rationals

Class Automaton

java.lang.Object

rationals.Automaton

All Implemented Interfaces:

Cloneable, Acceptor, Rational, StateMachine

public class Automaton
extends Object
implements Acceptor, StateMachine, Rational, Cloneable

A class defining Automaton objects This class defines the notion of automaton. Following notations are used to describe this class.

An automaton is a 5-uple A = (X , Q , I , T , D) where

• X is a finite set of labels named alphabet ,
• Q is a finite set of states,
• I, included in Q, is the set of initial states,
• T, included in Q, is the set of terminal states
• and D is the set of transitions, which is included in Q times X times Q (transitions are triples (q , l , q') where q, q' are states and l a label).

The empty word, usually denoted by epsilon will be denoted here by the symbol @.

In this implementation of automaton, any object may be a label, states are instance of class State and transitions are intances of class Transition. Only automata should create instances of states through Automaton method newState.

Version:

$Id: Automaton.java 15 2008-09-20 13:29:35Z oqube $

Author:

yroos@lifl.fr, bailly@lifl.fr

See Also:

State

Constructor Summary

Constructors

Constructor and Description
Automaton() Creates a new empty automaton which contains no state and no transition.
Automaton(StateFactory sf) Create a new empty automaton with given state factory.

Method Summary

Modifier and Type	Method and Description
Set<State>	accessibleAndCoAccessibleStates() Returns the set of all states which are co-accessible and accessible in this automaton.
Set<State>	accessibleStates() Returns the set of all accessible states in this automaton.
State	addState(boolean initial, boolean terminal) Returns a new instance of state which will be initial and terminal or not depending of parameters.
boolean	addTransition(Transition transition) Adds a new transition in this automaton if it is a new transition for this automaton.
boolean	addTransition(Transition transition, String ifInvalid)
Set<Object>	alphabet() Returns the alphabet - S - of this state machine.
Object	clone() returns a copy of this automaton.
Set<State>	coAccessibleStates() Returns the set of all co-accessible states in this automaton.
Set<Transition>	delta() Returns the set of all transitions of this automaton
Set<Transition>	delta(Set<State> s) Returns all transitions from a given set of states.
Set<Transition>	delta(State state) Return all transitions from a State.
Set<Transition>	delta(State state, Object label) Returns the set of all transitions of this machine starting from a given state and labelled with a given label.
Set<Transition>	deltaFrom(State from, State to)
Set<Transition>	deltaMinusOne(State st) Returns the set of states that can access the given states' set st.
Set<Transition>	deltaMinusOne(State state, Object label) Returns the set of all transitions of the reverse of this automaton
static Automaton	epsilonAutomaton() Returns an automaton which recognizes the regular language associated with the regular expression @, where @ denotes the empty word.
StateFactory	getStateFactory() Retrieves the state factory associated to this SM.
Set<State>	initials() Returns the set of initial states for this machine.
static Automaton	labelAutomaton(Object label) Returns an automaton which recognizes the regular language associated with the regular expression l, where l is a given label.
State	state(Object label) Create a new state with given label.
Set<State>	states() Returns the set of states Q associated with this automaton.
Set<State>	step(Set<State> s, Object o) Return the set of states accessible in one transition from given set of states s and letter o.
Set<State>	steps(List<?> word)
Set<State>	steps(Set<State> s, List<?> word) Return the set of states this SM will be in after reading the word from start states s.
Set<State>	terminals() Returns the set of terminal states T associated with this automaton.
String	toString() returns a textual representation of this automaton.
boolean	validTransition(Transition transition)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Automaton

public Automaton()

Creates a new empty automaton which contains no state and no transition. An empty automaton recognizes the empty language.

Automaton

public Automaton(StateFactory sf)

Create a new empty automaton with given state factory.

Parameters:

sf - the StateFactory object to use for creating new states. May be null.

Method Detail

getStateFactory

public StateFactory getStateFactory()

Description copied from interface: StateMachine

Retrieves the state factory associated to this SM.

