking containing one place of Ui and one place of Uj. The output is defined as follows: Let U be the number of units in the Nested-Unit Petri Net; caesar.bdd writes to the standard output a list of U*(U+1)/2 values corresponding to the lower half of a matrix indexed according to increasing unit numbers; the value written at the intersection of raw i and column j is equal to 1 if units Ui and Uj are concurrent, and 0 otherwise. The upper half of the matrix is not output because it is symmetric.

-creator
Display the name of the creator tool specified by the !creator pragma if it is present in the Nested-Unit Petri Net, or the empty string if this pragma is absent. This pragma is specified in the "PRAGMA CREATOR" section of the nupn format definition.

-dead-transitions (or -dead)
Explore the set of reachable markings to determine the set of "dead" transitions, i.e., transitions that are not enabled in any reachable marking. The output is defined as follows: Let T be the number of transitions in the Nested-Unit Petri Net; caesar.bdd writes to the standard output a list of T values corresponding to each transition and ordered according to increasing transition numbers; the value written for each transition is 1 if the transition is dead, and 0 otherwise.

-density
Display the density of the incidence matrice of the the Nested-Unit Petri Net, i.e., the number of arcs divided by twice the product of the number of places by the number of transitions.

-encodings
Display statistics about the number of bits required to represent the markings of the Nested-Unit Petri Net using various possible encodings.

-exclusive-places
Explore the set of reachable markings to determine the pairs of "exclusive" places, i.e., pairs of places Pi and Pj such that Pi = Pj or there exists no reachable marking containing both Pi and Pj. The exploration of the set of reachable markings may be incomplete if a timeout (see below) is specified. The NUPN is said to be "presumably unit safe" if either the exploration was complete and the NUPN was found to be unit safe, or the exploration was incomplete and the NUPN contains the "!unit_safe" pragma. The output is defined as follows: Let P be the number of places in the Nested-Unit Petri Net; caesar.bdd writes to the standard output a list of P*(P+1)/2 values corresponding to the lower half of a matrix indexed according to increasing place numbers; line i corresponds to place Pi (belonging to unit Ui) and raw j corresponds to place Pj (belonging to unit Uj); the value written at the intersection of raw i and column j is a character equal to:
- "=": if Pi = Pj (diagonal elements), or if the NUPN is presumably unit safe and both places belong to the same unit, i.e., Ui = Uj;
- "<": if the NUPN is presumably unit safe and the unit of Pi is contained in the unit of Pj, i.e., Sub* (Ui, Uj), where the Sub* predicate is specified in the nupn format definition;
- ">": if the NUPN is presumably unit safe and the unit of Pi contains the unit of Pj, i.e., Sub* (Uj, Ui);
- "~": if the NUPN is not presumably unit safe and both places are different and belong to the same unit, i.e., (Pi != Pj) and (Ui = Uj);
- "[": if the NUPN is not presumably unit safe and the unit of Pi is contained in the unit of Pj, i.e., Sub* (Ui, Uj);
- "]": if the NUPN is not presumably unit safe and the unit of Pi contains the unit of Pj, i.e., Sub* (Uj, Ui);
- "0": if none of the above applies, and a marking containing both Pi and Pj was reached;
- "1": if none of the above applies, and the exploration was complete and no marking containing both Pi and Pj was reached;
- ".": if none of the above applies, and the exploration was incomplete and no marking containing both Pi and Pj was reached.
In summary, two places are exclusive if their matrix cell is "=", "<", ">", or "1"; they are non-exclusive if their matrix cell is "0"; the answer is unknown if their matrix cell is "~", "[", "]", or ".". The upper half of the matrix is not output because it is symmetric, modulo permutations of "<" and ">", and of "[" and "]".

-height
Display the height of the unit tree of the Nested-Unit Petri Net. By convention, all leaf units have height one, and the root unit only increases the height if this unit has at least one local place.

-hwb
Display the HWB code of the Nested-Unit Petri Net. This code has the form height-width-bits, where the three fields are those numbers computed by options -height, -height, and -bits, respectively. Fields height and width are omitted if width is equal to bits, i.e., if the net does not have a "real" NUPN structure.

-initial-places
Display the list of places present in the initial marking. These places are displayed on a single line, separated with spaces.

-initial-tokens
Display the number of tokens present in the initial marking. If present in the Nested-Unit Petri Net, the !multiple_initial_tokens pragma is taken into account. This pragma is defined in the "PRAGMA MULTIPLE_INITIAL_TOKENS" section of the nupn format definition.

