SSL standalone.xml   Interaktion und
PortierbarkeitXML

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<!--  standalone.xml            KBMag documentation           Derek Holt -->
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<!--  Copyright (C) 1997-2017, Derek Holt.                               --> 
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<?xml version="1.0" encoding="UTF-8"?>

<Chapter ="chap-standalone">
<Heading>The stand-alone package</Heading>

<Index Key="stand-alone package">stand-alone package</Index> 

The &KBMAG; package contains &GAP; interfaces to many of java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 42
ating state automata (&fsa;) that are available in the
stand-alone.  We shall list these here, without giving much detail.
For more detail, the user could try lookingsource 
<File>gapFile>fsa4.<File>

<Section Label
<HeadingFunctions     automata/Heading>

<Index Key="finite state automata">finite state automata</Index> 

&fsa; are currently implemented as &GAP; records, as they were
previously in &GAP;3. This interface may be updated to the style of
&;  somestage.(that  abbreviation&;willbeusedfor
both singular and the plural.)
<P/>
fsa are  implemented as &GAP;records, as  were
the two components <C>type</C> and <C>size</C>, 
java.lang.StringIndexOutOfBoundsException: Range [17, 5) out of bounds for length 67
easiestpossibility  use 
type Csimple</C>, and then other java.lang.StringIndexOutOfBoundsException: Range [44, 44) out of bounds for length 38
There are several more complicated possibilities, which are used by
the other rewriting system functions. For example, there is the type
<C>identifiers</C>, for which fields <C>format</C> 
and <C>names</C> are necessary.
For example: 
<P/>
<Example>
<![CDATA[
gap> M := FreeMonoid( 3 );;
gap> alph := rec( type := "identifiers", size := 3,
>                 format := "dense", names := [M.1,M.2,M.3] );;
]]>
</Example>
defines a valid alphabet for an &fsa;.
The members of the alphabet are referred to as <C>letters</C>, and can be
represented either by a positive integer or by their name (usually
a generator of a free group or monoid) if they have one.
<P/>
The functions <Ref Func="ReductionAutomaton"/>,  
<Ref Func="WordAcceptor"/>,
<Ref Func="FirstWordDifferenceAutomaton"/The members thealphabet referredto  <><C,and  
<java.lang.StringIndexOutOfBoundsException: Range [9, 4) out of bounds for length 44
and <Ref java.lang.StringIndexOutOfBoundsException: Range [0, 13) out of bounds for length 4
java.lang.StringIndexOutOfBoundsException: Range [13, 9) out of bounds for length 50
Re Func/java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
functionFunc"/
or to read one  earliersectionsall return  fsa;.java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
In latter ,the  immediatelycall
<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 65
For ,running GAP java.lang.StringIndexOutOfBoundsException: Range [36, 35) out of bounds for length 54
<P/
mple
<[DATA
Example>
java.lang.StringIndexOutOfBoundsException: Range [2, 1) out of bounds for length 9
]
</Example>

<java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 3
   <Func Name=IsInitializedFSA 
     Arg="sa   
<Description>
 whether fsa;is arecord  valid java.lang.StringIndexOutOfBoundsException: Range [64, 62) out of bounds for length 69

<java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
<

<ManSection>a
   
<Description>
Description
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
a file=a >
/
/>
<java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<ManSectionjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
   <Arg "sa"  >java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
     Arg="alph > 
</Description
</ManSection>
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<P/>
The arguments of the following functions must be initialized &fsa;.
<P/>
</Description>
</ManSection>

<ection>
Func WriteFSA 
     Arg =fsa  >
<Description>
Displays  the <Func=DeterminizeFSA"/.
(In scription>
<
</java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0
</ManSectionArg=""/

<ManSection>
   <Name=IsDeterministicFSA 
     Arg = "fsa     Arg ="sa"/ 
<Description>
Tests whetherReturn, the records representing the  and state-java.lang.StringIndexOutOfBoundsException: Range [73, 74) out of bounds for length 73
 thebelow work only fordeterministic&;.
A deterministic &Returns the size of the alphabet of &fsa;.
be constructed with the function <Ref Func="DeterminizeFSA"/>.
<P/>
</Description>
</java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 4