Specified by:

getStateFactory in interface StateMachine

Returns:

a StateFactory instance

epsilonAutomaton

public static Automaton epsilonAutomaton()

Returns an automaton which recognizes the regular language associated with the regular expression @, where @ denotes the empty word.

Returns:

an automaton which recognizes @

labelAutomaton

public static Automaton labelAutomaton(Object label)

Returns an automaton which recognizes the regular language associated with the regular expression l, where l is a given label.

Parameters:

label - any object that will be used as a label.

Returns:

an automaton which recognizes label

addState

public State addState(boolean initial,
                      boolean terminal)

Description copied from interface: Rational

Returns a new instance of state which will be initial and terminal or not depending of parameters.

Specified by:

addState in interface Rational

Parameters:

initial - if true, the new state will be initial; otherwise this state will be non initial.

terminal - if true, the new state will be terminal; otherwise this state will be non terminal.

Returns:

a new state, associated with this automaton. This new state should be used only with this automaton in order to create a new transition for this automaton.

See Also:

Transition

alphabet

public Set<Object> alphabet()

Description copied from interface: StateMachine

Returns the alphabet - S - of this state machine.

Specified by:

alphabet in interface Rational

Specified by:

alphabet in interface StateMachine

Returns:

a Set of Object.

states

public Set<State> states()

Description copied from interface: Rational

Returns the set of states Q associated with this automaton.

Specified by:

states in interface Rational

Returns:

the set of states Q associated with this automaton. Objects which are contained in this set are instances of class State.

See Also:

State

initials

public Set<State> initials()

Description copied from interface: StateMachine

Returns the set of initial states for this machine.

Specified by:

initials in interface Rational

Specified by:

initials in interface StateMachine

Returns:

a Set of State objects.

See Also:

State

terminals

public Set<State> terminals()

Description copied from interface: Rational

Returns the set of terminal states T associated with this automaton.

Specified by:

terminals in interface Rational

Returns:

set of terminal states T associated with this automaton. Objects which are contained in this set are instances of class State.

See Also:

State

accessibleStates

public Set<State> accessibleStates()

Description copied from interface: Rational

Returns the set of all accessible states in this automaton.

Specified by:

accessibleStates in interface Rational

Returns:

the set of all accessible states in this automaton. A state s is accessible if there exists a path from an initial state to s. Objects which are contained in this set are instances of class State.

See Also:

State

coAccessibleStates

public Set<State> coAccessibleStates()

Description copied from interface: Rational

Returns the set of all co-accessible states in this automaton.

Specified by:

coAccessibleStates in interface Rational

Returns:

the set of all co-accessible states in this automaton. A state s is co-accessible if there exists a path from this state s to a terminal state. Objects which are contained in this set are instances of class State.

See Also:

State

accessibleAndCoAccessibleStates

public Set<State> accessibleAndCoAccessibleStates()

Description copied from interface: Rational

Returns the set of all states which are co-accessible and accessible in this automaton.

Specified by:

accessibleAndCoAccessibleStates in interface Rational

Returns:

the set of all states which are co-accessible and accessible in this automaton. A state s is accessible if there exists a path from an initial state to s. A state s is co-accessible if there exists a path from this state s to a terminal state. Objects which are contained in this set are instances of class State.

See Also:

State

delta

public Set<Transition> delta()

Description copied from interface: Rational

Returns the set of all transitions of this automaton

Specified by:

delta in interface Rational

Returns:

the set of all transitions of this automaton Objects which are contained in this set are instances of class Transition.

See Also:

Transition

delta

public Set<Transition> delta(State state,
                             Object label)

Description copied from interface: StateMachine

Returns the set of all transitions of this machine starting from a given state and labelled with a given label.

Specified by:

delta in interface Rational

Specified by:

delta in interface StateMachine

Parameters:

state - a state of this SM.

label - a label used in this SM.

Returns:

the set of all transitions of this automaton starting from state state and labelled by label. Objects which are contained in this set are instances of class Transition.

