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<!--  standalone.xml            KBMag documentation           Derek Holt -->
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<!--  Copyright (C) 1997-2017, Derek Holt.                               --> 
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java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76

<Label>HeadingThe java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 42
<Heading>The stand-alone package</Heading>

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

The &KBMAG; package contains &GAP; interfaces to many of the functions
for manipulating finite state automata (&fsa;) that are available in the
stand-for manipul finite
,theuser couldtry looking in the sourcefile
<gap/./.

<Heading>for manipulatingfinitestate </Heading
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<&GAP4at stage (ote theabbreviation fsa;will be  

&;arecurrently  ,astheyjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
previously in &where <C>type</C> is a string, and <C>size</C> a positive integer. 
&GAP;4 at someThe  possibilityis to  the
both<></C, no record components are necessary.
<P/>
The alphabet of an &fsa; is itself a record that must contain at least
the two components <C>type</C> and <C>size</C>, 
where <C>type</C> is a string, and <C>size</C> a positive integer. 
The easiest possibility is to use the
type <C>simple</C>, and then no other record components are necessary.
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 validjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
Theof  alphabetare  toas <letters<C> andcan be
Ref Func="SecondWordDifferenceAutomaton"/> 
a generator of a free group or monoid) if they have one.
<P/>
The functions <Ref Func="ReductionAutomaton"/>,  
<Ref Func="mentioned in earlier sections all return a &fsa;. 
<f Func="FirstWordDifferenceAutomaton"/>, 
<Ref Func="SecondWordDifferenceAutomaton"/> 
and <Ref Func="a &fsa; are to use the  <Ref ="FSA">  
mentioned in  allreturna&; 
The other possibilities for the user to construct
aInthe case theuser must   
Ref Func="InitializeFSA"/> on the record that has been read example running&GAP;from the package directory:
<PP/>
<<Example>
For <!CDATA[
<P/>
<>
<![CDATA[
gap> Read( "standalone/fsa_data/fsa_2" ]>
gap
]]>
</Example>

<ManSection>
   <Func ="
       fsa"/> 
<
Tests whether&;isa describinga  initialized &fsa;.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func
     Arg<Description>
<Description>
Initializes a record representing a &fsa; that has been read in from
a file.
<>
</
<Description>

<ManSection>
   <Func Name="FSA" 
     Arg = "lph"/ 
<<P>
Returns</escription
an initial/ManSection>
<P/>
The arguments of the following functions must be initialized &fsa;.
<P/>
</Description>
</>

<ManSection>
   <Func Name="WriteFSA" 
      = "  / 
<Description>
Displays &fsa; nicely. 
(In aArg ="alph"/ 
<P/>
</Description>
/ManSection

<ManSection>
   <Func Name="java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 4
     Arg = "java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 4
<Description>
ManS
   <Name=""
A deterministic     Arg =""/ 
beconstructedwith function Ref "">
<P/>
<scription>
<P/>

<ManSection>
   <Func Name="AlphabetFSA" 
       fsa">
   <FuncFunc Name"sDeterministicFSA"
      " >
<Description>
 respectively,alphabet state-et
of &fsa;.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="NumberOfStatesFSA" 
     Arg = "fsa"  /> 
<Description>
Returns the number of states of &fsa;.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="NumberOfLettersFSA" 
     Arg = "fsa"  /> 
   <Func Name="SizeOfAlphabetFSA" 
     Arg = "fsa"  /> 
<Many of functions  work only for deterministic &sa.
java.lang.StringIndexOutOfBoundsException: Range [23, 7) out of bounds for length 42
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
     ArgArg ="">
<>
Returns the listArg = "sa /> 
<P/>
</Description>
</ManSection>

<ManSection>
   <Return,respectively,the records representing the alphabet and state-set
     Arg ="sa  / 
<Description/Description>
Returns the>
<P/>
</>
</ManSection>   <unc Name"NumberOfStatesFSA" 

