## Event-based language equivalence check

The language equivalence check verifies whether two automata produce the same language, that is, at every point they are marked in the same way and can produce the same events. Note that even automata with a different number of locations or edges can be language equivalent.

All reachable locations of the automata are checked. In particular, it also checks locations that are outside the marked behavior (that is, reachable locations that are not marked and are not on a path to a marked location). To avoid false positives, you may want to ensure that both automata are trim.

One practical application is to verify whether a manually created supervisor is equivalent to an automatically generated one. If they are not, a counter example is produced.

The tool takes a CIF file containing exactly two automata, that must be deterministic, have the same alphabet, and have an initial location. In addition, the general event-based restrictions apply as well.

The language equivalence check tool can produce three different results:

- The output stating `Automata have the same language` when the two automata are language equivalent.

- The output stating `Automata have a different language` when an event can be performed in a location in one automaton, while from the equivalent location in the other automaton the same event cannot be performed.

- The output stating `Automata have a different language` when a location in one automaton is marked, while the equivalent location in the other automaton is not marked.

In the last two cases, the equivalent location is derived by walking from the initial location to the location of interest in both automata using the same sequence of events. When two automata are not language equivalent, a counter example is produced that shows the sequence of events to reach the equivalent locations.

### Starting the language equivalence check tool

The tool can be started in the following ways:

- In Eclipse, right click a `.cif` or `.cifx` file in the Project Explorer tab or Package Explorer tab and choose CIF synthesis tools Event-based synthesis tools Apply language equivalence check….

- In Eclipse, right click an open text editor for a `.cif` or `.cifx` file and choose CIF synthesis tools Event-based synthesis tools Apply language equivalence check….

- Use the `ciflngeqv` tool in a ToolDef script. See the scripting documentation and tools overview page for details.

- Use the `ciflngeqv` command line tool.

### Options

Besides the general application options, this application has the following options:

- Input file: The absolute or relative local file system path to the input CIF specification.