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Monitoring Refinement via Symbolic Reasoning

This project aims to develop efficient monitoring algorithms for concurrent data structures, e.g., locks, semaphores, atomic registers, stacks, queues.


This project is written in Ruby, and works “out of the box” without compilation nor installation, though does require a Ruby interpreter. Simply clone this repository, configure accordingly, and proceed to Usage instructions.

git clone

Below we provide instructions for configuration with your native Ruby installation, as well as alternative instructions for using a preconfigured virtual environment.

Configuration with Native Ruby Installation

In principle, this project works “out of the box” with the latest Ruby interpreters an a couple of supplementary “gems”. So is our experience with OS X and Linux, though we have not tested on Windows.


  • Ruby, version 2.0.0 or greater.
  • The ffi and os Ruby gems, installed via gem install ffi os.

Note This project also uses Z3 as a shared library. For convenience we provide the Z3 shared library prebuilt for 64bit OS X (Yosemite), 64bit Linux (OpenSUSE), and Windows in the xxx/ directory. Dependence on the platforms on which it was built is unclear. In the case that you encounter problems involving FFI or Z3, try to obtain Z3 on your own, and include the appropriate libz3.{dylib,so,dll} in your LIBRARY_PATH.

Preconfigured Virtual Environment

Alternatively, this project can be run in a preconfigured virtual machine using VirtualBox and Vagrant. Both are available for a wide range of systems, with great installation support.



First, start Vagrant in this project’s root directory (containing Vagrantfile):

vagrant up

This can take a few minutes the first time around, since it includes the download of a virtual machine image. When this step finishes, our virtual machine should be up and running — verify this with the vagrant status command. Open a shell to the running virtual machine via ssh:

vagrant ssh

and follow the Usage instructions below. When finished, simply close the SSH session, and halt, suspend, or destroy the virtual machine:

vagrant destroy


Files in this project are organized according to the following directory structure.

  • bin/ contains executable ruby programs:

    • logchecker.rb for checking history logs,
    • loggenerator.rb for generating history logs,
    • report.rb for generating benchmarking reports, and
    • experiments.rb for generating experimental data.
  • data/ contains various data:

    • histories/ contains history logs,
      • generated/ contains history logs generated from actual executions,
      • simple/ contains hand-crafted history logs,
    • reports/ contains reports benchmarking the performance of each algorithm,
    • experiments/ contains empirical measurements, and
    • plots/ contains visualizations of empirical measurements.
  • lib/ contains the source code of the checking algorithms.

  • pldi-2015-submission.pdf is a research paper accepted to PLDI 2015.

  • xxx/ contains prebuilt external shared-libraries for OS X, Windows, and Linux.


The logchecker.rb program checks whether an input history violates it’s corresponding object specification, via one of various algorithms. This program is invoked as follows:

./bin/logchecker.rb data/histories/simple/lifo-violation-dhk-2.log -a symbolic -v

This command runs the “symbolic” checking algorithm on the lifo-violation-dhk-2.log history. See History Input Format, below, for a description of the input format to logchecker.rb.

To see the list of options to logchecker.rb, run

./bin/logchecker.rb --help

An input history file is mandatory. The checking algorithm is given by the option -a/--algorithm. Valid choices include enumerate, symbolic, saturate, and counting.

When the “enumerate” and “symbolic” algorithms are used, the -c/--[no-]completion flag enables/disables the enumeration of history completions prior to the enumeration of linearizations. When the “symbolic” algorithm is used, the -i/--[no-]incremental flag enables/disables incremental assertions to the underlying theorem prover. For all algorithms, the -r/--[no-]remove-obsolete flag performs the match-removal optimization to remove operations deemed obsolete.

When the “counting” algorithm is used, the interval bound is specified via the -b/--interval-bound option — see Tractable Refinement Checking for Concurrent Objects for background on approximating refinement checking via interval bounding.

Generating History Logs

The loggenerator.rb program was used to generate the history logs in the histories/generated directory by pseudo-random execution of various objects from the Scal High-Performance Multicore-Scalable Computing suite. This program depends on an external library which is not currently included in this project, and is thus currently unusable. However, any available means of generating valid history log files, or simply using the pre-recorded histories in the data/histories directory, is compatible with the logchecker.rb program.

Benchmarking Reports

To generate reports benchmarking the performance of various algorithms with various parameters on the many history logs included in this project, run


The rightmost column v indicates whether a violation was discovered in the given history by the given algorithm: indicates “yes”, and - no. In case the given algorithm exceeds the given timeout, the value in the steps and time columns are marked with an asterisk. The default timeout is 5 seconds, and is adjustable via the --timeout option. To see the list of options to report.rb, run

./bin/report.rb --help

Previous runs of report.rb are logged in the data/reports directory.

Empirical Data

The empirical data used in the publication of this work is generated via the experiments.rb program. Results are stored in tab-separated-values (TSV) format in the data/experiments directory. Visualizations of this data are stored in the data/plots directory. The file data/plots/plot.html renders the data in a web browser, and is known to work with Safari.

History Input Format

The input to the history-checking algorithms is a text file specifying the execution history of an object via ordered method call and return actions. Each action must appear on a separate line. Call actions have the format

[ID] call MMM(V1, V2, …)

where ID is an operation identifier, MMM is a method name, and V1, V2, … is a possibly-empty sequence of argument values. Return actions have the format

[ID] return V1, V2, …

where ID is an operation identifier, and V1, V2, … is a possibly-empty sequence of return values. Each operation identifier may appear in at most 2 actions — one call and one return — and each identifiers appearing in a return action must appear in some prior call action. Lines beginning with # are ignored. For example, the following the history

[1] call push(a)
[2] call push(b)
[2] return
[3] call pop
[3] return a

is the concurrent history of a stack data structure, where the values a and b are pushed concurrently — operations 1 and 2 overlap — and the value a is popped while operation 1 is still pending — the return action of operation 1 has not occurred. Drawn as intervals spanned by the # symbol, this corresponds to the history

[1] push(a)*  ###
[2] push(b)   #
[3] pop => a    #

where the * symbol indicates that operation 1 is pending.

The directory data/histories contains many other example histories.

Note currently only support for atomic stack-based and queue-based collections has been implemented. To support additional classes of objects, their logical theories and matching functions must be added to lib/theories.rb and lib/matching.rb.

Note currently we assume that each history contains one of the following lines:

# @object atomic-stack
# @object atomic-queue

and uses only one of the following method name pairs: add/rem, put/get, push/pop, enqueue/dequeue. When in doubt, just follow the examples contained in data/histories.