Logo Relational Kleene Lattices

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Software : Kleenelattices

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Kleenelattices is composed of libraries and tools written in OCaml to compare identity-free regular expressions with intersection.

The webpage dedidated to this is located here : link. You will find there links to download the sources, access the github repository or look up the documentation.

Some online applications are also available below.

Equation checker

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How to use this :

Write down equations in the left-hand side fields of the applet, and see their validity just to their right (a green tick meaning yes and a red cross meaning no). The rightmost button allow you to see more details, and to hide them afterwards.

Equations should be entered like this: <expr1> <cmp> <expr2>.

An expression can use strings as variables/letters, and the operations:

  • <expr1> | <expr2>: the set union
  • <expr1> & <expr2>: the set intersection
  • <expr1> . <expr2>: the composition of relations
  • <expr1>+: the transitive closure of a relation.
  • <expr1>{int} : the iteration of a relation. For instance, (a.b){3} is a shorthand for (a.b).(a.b).(a.b).

You can also use brackets (...). The valid comparaisons <cmp> are:

  • <=: loose inclusion
  • >=: converse of the loose inclusion
  • <: strict inclusion
  • >: converse of the strict inclusion
  • =: equality
  • =/=: negation of the equality
  • <>: means that the two expressions are incomparable, i.e. neither one of them is included in the other.

For instance, (a|b)+.C & d < d & a.b.C & (d|a) is an acceptable equation.

Automaton visualizer

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Details of the resolution of an equation

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