Related Documents |
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Equation checker |
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Write an equation in the input field of the applet, and see its validity just to the right (a green tick meaning yes and a red cross meaning no).
Equations should be entered like this:
<expr1> <cmp> <expr2>
.
An expression can use strings as variables/letters, and the operations:
0
: the empty relation1
: the identity relation<expr1> | <expr2>
: the set
union<expr1> . <expr2>
: the
composition of relations<expr1>~
: the converse of a relation<expr1>*
: the reflexive transitive closure of a
relation.<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 (...)
. For
letters/variables, you may use a'
instead
of a~
. 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,
((1|a'|b)+|C)~.a=/=0
is an acceptable equation.
Automata builder |
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Simply input an automaton in the text box, choose from one of the constructions on the left scroll box, and click "Build" to generate the automaton and its closure.
An automaton is specified through the following syntax:
initial : <list of initial states separated by spaces> final : <list of final states separated by spaces> <source> -- <label> --> <target> <source> -- <label> --> <target> ...
See below for an example.
The KAC suite |
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