-mcc
Undocumented option used to prepare or complete the model forms of the Model Checking Contest. This option computes various structural and behavioural properties of the Nested-Unit Petri Net. The unit_safe pragma, if present, is taken into account. If the !multiple_arcs pragma or the !multiple_initial_tokens pragma is present in the Nested-Unit Petri Net, the -mcc option computes structural and behavioural properties for the original (non safe) Petri Net rather than for the NUPN itself.

-multiple-arcs
Display the arguments of the !multiple_arcs pragma if it is present in the Nested-Unit Petri Net, or the empty string if this pragma is absent. This pragma is specified in the "PRAGMA MULTIPLE_ARCS" section of the nupn format definition.

-multiple-initial-tokens
Display the arguments of the !multiple_initial_tokens pragma if it is present in the Nested-Unit Petri Net, or the empty string if this pragma is absent. This pragma is specified in the "PRAGMA MULTIPLE_INITIAL_TOKENS" section of the nupn format definition.

-places
Display the number of places in the Nested-Unit Petri Net.

-pnml
Write to the standard output the translation in PNML (Petri Net Markup Language) the network given as input in the NUPN format. The PNML output will contain a "NUPN-toolspecific" section as defined on the http://mcc.lip6.fr/nupn.php page. If the input network contains errors, the translation may stop prematurely, leaving an incomplete PNML file. It is therefore recommended to invoke the tool as follows:
caesar.bdd -pnml [ filename.nupn ] > filename.pnml || rm -f filename.pnml

-redundant-units
Display the numbers of all redundant units (i.e., units that have a single sub-unit, or that have no local place and are not the root unit), or the empty string if there are no such units in the Nested-Unit Petri Net.

-transitions
Display the number of transitions in the Nested-Unit Petri Net.

-units
Display the number of units in the Nested-Unit Petri Net.

-version
Display the current version number of the software.

-width
Display the width of the unit tree of the Nested-Unit Petri Net. By convention, this width is equal to the number of leaf units.

NUPN (Nested-Unit Petri Net) Format

See the nupn manual page for a detailed definition of the NUPN file format.

Interrupts

caesar.bdd handles certain POSIX interrupt signals (namely, SIGINT, SIGQUIT, SIGALRM, and SIGTERM) and adapt its behaviour in consequence. Upon reception of such a signal:

User-specified Timeouts

The environment variable $CAESAR_BDD_TIMEOUT can be used to specify a maximal duration for marking graph exploration. If this variable is set to a strictly positive integer N, the exploration of the marking graph will stop after N seconds. If this variable is not set or set to zero, no timeout will occur. Upon expiration of a timeout:

The functionality provided by this environment variable is not available on Windows.

Exit Status

The exit status of caesar.bdd may take the following values:
0:
normal termination (everything is alright)

1:
memory shortage (Petri Net and/or BDDs are too large)

2:
incorrect command-line arguments for caesar.bdd

3:
filename.nupn does not exist or is unreadable

4:
syntax or semantic error in filename.nupn

5:
caesar.bdd terminated by the user (SIGINT or SIGQUIT) or upon timeout (SIGALRM or SIGTERM)

Any other value corresponds to an unexpected error.

Authors

Damien Bergamini and Hubert Garavel (INRIA Rhone-Alpes)

Files

filename.nupn
Nested-Unit Petri Net (input)

filename.places
Table of place names (input, -mcc option only)

filename.trans
Table of transition names (input, -mcc option only)

Credits

To perform its structural analyses, caesar.bdd uses the Binary Decision Diagram package CUDD (Release 2.5.1) developed by Fabio Somenzi at the University of Colorado (Boulder, CO, USA).

Bibliography

[Gar15] Hubert Garavel. "Nested-Unit Petri Nets: A Structural Means to Increase Efficiency and Scalability of Verification on Elementary Nets." In R. Devillers and A. Valmari, editors, Proceedings of the 36th International Conference on Application and Theory of Petri Nets and Concurrency (PETRI NETS'15), Brussels, Belgium. Lecture Notes in Computer Science, vol. 9115, Springer, 2015. Related slideshow available from http://cadp.inria.fr/publications/Garavel-15-a.html

See Also

caesar

Additional information is available from the CADP Web page located at http://cadp.inria.fr

Directives for installation are given in files $CADP/INSTALLATION_*.

Recent changes and improvements to this software are reported and commented in file $CADP/HISTORY.

Bugs

Please report new bugs to Hubert.Garavel@inria.fr


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