## com.saxonica.fsa
Class FiniteStateMachine

    java.lang.Object
      com.saxonica.fsa.FiniteStateMachine

    public class FiniteStateMachine

extends java.lang.Object

Class representing a finite state machine, as a collection of states with transitions between them. The finite state machine allows states with counters. The static machine created by the schema compiler contains states of type AutomatonState; these may have a minOccurs and maxOccurs value. When such a state is entered at validation time, a CountingState is dynamically created that contains a pointer to the fixed AutomatonState plus an integer counter. Any transition that goes from the state to itself causes a new CountingState to be created with an incremented value of the counter (provided it does not exceed the maxOccurs()); any transition to a different state causes the counter to be checked against the minOccurs value.

Constructor Summary
`FiniteStateMachine(boolean determinized)` Create a finite state machine

Method Summary
`void` `allocateStateNumber(AutomatonState state)` Allocate a unique number to a state, and index the state from the FSM
`static NonDeterminizedState` `compileParticle(SchemaCompiler compiler, Particle particle, NonDeterminizedState endState, UserComplexType subjectType, FiniteStateMachine machine)` Static method to translate a particle to a Finite State Automaton, returning the start state of the FSA.
`static FiniteStateMachine` `determinize(FiniteStateMachine nfsa)` Determinize the finite state machine: that is, ensure that there are no ambiguous transitions from this state.
`void` `display()` Display the finite state machine.
`AutomatonState` `getInitialState()` Get the initial state of this finite state machine
`int` `getNumberOfStates()` Determine the number of states in this finite state machine
`AutomatonState` `getState(int number)` Get the state with a given unique state number
`void` `serialize(SchemaModelSerializer serializer)` Output a reppresentation of this finite state machine
`void` `setInitialState(AutomatonState initialState)` Set the initial state of this finite state machine
`static java.lang.String` `subsumesMachine(FiniteStateMachine base, FiniteStateMachine sub, SchemaCompiler compiler)` Test whether one finite state machine subsumes another FSM: that is, whether for each path through the second FSM, there is a corresponding path through the first FSM.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### FiniteStateMachine

    public FiniteStateMachine(boolean determinized)

  Create a finite state machine

  Parameters:
    `determinized` - true if this machine is determinized

Method Detail

### allocateStateNumber

    public void allocateStateNumber(AutomatonState state)

  Allocate a unique number to a state, and index the state from the FSM

  Parameters:
    `state` - the state whose number is to be allocated

### getNumberOfStates

    public int getNumberOfStates()

  Determine the number of states in this finite state machine

  Returns:
    the number of states

### getInitialState

    public AutomatonState getInitialState()

  Get the initial state of this finite state machine

  Returns:
    the initial state

### setInitialState

    public void setInitialState(AutomatonState initialState)

  Set the initial state of this finite state machine

  Parameters:
    `initialState` - the initial state

### getState

    public AutomatonState getState(int number)

  Get the state with a given unique state number

  Parameters:
    `number` - the number of the state
  Returns:
    the state with this unique state number

### compileParticle

    public static NonDeterminizedState compileParticle(SchemaCompiler compiler,
                                                       Particle particle,
                                                       NonDeterminizedState endState,
                                                       UserComplexType subjectType,
                                                       FiniteStateMachine machine)
                                                throws SchemaException,
                                                       UnresolvedReferenceException

  Static method to translate a particle to a Finite State Automaton, returning the start state of the FSA. This precisely follows Henry Thompson's and Richard Tobin's algorithm, published here

  Parameters:
    `compiler` - user for error reporting
    `particle` - the particle to be compiled, which is either an ElementDeclaration, a WildCard, a choice, or a sequence
    `endState` - the State representing the final state of the automaton
    `subjectType` - the complex type to which this particle belongs
    `machine` - the finite state machine to which the state belongs
  Returns:
    the initial state of the new Automaton
  Throws:
    `SchemaException`
    `UnresolvedReferenceException`

### display

    public void display()

  Display the finite state machine. This is a diagnostic method for internal use. Output is written to System.err.

### subsumesMachine

    public static java.lang.String subsumesMachine(FiniteStateMachine base,
                                                   FiniteStateMachine sub,
                                                   SchemaCompiler compiler)

  Test whether one finite state machine subsumes another FSM: that is, whether for each path through the second FSM, there is a corresponding path through the first FSM. The algorithm used is as published by Thompson and Tobin, XML Europe 2003.

  Parameters:
    `base` - the first FSM (representing the base type)
    `sub` - the other FSM (representing the type that is derived by restriction, validly or otherwise)
    `compiler` - used for error reporting
  Returns:
    null indicating that the first machine does indeed subsume the other; or a string indicating why it doesn't.

### determinize

    public static FiniteStateMachine determinize(FiniteStateMachine nfsa)
                                          throws SchemaException

  Determinize the finite state machine: that is, ensure that there are no ambiguous transitions from this state. When presented with an input token, the FSA can then examine the specific transitions from this state and either choose one of them, or throw an error.

  This is a revised implementation, based more closely on Aho and Ullman p93, to try to eliminate the rare problems that occur when a state has two transitions for the same symbol. (Given UPA, this should occur only with nested loops, e.g. (a{10,11}){1,3} which allows a sequence of 10, 20, 30, 11, 22, or 33 a's.)

  Parameters:
    `nfsa` - the finite state machine to be determinized
  Returns:
    the new deterministic finite state machine
  Throws:
    `SchemaException`

### serialize

    public void serialize(SchemaModelSerializer serializer)
                   throws XPathException

  Output a reppresentation of this finite state machine

  Parameters:
    `serializer` - the schema model serializer to which this representation is to be written
  Throws:
    `XPathException` - if any error occurs during serialization

Copyright (c) Saxonica Limited. All rights reserved.