See Also:

Transition

deltaFrom

public Set<Transition> deltaFrom(State from,
                                 State to)

Specified by:

deltaFrom in interface Rational

Parameters:

from - start

to - end

Returns:

delta from start to end

delta

public Set<Transition> delta(State state)

Description copied from interface: StateMachine

Return all transitions from a State.

Specified by:

delta in interface Rational

Specified by:

delta in interface StateMachine

Parameters:

state - start state

Returns:

a new Set of transitions (maybe empty)

delta

public Set<Transition> delta(Set<State> s)

Description copied from interface: StateMachine

Returns all transitions from a given set of states.

Specified by:

delta in interface StateMachine

Parameters:

s - a Set of State objects

Returns:

a Set of Transition objects

deltaMinusOne

public Set<Transition> deltaMinusOne(State state,
                                     Object label)

Returns the set of all transitions of the reverse of this automaton

Specified by:

deltaMinusOne in interface Rational

Parameters:

state - state

label - label

Returns:

the set of all transitions of the reverse of this automaton. A reverse of an automaton A = (X , Q , I , T , D) is the automaton A' = (X , Q , T , I , D') where D' is the set { (q , l , q') | (q' , l , q) in D}. Objects which are contained in this set are instances of class Transition.

See Also:

Transition

addTransition

public boolean addTransition(Transition transition)

Description copied from interface: Rational

Adds a new transition in this automaton if it is a new transition for this automaton. The parameter is considered as a new transition if there is no transition in this automaton which is equal to the parameter in the sense of method equals of class Transition.

Specified by:

addTransition in interface Rational

Parameters:

transition - the transition to add.

Returns:

false if the transition is invalid

validTransition

public boolean validTransition(Transition transition)

Specified by:

validTransition in interface Rational

Parameters:

transition - transition to check

Returns:

true if the transition is valid and will not cause a NoSuchStateException to be thrown. A NoSuchStateException is thrown if if transition is null or if transition = (q , l , q') and q or q' does not belong to Q the set of the states of this automaton.

addTransition

public boolean addTransition(Transition transition,
                             String ifInvalid)

Specified by:

addTransition in interface Rational

Parameters:

transition - transition to add

ifInvalid - message to use in IllegalArgumentException if transition is invalid; if null, no exception is thrown

Returns:

false if the transition is invalid

toString

public String toString()

returns a textual representation of this automaton.

Overrides:

toString in class Object

Returns:

a textual representation of this automaton based on the converter toAscii.

See Also:

toAscii

clone

public Object clone()

returns a copy of this automaton.

Overrides:

clone in class Object

Returns:

a copy of this automaton with new instances of states and transitions.

steps

public Set<State> steps(List<?> word)

Specified by:

steps in interface Acceptor

Parameters:

word - words

Returns:

State steps for the input words

steps

public Set<State> steps(Set<State> s,
                        List<?> word)

Description copied from interface: StateMachine

Return the set of states this SM will be in after reading the word from start states s.

Specified by:

steps in interface StateMachine

Parameters:

s - the set of starting states

word - the word to read.

Returns:

the set of reached states. Maybe empty or null.

step

public Set<State> step(Set<State> s,
                       Object o)

Description copied from interface: StateMachine

Return the set of states accessible in one transition from given set of states s and letter o.

Specified by:

step in interface StateMachine

Parameters:

s - the starting states

o - the letter

Returns:

a set of reachable states. Maybe empty or null.

deltaMinusOne

public Set<Transition> deltaMinusOne(State st)

Description copied from interface: StateMachine

Returns the set of states that can access the given states' set st. This is the inverse relation of d

Specified by:

deltaMinusOne in interface Rational

Specified by:

deltaMinusOne in interface StateMachine

Parameters:

st - end states

Returns:

a set of states that can reach st. May be empty or null.

state

public State state(Object label)

Create a new state with given label. The state is created with as neither initial nor terminal.

Parameters:

label - the state's label. May not be null.

Returns:

the newly created state.