<Description>
    =DenseDTableFSA" 
      Arg = "fsa" /> 
<Description>
&fsa; java.lang.StringIndexOutOfBoundsException: Range [0, 10) out of bounds for length 4
of lists where the<>eM-entryin <><> inneris
<Ref Func="TargetDFA"/>, java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 21
<P/>
</Description>
</anSection

<ManSection
   <Func Name="SparseTableFSA" 
     Arg = "fsa" /></
<Description>/java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
as list lists
where each entry java.lang.StringIndexOutOfBoundsException: Range [5, 1) out of bounds for length 21
o-element>et<C of integersrepresents a transition
from state number <M>s</P>
under letternumber M>/>java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
We  also  Me=0<M,representing with nolabel
(<   Arg="sa" >
<P/>
<n>
</java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<ManSection>
   <unc Name"argetDFA 
     "  /> 
<Description>
&;mustbea java.lang.StringIndexOutOfBoundsException: Range [31, 29) out of bounds for length 72
of a letter of the alphabet, and <M>s</M> a number of a state of &fsa;<>
java.lang.StringIndexOutOfBoundsException: Range [19, 3) out of bounds for length 85
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="TargetsFSA" 
      Arg = "fsa he <M></M>-h  in  <M></>-th inner list is
<Description>
Similar to <Ref Func="TargetDFA"/>,  but &fsa; need not be deterministic, and a list
of targets is returned.
<P/>
</Description>/Description>
</ManSection>

<
   me="" 
     Arg = "   <Func Name"SparseTableFSA" 
<Description>
Similar to <Ref Func="TargetsFSA"/>,  
but the list      Arg = "fsa = "sa"/>
Note that <M>e<M> can alsobe zero here.
<P/>
</Description>
</ManSection>

<ManSection>
   < Name=WordTargetDFA" 
     Arg = "fsa w"  /> 
<is a two- list <C>[e,]<C of integers that represents a transition
&sa; must be  must be a deterministic &fsa;, and <M>w</M> should be a list of integers
or a  in the alphabet(in the case when the alphabet is defined
from a free group or ). The target of the initial state of &fsa;
under <M>w</M> is returned, or <M(M\epsilon<M> transitions).
<P/>
</Description>
</java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 4


   <Func   < =TargetDFA 
"sa w"  /> 
<Description>
&fsa; must be a deterministic &Description>>
oraword in  alphabet(nthe  when the  is 
fromof a  of thealphabet,and <M><M>a  of a  of&sa;java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71

<P/>
</Description>/Description>
/>

<ManSectionManSection
   ="AddStateFSA"
     Arg = "fsa" /> 
<Description>
Adds an extra non-accepting state to &fsa; with no transitions to or from it.
<P/>
<n>
</ManSection>

<ManSection>
   <Func   targets is returned.
     Arg = "fsa" /> 
<Description>
Deletes the highest numbered state together with all transitions to and from
it  &fsa;.Use<Ref Func="ermuteStatesFSA"/>  first to delete a different state.
<P/>
/Description>>
</ManSection>

<ManSection>
   <Func Name="but the list of sources of  to <M>s</M> <>e<M>is . 
     ="fsap /> 
<Description>
<M>/escription>
java.lang.StringIndexOutOfBoundsException: Range [11, 5) out of bounds for length 33
The states arepermuted, where the original state number <M>n</M> becomes
the new state number <M>n^p</M>.
<  <Func Name="WordTargetDFA" 
</Description>
</ManSection>

<ManSection>
e="java.lang.StringIndexOutOfBoundsException: Range [67, 29) out of bounds for length 67
     Arg = "fsa [,name]"  /> 
<Description>
Adds an extra letter to,or M0</> if there is no such target.
java.lang.StringIndexOutOfBoundsException: Range [6, 2) out of bounds for length 69
<C>name</>specifies the element thisthis free structure correspondingFunc Name=IsAcceptedWordDFA"
the new letter.
<P/>
</&fsa;must be a deterministic &fsa, and <M>w</M> should be a list of integers
</ManSectionthe alphabet (n the case when the alphabet is defined

