Rubicon is based on

• [1] Model Checking Finite-Horizon Markov Chains with Probabilistic Inference. Steven Holtzen, Sebastian Junges, Marcell Vazquez-Chanlatte, Todd Millstein, Sanjit A. Seshia and Guy Van den Broeck, CAV 2021.

This prototype uses (the python bindings of) Storm [2] to model check finite horizon properties of DTMCs. It does so by translating DTMCs in the PRISM-language into Dice [3] and running inference with Dice.

We provide a docker container

docker pull sjunges/rubicon:cav21

or when downloaded from an (unpacked) archive:

docker load -i rubicon_docker.tar

The container is based on an container for the probabilistic model checker as provided by the storm developers, see this documentation.

The following command will run the docker container (for Windows platforms, please see the documentation from the storm website).

docker run --mount type=bind,source="$(pwd)",target=/data -w /opt/rubicon -it --name rubicon sjunges/rubicon:cav21

To export files out of the Docker image, files that are in the /data directory inside the image are available on the host system in the current working directory.

Note We tested these docker containers with 6GB of memory.

Note This docker container may yield difficulties running on the new Mac M1 Chipset. The following link shows how to run this docker in emulation, and may resolve these issues.

Users of an artifact/Docker container can skip this step.

• Install Storm and Stormpy from source as usual.
  • but using this repository for Storm
  • and this repository for Stormpy (Note: These branches are in the process of being merged back into Storm(py) version 1.7.0)
• Install Dice from source from this branch

First and foremost, Rubicon translates Prism programs and properties to equivalent Dice programs.

python rubicon/rubicon.py --prism examples/factory/factory3.prism --prop 'P=? [F<=2 "allStrike"]' --output "factory-3-2.dice"

Rubicon will give limited logging output and creates a dice file called factory-3-2.dice. Some files require additional constants to be set, as standard for prism files:

python rubicon/rubicon.py --prism examples/parqueues/queue-8.nm --prop 'P=? [F<=8 "target"]' -const "N=4" --output "queue-8-4-8.dice"

Rubicon can be used to invoke Dice directly. In the docker container, first run:

eval $(opam env)

Then:

python rubicon/rubicon.py --prism examples/factory/factory3.prism --prop 'P=? [F<=2 "allStrike"]' --output "factory-3-2.dice" --run-dice 

This provides logging output and includes the resulting probability on the last line.

We provide a couple of arguments to set-up Dice:

• --dice-cwd The working directory from which to run Dice. Defaults to ..
• --dice-cmd The command with which to invoke dice, defaults to dice.
• --dice-to A timeout, default is 1800 seconds.
• --dice-args A string with further arguments to be passed to Dice.

To reproduce the experiments from [1], we provide some convenience scripts. We first go through the steps of reproducing data, then give some general usage rules. Throughout, we assume you use the Docker container.

First, inside the Docker container, set up the environment by executing:

eval $(opam env)

To easily execute all the commands in this section with a 100-second timeout, from the /opt/rubicon directory in the docker image execute:

./reference-scripts/scaling.sh
./reference-scripts/symbolic.sh

You can change the top line in scaling.sh to generate a different time-out. Together these commands can take hours to run. To speed things up, you can replace the timeouts in scaling.sh with your preferred timeout in seconds. We now go through these commands step by step.

The following commands each generate a CSV file that contains the data that is used to generate each figure. All experiments are run with a default timeout of 1800 seconds; if the time to run the experiment exceeds this amount then the time and final result will both be reported as -1.

To generate a CSV file for Figure 1c, please run:

python rubicon/regression.py --export-csv "fig1c.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add factory -H 10 -N 5 -N 9 -N 12 -N 13 -N 15 -N 17 -N 19

This will create a series of benchmark evaluations with horizon 10 (-H 10) and 8, 10, 13, 15, 17, and 19 parallel factories. This generates a file fig1c.csv which has the following contents when run with a 3-second timeout (note that precise numbers may vary due to differences in the running environment, but the important thing is that the relative trend of rubicon scaling to more states holds).

family, instance,dice-time,dice-result,storm-sparse-time,storm-sparse-result,storm-dd-time,storm-dd-result
factory,N=5;horizon=10,0.01,0.04459,0.02,0.04459,0.17,0.04459
factory,N=9;horizon=10,0.04,0.00054,0.19,0.00054,-1.00,-1.00000
factory,N=12;horizon=10,0.53,0.00003,-1.00,-1.00000,-1.00,-1.00000
...

• Note here that, for N=9 factories, storm using the dd option is timing out (since the result and time are both listed as -1).
• To compare this output with Figure 1c, the black curve lists dice-time, the red curve lists storm-sparse-time, and the blue curve lists storm-dd-time. We do not include in this repository the ability to reproduce the green prism curve; it is not a critical comparison since its performance is dominated by storm.
• If you want to export fig1c.csv from the Docker image, copy it into the /data directory which will place the file in the current working directory outside of the image.

Moving on to the other figures:

Figure 9a:

python rubicon/regression.py --export-csv "fig9a.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add weatherfactory -H 10 -N 9 -N 12 -N 15 -N 17

This generates a CSV of the following format (when run with a 3-second timeout):

family, instance,dice-time,dice-result,storm-sparse-time,storm-sparse-result,storm-dd-time,storm-dd-result
weatherfactory,N=9;horizon=10,0.15,0.00000,0.60,0.00000,-1.00,-1.00000
...

• In Figure 9, the black curve corresponds to dice-time, the green curve corresponds to storm-sparse-time, and the red curve corresponds to storm-dd-time.
• All the following subsequent commands follow the same output format.