<ManSection>
   <Func Name="AlphabetFSA" 
     ="sa"/
   <Func Name="StatesFSA"Description
      f"/ 
<java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 4
 , java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 73
of=f"/
<P/>
<Description
n

</Descriptio
   <=
     Arg =     
<>
Returns<Func Name=DenseDTableFSA"java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="of lists, where the <M, wherethe M></>th  in the <M><M>th inner list 
     Arg = "fsa"  /> 
   <Func Name="SizeOfAlphabetFSA" P/>
     Arg = "fsa</anSection>
<<>
java.lang.StringIndexOutOfBoundsException: Range [3, 1) out of bounds for length 31
</
</escription>
</ManSection>

<ManSection>
   <Func Name="   <Func Name="AcceptingStatesFSAa  of ,
     Arg = "fsa"  /> 
<Description>
Returns- list <C>e,]/> of  that java.lang.StringIndexOutOfBoundsException: Range [65, 62) out of bounds for length 75
</
</under letterletter number<>eM>.
</ManSection>

<ManSection>
   <FuncWecan also have<>e0/>, transitions  label
        =f"/> 
<</Descriptio
ManSection>
<P/>
</Description>
</ManSection>

<ManSection<unc ="argetDFA"
   <Func Name="Arg = "fsa e s
      fsa   adeterministic &fsa;, <M>e</M> should be a number or name
<escription
&fsa; must be The target of <M>s</M> under <java.lang.StringIndexOutOfBoundsException: Range [0, 31) out of bounds for length 4
>M-entrythe>s/-inneris
<Ref Func="TargetDFA"/>, calledjava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
<>

<

<   <Func NaSourcesFSA
   =java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 31
     Arg f" 
<Description>
Note M/>can  java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
where Func=java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 30
element[t/>  
from state number &;java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 78
under letter number <orword in   
We can also a  monoid. ofjava.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 70
(>/>)java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
<P/>
</Description>
</ManSection>

<ManSection>
   FuncName"argetDFA"
     Arg = "java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 23
<>
&fsaor a word in thealphabet ( casewhen thealphabetisdefined
of aletterofthe alphabet <M><>anumberof  state of &sa.
The target of <M>s</M> under <M>e</M
<P/>
<Description>
</ManSection

<>
   <Func <Func Name"
      Arg = "fsajava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
<Description>
Similar to java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
<P/java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
</Description>
</fromfsa. "java.lang.StringIndexOutOfBoundsException: Range [51, 46) out of bounds for length 85

<
   <Func 
     Arg = "fsa e s"  /> 
<Description>
Similar to <Ref Func="TargetsFSA"/>,  
transitionsMs/> nder <>e/  returned 
Note that <M>e</M> can also be zero here.Arg  "fsa "/>
<P/>
</escription>
</where &fsa; has <M>ns</M> states.

<ManSection java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 73
  java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 30
     Arg
<DescriptionAddLetterFSA" 
&fsa; must be a deterministic &fsa;, and <M>w</M> should be a list of integers
or a word in the alphabet (in the case when the alphabet is defined
from a free group or monoid). The target of java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 29
ned <>0/> no .
<P/>
</Description>
</ManSection>

<If the alphabet of &fsa; is defined over a free group orC><C the of thisfree  to
   <FuncName="
     Arg = "fsa w"  /> 
>
 a&; java.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 78
  (  java.lang.StringIndexOutOfBoundsException: Range [60, 59) out of bounds for length 67
afreegroupor.java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 72
java.lang.StringIndexOutOfBoundsException: Range [12, 3) out of bounds for length 22
<P/>
<>
<java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<ManSection>
   </java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
     ManSectionjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
<Description>
a -java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 77
<P/>
/java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
</ManSection>

<ManSection java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 75
   <Func Name="the new letter number <M>n^p</M>.
     Arg = "java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 4
<java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
Deletes the highest numbered Djava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
it &; RefFunc=">firsttodeletea java.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 85
<P/>
</Description>
</ManSection>

