Created: 2011-07-15 06:29
Updated: 2019-03-01 21:12
License: gpl-3.0

libVATA - A C++ library for efficient manipulation with non-deterministic finite (tree) automata

Build Status


libvata is a highly optimised non-deterministic finite tree automata library. The main focus of the library is to be used in formal verification, but we believe that it can be effectively used in other domains as well. There are two supported encoding of tree automata supported by the library: explicit and semi-symbolic. The semi-symbolic encoding uses multi-terminal binary decision diagrams (MTBDDs) for storing the transition table of the automaton. It is intended to be used for automata with large alphabets, which appear in several formal verification techniques using tree automata, e.g., in the context of verification of programs with complex dynamic data structures, such as the abstract regular tree model checking (ARTMC), or decision procedures of several logics, such as the monadic second-order logic (MSO) or the weak second-order theory of k successors (WSkS). Moreover, the library can also be used for finite word automata (which are, basically, unary trees).


It is highly recommended to use a recent Linux distribution for experimenting with libvata (the library was thoroughly tested on the Debian GNU/Linux distribution). In order to be able to download the library, you need to have the git version control system installed.

To download the library, run

  $ git clone git://

This creates a local independent copy of the source code repository.


In order to compile the library and the command-line interface to the library the following packages need to be installed on your system:

  git (>=
  cmake (>= 2.8.2)
  gcc (>= 4.8.0)
  libboost-filesystem-dev (>= 1.54.0)
  libboost-system-dev (>= 1.54.0)
  libboost-test-dev (>= 1.54.0)


For compiling the source code of the library and the command-line interface with compiler optimisations turned on, issue the following command in the root directory of the library:

  $ make release

In order to compile the library into a form suitable for debugging (i.e., with optimisations turned off and some additional runtime checks enabled, issue the following command:

  $ make debug

It is recommended to run

  $ make test

from the repository's root directory after compiling the code to run several unit tests and check that the compiled code passes them all.

Compiling with LLVM (experimental)

Run either

  $ CXX=clang++ make release


  $ CXX=clang++ make debug

Command-Line Interface

The compiled command-line interface is located in


The up-to-date list of supported operations and arguments is available through

  $ ./vata help


Loading an automaton

In order to load and dump (to, e.g., check that the format of an input file is correct) automaton in file 'aut_file', run

  $ ./vata load aut_file

Union of automata

To create an automaton that accepts a language which is the union of languages of automata from files 'aut_file1' and 'aut_file2', run

  $ ./vata union 'aut_file1' 'aut_file2'

Using the VATA API

See the 'examples/' directory for examples of using the library's API.

See 'cli/' for a production wrapper over the library.

Running Performance Tests

In order to run performance tests of various tree automata inclusion checking algorithms, there exists a bash script that executes them and collects the results. To run the standard set of experiments, execute

  $ tests/ automata/artmc_timbuk 30


  • tests/ ... path to the script executable, the script also contains the list of algorithms to evaluate; for list of all algorithms, see tests/

  • automata/artmc_timbuk ... path to the directory containing files with tree automata; the script runs the inclusion test for each pair of automata in the directory

  • 30 ... timeout for each test (in seconds)

Input Format

libvata so far supports only the Timbuk format of tree automata. The format is specified by the following grammar with the start symbol :

  <file>            : 'Ops' <label_list> <automaton>

  <label_list>      : <label_decl> <label_decl> ... // a list of label declarations

  <label_decl>      : string ':' int // a symbol declaration (the name and the arity)

  <automaton>       : 'Automaton' string 'States' <state_list> 'Final States' <state_list> 'Transitions' <transition_list>

  <state_list>      : <state> <state> ... // a list of states

  <state>           : string // the name of a state

  <transition_list> : <transition> <transition> ... // a list of transitions

  <transition>      : <label> '(' <state> ',' <state> ',' ... ')' '->' <state> // a transition

  <label>           : string // the name of a label

An example could look like this:

Ops a:0 b:1 c:2

Automaton A
States q0 q1 q2
Final States q2 
a() -> q0
b(q0) -> q1
c(q1, q1) -> q1
c(q1, q1) -> q2
c(q2, q2) -> q2


This work was supported by the Czech Science Foundation (within projects P103/10/0306 and 102/09/H042), the Czech Ministry of Education (projects COST OC10009 and MSM 0021630528), and the EU/Czech IT4Innovations Centre of Excellence project CZ.1.05/1.1.00/02.0070.


If you have further questions, do not hesitate to contact the authors:

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