Figure 9b:

python rubicon/regression.py --export-csv "fig9b.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 13 -H 10 -H 20 -H 30 -H 40

Figure 9c:

python rubicon/regression.py --export-csv "fig9c.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 13 -H 10 -H 20 -H 30 -H 40 --asym

Figure 9d:

python rubicon/regression.py --export-csv "fig9d.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 17 -H 10 -H 20 -H 30 -H 40

Figure 9e:

python rubicon/regression.py --export-csv "fig9e.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 17 -H 10 -H 20 -H 30 -H 40 --asym

Figure 9f:

python rubicon/regression.py --export-csv "fig9f.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 19 -H 10 -H 20 -H 30 -H 40

Figure 9g:

python rubicon/regression.py --export-csv "fig9g.csv" include-dice --cwd "/opt/rubicon" --cmd "dice" -TO 1800 include-storm --cmd "storm" -TO 1800 include-storm --cmd "storm" -TO 1800 --add herman -N 19 -H 10 -H 20 -H 30 -H 40 --asym

Table 1 (left column):

Inside /opt/rubicon execute ./reference-scripts/symbolic.sh, which will print something like the following output:

root@0eb42b351faa:/opt/rubicon# ./reference-scripts/symbolic.sh 
Making symbolic dice files
[WARNING] Running as root is not recommended
2021-04-28 15:59:57,239 - __main__ - Translating examples/factory/factory15-par.prism to factory-15-sym.dice
2021-04-28 15:59:57,365 - __main__ - Translating examples/factory/factory12-par.prism to factory-12-sym.dice
2021-04-28 15:59:57,490 - __main__ - Translating examples/herman/herman-13-random-parametric.prism to herman-13-sym.dice
2021-04-28 15:59:57,615 - __main__ - Translating examples/herman/herman-17-random-parametric.prism to herman-17-sym.dice
Done making dice files, running benchmarks
================================================================================
12 Factory Compilation time
================[ Total time ]================
0.177648067474
================================================================================
12 Factory Total WMC time
================[ Joint Distribution (Substituting 'examples/factory-params/factory-par-12-H=5.dice.0.eval') ]================
Value   Probability
(true, true)    0.
(true, false)   0.00177919660807
(false, true)   0.
(false, false)  0.998220803392

================[ Joint Distribution (Substituting 'examples/factory-params/factory-par-12-H=5.dice.1.eval') ]================
Value   Probability
(true, true)    0.
(true, false)   0.00270081926558
(false, true)   0.
(false, false)  0.997299180734

================[ Joint Distribution (Substituting 'examples/factory-params/factory-par-12-H=5.dice.2.eval') ]================
Value   Probability
(true, true)    0.
(true, false)   4.80748360904e-05
(false, true)   0.
(false, false)  0.999951925164

================[ Joint Distribution (Substituting 'examples/factory-params/factory-par-12-H=5.dice.3.eval') ]================
Value   Probability
(true, true)    0.
(true, false)   2.53134737218e-05
(false, true)   0.
(false, false)  0.999974686526

================[ Joint Distribution (Substituting 'examples/factory-params/factory-par-12-H=5.dice.4.eval') ]================
Value   Probability
(true, true)    0.
(true, false)   0.000160701728645
(false, true)   0.
(false, false)  0.999839298271

================[ Total time ]================
2.38292193413
================================================================================
15 Factory Compilation Time
================[ Total time ]================
2.58312606812
================================================================================
15 Factory Total WMC
...

To interpret this output and build the table:

• The "Rubicon build" sub-column is read off of the "Compilation Time" timing results. For instance, in the above, the "Factories 12 rubicon build time" is 0.177648067474.
• The "Rubicon WMC" time is retrieved by subtracting the total time by the compilation time and then dividing by 5. For instance, the "Factories 12 WMC Time" entry is computed as (2.38292193413 - 0.17776)/ 5 =0.441032387.

Note again that there may be slight differences in timings between these exact results and those in the paper due to differing environments.

Table 1 (middle column): From the following output of storm, we distilled the build and model checking times.

./reference-scripts/storm-sample-add.sh /opt/storm/build/ examples/ 1800

(Notice that we add a small example to test our setup). The 1800 refers to the timeout in seconds.

Table 1 (right column): From the following output of storm, we concluded all benchmarks timed out.

./reference-scripts/storm-solution-function.sh /opt/storm/build/ examples/ 1800

(Notice that we add a small example to test our setup). The 1800 refers to the timeout in seconds.

You can use our regression suite to generate many more tests.

python rubicon/regression.py brp -N 4 -N 8 -MAX 2 -MAX 3 -H 10 -H 20 

We refer to running python/regression.py --help for options.

If things ever break, be sure to check out the logfile rubicon-regression.log.

As the examples above exemplify: the script allows to configure the script to run Dice (from commandline) directly: A particularly helpful feature is the ability to only check whether the Dice can be parsed, which can be invoked with:

python rubicon/regression.py include-dice --cwd "/opt/rubicon" --cmd "dice" --only-parse weatherfactory -H 10 -H 15 -N 8 -N 10 

The docker container is built using the included Dockerfile. The container is based on an container for the probabilistic model checker as provided by the storm developers, see this documentation The container can be built by executing a command in the rubicon directory like:

docker build --tag rubicon:1.0 .

• [2] https://www.stormchecker.org
• [3] https://github.com/SHoltzen/dice/

• Q: I got a FileNotFoundError: [Errno 2] No such file or directory: 'dice' error!

  A: Please run eval $(opam env) and then try again.

• Q: How can I install things in the docker image?

  A: Use apt-get, for instance apt-get install vim

• Q: Help I got docker: Got permission denied while trying to connect to the Docker daemon socket

  A: Run docker using administrative rights (sudo)