<ManSection>
   <java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 4
     </ManSection>
<java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Range [15, 2) out of bounds for length 52
where &fsa; has <M>ns</M> statesjava.lang.StringIndexOutOfBoundsException: Range [5, 1) out of bounds for length 27
java.lang.StringIndexOutOfBoundsException: Range [34, 3) out of bounds for length 73
the new state number <M>n <e<> there.
<>
</Description>
</ManSection>

<>
   <
     <ManSection
<DescriptionFunc Name=SetAcceptingFSA" 
Adds      Ar =fsflag"  / 
If theDescription>
<</>specifies the element of  free structure correspondingto
the new letter.
<P/>
</Description>
</ManSection>

<anSection>
   <Func Name="DeleteLetterFSA" 
     Arg = "fsa"  /> 
<Description>
java.lang.StringIndexOutOfBoundsException: Range [11, 7) out of bounds for length 76
from the alphabet of &fsa;. 
java.lang.StringIndexOutOfBoundsException: Range [12, 3) out of bounds for length 72
<P/>
</Description>
</java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 0

<ManSection="etInitialFSA"
   <Func Name Arg ="fsa s flag" /> 
      = "fsa p"  /> 
<Description>
<M>p</M> should be a permutation of <M>[1..na]</M>, where the alphabet of
&fsa; has <M>na<M>letters.
The letters are permuted, where the original letter number <M>n</M> becomes
the new letter number <M>ni java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 45
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="AddEdgeFSA" 
     Arg = java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 4
<java.lang.StringIndexOutOfBoundsException: Range [3, 1) out of bounds for length 32
Testsfsa ; is,whether all states can be
and letter <M>e</M>. 
If there is already fromthe initial statesjava.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="DeleteEdgeFSA" 
     Arg = "fsa e s t"  /> 
<Description>
  transition  &sa;  source <><M> target<></java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
and letter <M>e</M>, if there is one.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func =SetAcceptingFSA" 
     Arg = "fsa s flag"  /> 
<Description>
<C>flag</C/>
is made acceptingjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 12
<P/>
</Description>
</anSection>


   <Func Name="java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 11
    Arg = "/escription>
<Description>/anSection>
<C>flag</C> should be <C>true</C> or <C>false</C>, and state number <M>s</M> 
is made<ManSectionjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
<P/>
<java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
</ManSection>

<ManSection>
   <Func Name="IsAccessibleFSA" 
     Arg = "fsa" /> 
<Description>
Tests whether &fsa; is accessible; that is, whetheraccepting state cannot be reached, thus rendering it trim
reached from the initial states.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="AccessibleFSA" 
     Arg = "fsa" /> 
<Description>
Removes all inaccessible states from &fsa; thus rendering it accessible
without altering its language.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="IsTrimFSA" 
     Arg = "fsa" /> 
<Description>
Tests whether &fsa; is trim; that is, whether all states can be
reached from the initial states, and a final state can be reached from
all states.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="TrimFSA" 
     Arg = "fsa"</>
<Description>
emoves all inaccessible states from &fsa; and all states from which an
accepting state cannot be reached, thus rendering it trim
without altering its language.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="IsBFSFSA" 
     Arg = "fsa" /> 
<Description>
Tests whether &fsa; is in <C>bfs</C> (breadth-first-search) form; that is,
whether   <Func Name="IsBFSFSA" 
appear in ascending order if one scans the transition table first
by state number and then by alphabet number. Note that &fsa; must
be accessible for it to be     Arg = "sa"/>
<P/java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
</escription>
</ManSection>

<ManSection>
   <Func Name="BFSFSA" 
     Arg = "fsa" /> 
<Description>
Replaces &fsa; by one with the same language but in <C>bfs</C> form.
This can beuseful  comparing languages  two &;
Inappear   order  one  thetransition table first
are applied in turn to a deteministic &fsa;, 
thentheresulting transition table is
uniquely determined by the language of the &fsa;.
<P/>
</Description>
</ManSection>