<ManSection>
   <Func Name="DeleteLetterFSAfrom a free group or monoid) This function tests whether <M>w</M> is in
     the language of &fsa;.
<Description>
Deletes the highest numbered/Description
from <ManSection>
Use <Ref Func=
P/>
</Description>
</ManSection>

<>
   <Func Name="PermuteLettersFSA" 
     Arg = "fsa p"  /> 
<Adds an extrnon-ccepting state to &fsa; with no transitions to or from it.
<M>p<Description>
&fsa; has <M>na</M> letters.
The letters are permuted, where the original letter number <M>n</M> becomes
java.lang.StringIndexOutOfBoundsException: Range [28, 3) out of bounds for length 33
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="AddEdgeFSA" 
     Arg = "fsa e s t"  /> 
<escription>
Adds an extra transition to &fsa; with source <M>s</M>it from  fsa; Use <Ref Func=PermuteStatesFSA/  first  delete a differentstate.
and letterjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
If there is already such a transition, then this function does nothing.
<P/>
</Description>
</>

<ManSection>
   <Func M>p</M> should be a permutation of <M>[1..ns]</M>, 
     Arg = "fsa e s t"  /> 
<Description>
Deletes the transition from &The states are permuted, where the original state number <M>n</M> becomes
and letter <>e<M, if  is one.
<P/>
<</java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
</ManSection

<
   <Name"etAcceptingFSA
     g="sa  "  / 
<escription
<C>C>nameC theof this  java.lang.StringIndexOutOfBoundsException: Range [73, 74) out of bounds for length 73
isMjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 12
<P/>
</Deletes the highest numbered letter together with all associated transitions
</Use <Ref Func="PermuteLettersFSA"/>  first to delete

<ManSection>
me" 
    =  "/> 
<Arg="java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 23
<C>flag</C> should be <&fsa; has <M>na</M> lettna/>java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 28
is made initial 
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="IsAccessibleFSA" 
     Arg = "fsa" /> 
<Description>
Tests whether &; is accessible;that  java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 69
reached theinitial .
<P/>
</Description>
</ManSection>

<ManSection>
   <ManSectionjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
     Arg = "fsa" /> 
<Deletesthe transitionfrom&;with Ms/>  Mt</>
Removes all inaccessible states from &fsa; thus rendering it accessible
without altering java.lang.StringIndexOutOfBoundsException: Range [0, 20) out of bounds for length 4
<P< Name="java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
</Description>
<ManSection

<ManSection>
   <Func Name="IsTrimFSA" 
     Arg = "fsa" /> 
<Description>
Tests whether &fsaManSection>
reached from
all states.
<P/>
D>
/java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<>
   <Func Name="TrimFSA" 
     Arg = "fsa" /<Description>
<Description>
Removes all inaccessible states from &fsa; and all states from which an
java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 57
java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0
<
/
<java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 71

<java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 0
   java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 25
      "">
<Description>P>
Tests whether &fsa; is in <C>bfs</C> (breadthDjava.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
whether the initial statescan be usefulfor the languagesof two &fsa;
appear inascending order ifscans java.lang.StringIndexOutOfBoundsException: Range [54, 53) out of bounds for length 65
by  java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 38
be accessibleManSection
<P/>
ption>
</ManSection>

<ManSection>
   <Func Name="BFSFSA" 
     Arg="fsa"/>
<Description>
 &sa;by  with same  but in<C>fs/>form
This can be not, then <Ref Func="TrimFSA"/>  must be called first.
In fact <Ref>
are applied in turn to a deteministic &fsa;, 
then<ManSection>
uniquely determined by the language of the &fsa;.
<P/>
</escription>
</ManSection>

<ManSection>
   <Func Name=   FuncName"LEnumerateDFA" 
     Arg = "fsa     Arg  "fsa max"  / 
<Description>Thewords inthelanguage of &sa length <>l<M>satisfying
esize of  accetedlanguage of &fsa;, which must be deterministic.
This be lists of integers, for<>simple</E type , of lists of
If not, then <Ref Func="TrimFSA"/>  must be calledwords  the underlying free group or monoid  alphabetsof type
/>
<
</java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
A"
     Arg<>   <Heading
<java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
he inoff;of  Ml/>
<M>min \le   ofexcept< =DeterminizeFSA"> takejava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
be lists  integers,for<>simple<E type alphabets,of  of
words in the underlying as output.
<<P>
<P/<
<Description
</     Arg = " >

