Table of Contents
bcg_cmp - equivalence comparison of normal, probabilistic, or stochastic
labeled transitions systems (LTS) encoded in the BCG format
bcg_cmp
[
bcg_options] [
-strong |
-branching |
-divbranching |
-observational |
-sharp [
-total
|
-partial |
-gate]
sharp_filename] |
-divsharp [
-total |
-partial |
-gate]
sharp_filename]
[
-normal |
-prob |
-rate [
-self]] [
-epsilon eps] [
-format format_string] [
-class
class_file] [
-diag [
-bfs|
-dfs]
diag_file.bcg]
input_1.bcg input_2.bcg
where bcg_options
is defined below (see GENERAL OPTIONS).
bcg_cmp takes as inputs the BCG
graphs input_1.bcg and input_2.bcg, and compares these graphs according to
some bisimulation relation.
bcg_cmp implements various algorithms
to perform comparison of graphs encoded in the BCG format according to
strong bisimulation, branching bisimulation, divbranching bisimulation,
observational equivalence, sharp bisimulation, or divsharp bisimulation.
A graph input by
bcg_cmp can be:
- either a "normal" LTS, whose transitions
are either labelled with "normal" labels or with the "internal" label (usually
noted "tau" in the scientific literature and displayed as the character
string "
i" by the various BCG tools), - or a "probabilistic LTS": these
are LTS with "normal" labelled transitions, as well as "special" transitions,
whose labels are either of the form "
prob %p" or "label; prob %p", where %p
denotes a floating-point number in the range ]0..1] and label denotes a character
string that does not contain the ";" character. For each state, the sum
of "%p" values on special transitions leaving the state must be less or
equal than 1 (see ANNEX 1 of the bcg_min
manual page for a discussion
on how the probabilistic LTS model generalizes other theoretical models
published in the literature), - or a "stochastic LTS": these are LTS with
"normal" labelled transitions, as well as "special" transitions, whose
labels are either of the form "
rate %f" or "label; rate %f", where %f denotes
a strictly positive floating-point number and label denotes a character
string that does not contain the ";" character (see ANNEX 2 of the bcg_min
manual page for a discussion on how the stochastic LTS model of bcg_min
generalizes other theoretical models published in the literature).
The following
bcg_options are currently supported:
-version,
-create,
-update,
-remove,
-cc,
-tmp,
-uncompress,
-compress,
-register,
-short,
-medium,
and
-size. See the
bcg
manual page for a description of these options.
The following options are also supported:
- -strong
- Perform
LTS comparison according to strong bisimulation [Par81]. On (Discrete or
Continuous Time) Markov Chains and on Markov Reward Models, this equivalence
agrees with lumpability of [KS76,KSK76,Buc94,Hil94] (see ANNEX 1, ANNEX 2,
and BIBLIOGRAPHY of the bcg_min
manual page). Default option.
- -branching
- Perform LTS comparison according to branching bisimulation [GW96]. It is
worth noticing that the notion of branching bisimulation is rather meaningless
for probabilistic systems. Not a default option.
- -divbranching
- Perform LTS
comparison according to divbranching (shorthand for divergence-preserving
branching) bisimulation [GW96]. Divbranching bisimulation differs from branching
bisimulation only in the way cycles of internal transitions (also called
divergences) are treated. It is known that all states traversed by a cycle
of internal transitions belong to the same branching equivalence class.
While divergences are ignored by ordinary branching bisimulation, they
are assimilated to a self-looping internal transition in each such equivalence
class by divbranching bisimulation. Unlike branching bisimulation, divbranching
bisimulation preserves inevitability properties. Like branching bisimulation,
it is worth noticing that the notion of divbranching bisimulation is rather
meaningless for probabilistic systems. Not a default option.
- -observational
- Perform LTS comparison according to observational equivalence [Mil89]. It
is worth noticing that observational equivalence is computationally more
expensive than branching bisimulation, so that comparison may fail even
for graphs containing only few thousands of states. To reduce the risk of
failure, in a first step the input graphs are automatically reduced according
to branching bisimulation. This is sound because branching bisimulation
is a graph relation stronger than observational equivalence. However, this
optimisation is not applied if the -class option is set, so that bcg_cmp
can print the equivalence classes relatively to the states of the input
graphs, instead of the states of the branching minimal intermediate graph
produced in the first step. This option cannot be combined with neither
-prob nor -rate options. Not a default option.
- -sharp [ -total|-partial|-gate ] sharp_filename
- Perform LTS comparison according to sharp bisimulation (the variant of
the bisimulation defined in [LMM20] that does not preserve the divergences
present in input1.bcg and input2.bcg), using the rules defined in sharp_filename
to partition labels between strong and weak actions. See Section FORMAT
FOR SHARP LABEL PARTITIONING of the bcg_min
manual page for details
on the syntax of sharp_filename. The -total, -partial, and -gate options specify
the "total matching", "partial matching", and "gate matching" semantics,
respectively.
In "total matching" semantics, the regular expressions contained
in sharp_filename denote full labels (i.e., gates possibly followed by experiment
offers). A label matches if it matches some rule in sharp_filename entirely.
In "partial matching" semantics, the regular expressions contained in
sharp_filename denote substrings of labels. A label matches if it contains
a substring that matches some rule in sharp_filename.
At last, in "gate
matching" semantics, the regular expressions contained in sharp_filename
denote gates. A label matches if its first word (called gate) matches some
rule in sharp_filename. In this case, regular expressions in sharp_filename
should not contain characters forbidden in gate identifiers (e.g., " ", "(",
or "!").
Option -total is the default.