<>
   <Func>
     Arg = "fsa" /> 
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        >
This onlyReplaces&  one the language  C><C .
If
<P/>
njava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
/java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<ManSection/java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
< =java.lang.StringIndexOutOfBoundsException: Range [30, 28) out of bounds for length 30
     =" minmax"  >
<Description>
The  in  language of &sa;of  M>l/M 
<M size ofthe java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 71
integers Esimple>alphabets java.lang.StringIndexOutOfBoundsException: Range [67, 68) out of bounds for length 67
inunderlying  orfor 
<E>identifiers</E>.
<P/>
</Description
</ManSection/Description>

</Section> 

<!-- -------------------------------

<Section Label="sec-ext-   <Func Name="LEnumerateDF 
<Heading>unctionscalling externalprograms/Heading>

<Index Key="external programs">external programs</Index> words the language  &sa  length<></>satisfying

The remaining &fsa; functions all call external programs from the
standalone.All them  RefFunc"" take only
deterministic &fsa; as input, and all of be of  <simple/>type  listsof
 .
</>

ManSection>
   <Func</>
fsa"/ 
<
eturns a deterministic &fsa;with thesame language as&;
<P/>
<Description
</

<<eadingFunctions external programs/eading>
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      ="fsa / 
<Description>
Returns a &fsa; with the same language as &fsa; and java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
 of java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
<P/>
standalone.All of  except RefFunc=DeterminizeFSA"/>  take only
</ManSection>

<ManSection>
   " 
     Arg = as .
<Description>
ReturnsManSectionjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
complement of that of &fsa;     Arg =fjava.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 20
<P/>
</>
</ManSection>

<ManSection>
   <Func Name=</>
     Arg = "fsa" /> 
<Description>
Returns a &fsa; whose language is <M>L^{*}</M>, where<M>L/M 
is thee of fsa;
<<ManSection>
</ManSection>

<ManSection>
   <Func Name="java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 0
     Arg = "fsa" /> 
<Description>
Returns &fsa;whose language consists of the reversed words in the language
of &fsa;.
     Arg ="fsa" / 
<escription>

<ManSection>
   <Func Name="ExistsFSA" 
     Arg = "fsa" /> 
<escription
&fsanumberof .
 &;  returnedthat  aword Mw_1 in^{*}/>
java.lang.StringIndexOutOfBoundsException: Range [6, 2) out of bounds for length 56
with java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</>
</Description>
</ManSection>

<ManSection>
    Name"SwapCoordsFSA" 
    Arg = "fsa" /java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
<escription>
&fsa; should be two-variable &fsa; on an alphabet <M>A</M>. 
 -variable fsa;on <></    accepts<>w_1w_2<M> 
if and</>
<P/>
</Description>
</<Description>

<ManSection>
   <anSectionjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
Arg="sa1 "/ 
<>
&;and&sa2   thesamealphabet.The returned &fsa; 
equalto the  of  of fsa1;and &fsa2;
<P<Descriptionjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
<< Name""
<java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<ManSection>
   <Func Name="OrFSA" 
Arg="sa1 fsa2"/>
<Description>
&  fsa2 musthave same alphabet.The  &sa;
java.lang.StringIndexOutOfBoundsException: Range [13, 8) out of bounds for length 58
</
</Description>
</ManSection>

<>
< Name=ConcatFSA 
     Arg =<escription>
<&fsa; shouldtwo- &sa;on   <></M> 
&sa1  &sa2;must have  same alphabet.Thereturned &fsa; accepts
words     word<>w_2 in^*<M 
languages of &fsa1; and &fsa2with M(w_2</M> in the language of &fsa;.
<P/>
<Description>
</ManSection>

<ManSection>
    Name"LanguagesEqualFSA" 
     Arg= fsa2"/ 
<Description>
&fsa1; and &<anSection
whether   <Func Name=SwapCoordsFSA"
returns <C>true<C> or C>false<C>
<<Desription>
</Description>
</ManSection>

<ManSection>
   <unc ="GrowthFSA" 
      = "fsa"/ 
<Description>
Returns <P/java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
This is<ManSection>
in itsTaylor  is equal to the number  wordsof  <><M 
in the accepted language of &sa.
<P/>
Ifthecoefficients in thisrational  are larger than about M>16000<Mjava.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
henstrange error messages will appear and <C>ail<C>will be returned.
<P/>
</Description>
</ManSection>

</Section> 

</Chapter>