GAP (PatternClass) - Chapter 10: Miscellaneous functions

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10 Miscellaneous functions
10.1 Automaton Manipulation
10.1-1 LoopFreeAut
10.1-2 LoopVertexFreeAut

### 10 Miscellaneous functions

This temporary chapter is dedicated to miscellaneous functions that are relevant to some specific ongoing research questions.

#### 10.1 Automaton Manipulation

##### 10.1-1 LoopFreeAut

`‣ LoopFreeAut`( aut ) | ( function )

Returns: An automaton without any loops of length 1.

`LoopFreeAut` builds the subautomaton of `aut` that does not contain any loops of length 1, except for the sink state.

    gap> a:=Automaton("det",4,3,[[2,4,3,3],[4,4,1,4],[3,1,2,4]],[1],[2]);
    < deterministic automaton on 3 letters with 4 states >
    gap> Display(a);
       |  1  2  3  4
    -----------------
     a |  2  4  3  3
     b |  4  4  1  4
     c |  3  1  2  4
    Initial state:   [ 1 ]
    Accepting state: [ 2 ]
    gap> b:=LoopFreeAut(a);
    < deterministic automaton on 3 letters with 5 states >
    gap> Display(b);
       |  1  2  3  4  5
    --------------------
     a |  2  4  5  3  5
     b |  4  4  1  5  5
     c |  3  1  2  5  5
    Initial state:   [ 1 ]
    Accepting state: [ 2 ]
    gap>

##### 10.1-2 LoopVertexFreeAut

`‣ LoopVertexFreeAut`( aut ) | ( function )

Returns: An automaton without any vertices that had loops of length 1.

`LoopVertexFreeAut` builds the subautomaton that does not contain the vertices and transitions of vertices in `aut` that have loops of length 1. The function minimalises and determinises the automaton before returning it, which might change the numbering on the vertices, but the returned automaton is isomorphic to the subautomaton of `aut`.

    gap> a:=Automaton("det",4,3,[[2,4,3,3],[4,4,1,4],[3,1,2,4]],[1],[2]);
    < deterministic automaton on 3 letters with 4 states >
    gap> Display(a);
       |  1  2  3  4
    -----------------
     a |  2  4  3  3
     b |  4  4  1  4
     c |  3  1  2  4
    Initial state:   [ 1 ]
    Accepting state: [ 2 ]
    gap> b:=LoopVertexFreeAut(a);
    < deterministic automaton on 3 letters with 3 states >
    gap> Display(b);
       |  1  2  3
    --------------
     a |  2  2  1
     b |  2  2  2
     c |  3  2  2
    Initial state:   [ 3 ]
    Accepting state: [ 1 ]
    gap>

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