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4.6 Interface to the DD Package

NuSMV uses the state of the art BDD package CUDD [Som98]. Control over the BDD package can very important to tune the performance of the system. In particular, the order of variables is critical to control the memory and the time required by operations over BDDs. Reordering methods can be activated to determine better variable orders, in order to reduce the size of the existing BDDs. Reordering methods can be activated either

Reordering of the variables can be triggered in two ways: by the user, or by the BDD package. In the first way, reordering is triggered by the interactive shell command dynamic_var_ordering with the -f option.

Reordering is triggered by the BDD package when the number of nodes reaches a given threshold. The threshold is initialized and automatically adjusted after each reordering by the package. This is called dynamical reordering, and can be enabled or disabled by the user. Dynamic reordering is enabled with the shell command dynamic_var_ordering with the option -e, and disabled with the -d option.

Environment Variable: enable_reorder
Specifies whether dynamic reordering is enabled (when value is `0') or disabled (when value is `1').

Environment Variable: reorder_method
Specifies the ordering method to be used when dynamic variable reordering is fired. The possible values, corresponding to the reordering methods available with the CUDD package, are listed below. The default value is sift.

sift:
Moves each variable throughout the order to find an optimal position for that variable (assuming all other variables are fixed). This generally achieves greater size reductions than the window method, but is slower.
random:
Pairs of variables are randomly chosen, and swapped in the order. The swap is performed by a series of swaps of adjacent variables. The best order among those obtained by the series of swaps is retained. The number of pairs chosen for swapping equals the number of variables in the diagram.
random_pivot:
Same as random, but the two variables are chosen so that the first is above the variable with the largest number of nodes, and the second is below that variable. In case there are several variables tied for the maximum number of nodes, the one closest to the root is used.
sift_converge:
The sift method is iterated until no further improvement is obtained.
symmetry_sift:
This method is an implementation of symmetric sifting. It is similar to sifting, with one addition: Variables that become adjacent during sifting are tested for symmetry. If they are symmetric, they are linked in a group. Sifting then continues with a group being moved, instead of a single variable.
symmetry_sift_converge:
The symmetry_sift method is iterated until no further improvement is obtained.
window{2,3,4}:
Permutes the variables within windows of n adjacent variables, where n can be either 2, 3 or 4, so as to minimize the overall BDD size.
window{2,3,4}_converge:
The window{2,3,4} method is iterated until no further improvement is obtained.
group_sift:
This method is similar to symmetry_sift, but uses more general criteria to create groups.
group_sift_converge:
The group_sift method is iterated until no further improvement is obtained.
annealing:
This method is an implementation of simulated annealing for variable ordering. This method is potentially very slow.
genetic:
This method is an implementation of a genetic algorithm for variable ordering. This method is potentially very slow.
exact:
This method implements a dynamic programming approach to exact reordering. It only stores a BDD at a time. Therefore, it is relatively efficient in terms of memory. Compared to other reordering strategies, it is very slow, and is not recommended for more than 16 boolean variables.
linear:
This method is a combination of sifting and linear transformations.
linear_conv:
The linear method is iterated until no further improvement is obtained.

Command: dynamic_var_ordering [[-d] | [-e method] | [-f method] [-h]]
Controls the application and the modalities of (dynamic) variable ordering. When no options are specified, the current status of dynamic ordering is displayed. At most one of the options -e, -f, and -d should be specified.

Dynamic ordering may be time consuming, but can often reduce the size of the BDDs dramatically. A good point to invoke dynamic ordering explicitly (using the -f option) is after the commands build_model, once the transition relation has been built. It is possible to save the ordering found using write_order in order to reuse it (using build_model -i file) in the future.

-d
Disables dynamic ordering.
-f method
Forces reordering of variables with the specified method.
-e method
Enables dynamic ordering to trigger automatically whenever a certain threshold on the overall BDD size is reached.

method must be one of the values allowed for the environment variable reorder_method.

Command: print_bdd_stats [-h]
Prints the statistics for the BDD package. The amount of information depends on the BDD package configuration established at compilation time. The configuration parameters are printed out too. More information about statistic and parameters can be found in the documentation of the CUDD Decision Diagram package.

Command: set_bdd_parameters [-h] [-s]
Creates a table with the value of all the flags currently active in NuSMV and change accordingly the configurable parameters of the BDD package.
-s
Print the bdd parameter and statistics after the modification.

The command uses the global DD manager and the set of pairs (variable,value) of the NuSMV environment, the function sets specific BDD parameters to the given values. This command works in conjunction with `print_bdd_stats'.
`print_bdd_stats' first prints a report of the parameters and statistics of the DD manager. By using the command `set', the user may modify the value of any of the parameters of the underlying BDD package. The way to do it is by setting a value in the variable `BDD.parameter name' where `parameter name' is the name of the parameter exactly as printed by the `print_bdd_stats' command.
The most important parameters are:

These parameters can have a big impact on the performances. See the documentation of the CUDD Decision Diagram package for a more detailed explanation of the meaning of these parameters and how they can affect performances.


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