This option cannot be combined with
neither -prob nor -rate options. Not a default option.
- -divsharp [ -total|-partial|-gate
] sharp_filename
- Perform LTS comparison according to divsharp bisimulation
(the variant of the bisimulation defined in [LMM20] that preserves the
divergences present in input1.bcg and input2.bcg). See -sharp option above
for the partitioning of labels between strong and weak actions. This option
cannot be combined with neither -prob nor -rate options. Not a default option.
- -normal
- Consider input_1.bcg and input_2.bcg as normal LTSs. With this option,
labels of the form "
rate %f" or "label; rate %f" or "prob %p" or "label; prob %p"
are processed as ordinary labels, without special meaning attached. Default
option.
- -prob
- Consider input_1.bcg and input_2.bcg as probabilistic LTSs. With
this option, each label of the form "
prob %p" or "label; prob %p" is recognized
as denoting a probabilistic transition with probability %p. bcg_cmp will
stop with an error message if, for some probabilistic transition, %p is
out of ]0..1], or if the probabilistic transitions going out of the same
state have a cumulated sum strictly greater than 1. With this option, labels
of the form "rate %f" or "label; rate %f" are processed as ordinary labels.
Not a default option.
- -rate [ -self ]
- Consider input_1.bcg and input_2.bcg as
stochastic LTSs. With this option, each label of the form "
rate %f" or "label; rate %f"
is recognized as denoting a stochastic transition with rate %f. bcg_cmp
will stop with an error message if, for some stochastic transition, %f
is less or equal to 0. If the -branching or the -divbranching option is selected,
and some state has both an outgoing stochastic transition and an outgoing
internal (i.e., "tau") transition, bcg_cmp will print a warning and ignore
the stochastic transition in order to preserve the notion of maximal progress.
With this option, labels of the form "prob %p" or "label; prob %p" are processed
as ordinary labels. Not a default option.
If -self sub-option is given, all self loops (i.e., transitions that remain
within the same equivalence class) having labels of the form "rate %f"
are ignored. This implements the weak Markovian equivalences described in
[Bra02] and [BHKW05]. Not a default sub-option.
- -epsilon eps
- Set the precision
of floating-point comparisons to eps, where eps is a real value. When eps
is out of [0..1[, bcg_cmp reports an error. Default value for eps is 1E-6.
- -format format_string
- Use format_string to control the format of the floating-point numbers contained
in transition labels (these numbers correspond to the occurrences of
%f
and %p mentioned in section DESCRIPTION above). The value of format_string
should obey the same conventions as the format parameter of function sprintf(3C)
for values of type double. Default value for format_string is "%g", meaning
that floating-point numbers are printed with at most six digits after the
"." (i.e., the radix character). Other values can be used, for instance "%.9g"
to obtain nine digits instead of six, or by replacing the "%g" flag with
other flags, namely "%e", "%E", "%f", "%G", possibly combined with additional
flags (e.g., to specify precision).
- -class class_file
- If class_file is the character
'-', then display the equivalence classes on standard output. Otherwise, display
the equivalence classes in a file named class_file. Not a default option.
- -diag [-bfs|-dfs] diag_file.bcg
- When the comparison of input_1 and input_2 yields
FALSE, generate a diagnostic (counterexample) in BCG format (see the bcg
manual page for details) explaining this result. The diagnostic is generated
by the bisimulator
tool of CADP, in the file diag_file.bcg. This option
has no effect when the comparison of input_1 and input_2 yields TRUE, since
in this case the diagnostic would be larger than input_1 and input_2, and
would not bring any useful information.
Option -bfs or -dfs, if present, is
passed to bisimulator
. Option -bfs may be slightly slower but generates
smaller diagnostics than option -dfs. Option -bfs is the default option.
Note
that diagnostics are generated only for comparisons of normal LTSs and
according to strong bisimulation, branching bisimulation, divbranching
bisimulation, and observational equivalence. In particular, if the -diag
option is used in combination with any of the -sharp, -divsharp, -prob, and
-rate options, then a warning is issued and no diagnostic is generated.
The
BCG file containing the diagnostic can be visualized using the bcg_draw
and bcg_edit
tools of CADP (see respective manual pages for details).
The diagnostic is a directed acyclic graph included (modulo the preorder
corresponding to the equivalence relation considered) both in input_1 and
input_2.
If the diagnostic is a sequence of transitions, it will also be
displayed on standard output using the simple SEQ format (see the seq
manual page for the definition of this format). Not a default option.
Note:
Options -strong, -branching, -divbranching, -sharp, -divsharp, and -observational
are mutually exclusive. If they occur simultaneously on the command line,
the option occurring last is selected.
Note: Options -normal, -prob, and
-rate (with or without -self sub-option) are mutually exclusive. If they occur
simultaneously on the command line, the option occurring last is selected.
See the
bcg
manual page for a description
of the environment variables used by all the BCG application tools.
Exit status is 0 if everything is alright, 1 otherwise.
bcg_cmp
was developped by Frederic Lang (INRIA/CONVECS). It shares a substantial
amount of code with
bcg_min. See the
bcg_min
manual page for more
information.
- input_1.bcg
- BCG graph (input)
- input_2.bcg
- BCG graph
(input)
- input_1@1.o
- dynamic library (input or output)
- input_2@1.o
- dynamic
library (input or output)
- $CADP/bin.`arch`/bcg_cmp
- ``bcg_cmp'' binary program
See the bcg
manual page for a description of the other files.
bcg
,
bcg_min
,
seq
,
sprintf(3C)
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.
Please report bugs to
[email protected].
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