R   &fsa;  language  fsa;

<!-- -----<>

<
<> calling external</eading>

<Index Key="external programs">external programsArg="fsa"/java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20

The remaining &fsa; functions all call external programs from thenumber ofstates.
  them< "java.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 70
deterministic &<Func Name="NotFSA
asoutput
<P/>

<>
   <Func Name="DeterminizeFSA" 
     Arg="sa" /> 
<Description>
Descriptionjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
<> M<>
</ languagof&.
/java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13

<
   < a& java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 77
       >
Djava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
Returns a &<>
number states
<P/Anfsais accepts a <>\ A{*}<M 
</if and only if there exists a word <M>w_2 \in A^{*}</M> 
</ManSection>

<ManSection>
   <FuncPjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
        <Func= 
<Arg= fsa > 
Returns a &fsa; with the Djava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
complement of that Atwovariable&; <A/>isreturned that accepts M(,)/>
Pjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
/Description>
</ManSection>

<>
   <Func Name="StarFSA" 
       ffsa2 >
<Description
&fsa1  &;musthave  . returned&;has
language   theintersectionthoseof &  &;
<>
</ManSection>

<ManSection>
   Func =ReverseFSA 
     Arg = "fsa" <ManSection>
<Description>
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
of &fsa      ="sa1  >
</&fsa1and&;must  the.Thereturned&;has
</language equal to the union of those of &fsa1; and &fsa2;P>

<ManSection>
   <ManSection
   Func ="
<>
 be variable &sa;analphabet <A/M>
&;and f the . java.lang.StringIndexOutOfBoundsException: Range [60, 59) out of bounds for length 73
ifand only if thereexists a M>w_2\ A{}/>
<>w_1,)</> injava.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 47
/java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
</<Func= 
</     Arg =   "fsa1  >

M>
   Func" 
     Arg = true/><>/>
cjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
&<Name
A twoArg = "fsa >
if <>
<P>
</Description>
</ManSection>

<
   <Func Name="AndFSA" 
     Arg = "fsa1 fsa2" /> 
<in its Taylor expansiontoof lengthMn/>
&fsa1; theoff;
language equal   functionthan<16000/>
<P/>
</Descriptiont  and<>/>be 
</ManSection>

<ManSectionjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
   <Func
     Arg = "fsa1 fsa2"  /> 
<Description>
&fsa1; and &fsa2; must have the same alphabet. The returned &fsa; has
language equal to the union of those of &fsa1; and &fsa2;.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="ConcatFSA" 
     Arg = "fsa1 fsa2"  /> 
<Description>
&fsa1; and &fsa2; must have the same alphabet. The returned &fsa; accepts
words of the form <M>w_1w_2</M>, where <M>w_1</M> and <M>w_2</M> are in the 
languages of &fsa1; and &fsa2;, respectively.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="LanguagesEqualFSA" 
     Arg = "fsa1 fsa2" /> 
<Description>
&fsa1; and &fsa2; must have the same alphabet. This function tests
whether the languages of &fsa1; and &fsa2; are equal, and
returns <C>true</C> or <C>false</C>.
<P/>
</Description>
</ManSection>

<ManSection>
   <Func Name="GrowthFSA" 
     Arg = "fsa" /> 
<Description>
Returns the growth function of &fsa;. 
This is a rational function, of which the the coefficient of <M>x^n</M> 
in its Taylor expansion is equal to the number of words of length <M>n</M> 
in the accepted language of &fsa;.
<P/>
If the coefficients in this rational function are larger than about <M>16000</M>
then strange error messages will appear and <C>fail</C> will be returned.
<P/>
</Description>
</ManSection>

</Section> 

</Chapter>