Package dk.brics.automaton

Class Automaton

java.lang.Object

dk.brics.automaton.Automaton

All Implemented Interfaces:

Serializable, Cloneable

public class Automaton
extends Object
implements Serializable, Cloneable

Finite-state automaton with regular expression operations.

Class invariants:

• An automaton is either represented explicitly (with State and Transition objects) or with a singleton string (see getSingleton() and expandSingleton()) in case the automaton is known to accept exactly one string. (Implicitly, all states and transitions of an automaton are reachable from its initial state.)
• Automata are always reduced (see reduce()) and have no transitions to dead states (see removeDeadTransitions()).
• If an automaton is nondeterministic, then isDeterministic() returns false (but the converse is not required).
• Automata provided as input to operations are generally assumed to be disjoint.

If the states or transitions are manipulated manually, the restoreInvariant() and setDeterministic(boolean) methods should be used afterwards to restore representation invariants that are assumed by the built-in automata operations.

Author:

Anders Møller <amoeller@cs.au.dk>

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final int	MINIMIZE_BRZOZOWSKI	Minimize using Brzozowski's O(2n) algorithm.
static final int	MINIMIZE_HOPCROFT	Minimize using Hopcroft's O(n log n) algorithm.
static final int	MINIMIZE_HUFFMAN	Minimize using Huffman's O(n2) algorithm.
static final int	MINIMIZE_VALMARI	Minimize using Valmari's O(n + m log m) algorithm.

Constructor Summary

Constructors

Constructor	Description
Automaton()	Constructs a new automaton that accepts the empty language.

Method Summary

Modifier and Type	Method	Description
void	addEpsilons(Collection<StatePair> pairs)	See BasicOperations.addEpsilons(Automaton, Collection).
Automaton	clone()	Returns a clone of this automaton.
Automaton	complement()	See BasicOperations.complement(Automaton).
Automaton	compress(String set, char c)	See SpecialOperations.compress(Automaton, String, char).
Automaton	concatenate(Automaton a)	See BasicOperations.concatenate(Automaton, Automaton).
static Automaton	concatenate(List<Automaton> l)	See BasicOperations.concatenate(List).
void	determinize()	See BasicOperations.determinize(Automaton).
boolean	equals(Object obj)	Returns true if the language of this automaton is equal to the language of the given automaton.
void	expandSingleton()	Expands singleton representation to normal representation.
Set<State>	getAcceptStates()	Returns the set of reachable accept states.
String	getCommonPrefix()	See SpecialOperations.getCommonPrefix(Automaton).
Set<String>	getFiniteStrings()	See SpecialOperations.getFiniteStrings(Automaton).
Set<String>	getFiniteStrings(int limit)	See SpecialOperations.getFiniteStrings(Automaton, int).
Object	getInfo()	Returns extra information associated with this automaton.
State	getInitialState()	Gets initial state.
Set<State>	getLiveStates()	Returns the set of live states.
int	getNumberOfStates()	Returns the number of states in this automaton.
int	getNumberOfTransitions()	Returns the number of transitions in this automaton.
String	getShortestExample(boolean accepted)	See BasicOperations.getShortestExample(Automaton, boolean).
String	getSingleton()	Returns the singleton string for this automaton.
Set<State>	getStates()	Returns the set of states that are reachable from the initial state.
Set<String>	getStrings(int length)	See SpecialOperations.getStrings(Automaton, int).
int	hashCode()	Returns hash code for this automaton.
static Automaton	hexCases(Automaton a)	See SpecialOperations.hexCases(Automaton).
Automaton	homomorph(char[] source, char[] dest)	See SpecialOperations.homomorph(Automaton, char[], char[]).
Automaton	intersection(Automaton a)	See BasicOperations.intersection(Automaton, Automaton).
boolean	isDeterministic()	Returns deterministic flag for this automaton.
boolean	isEmpty()	See BasicOperations.isEmpty(Automaton).
boolean	isEmptyString()	See BasicOperations.isEmptyString(Automaton).
boolean	isFinite()	See SpecialOperations.isFinite(Automaton).
boolean	isTotal()	See BasicOperations.isTotal(Automaton).
static Automaton	load(InputStream stream)	Retrieves a serialized Automaton from a stream.
static Automaton	load(URL url)	Retrieves a serialized Automaton located by a URL.
static Automaton	makeAnyChar()	See BasicAutomata.makeAnyChar().
static Automaton	makeAnyString()	See BasicAutomata.makeAnyString().
static Automaton	makeChar(char c)	See BasicAutomata.makeChar(char).
static Automaton	makeCharRange(char min, char max)	See BasicAutomata.makeCharRange(char, char).
static Automaton	makeCharSet(String set)	See BasicAutomata.makeCharSet(String).
static Automaton	makeDecimalValue(String value)	See BasicAutomata.makeDecimalValue(String).
static Automaton	makeEmpty()	See BasicAutomata.makeEmpty().
static Automaton	makeEmptyString()	See BasicAutomata.makeEmptyString().
static Automaton	makeFractionDigits(int i)	See BasicAutomata.makeFractionDigits(int).
static Automaton	makeIntegerValue(String value)	See BasicAutomata.makeIntegerValue(String).
static Automaton	makeInterval(int min, int max, int digits)	See BasicAutomata.makeInterval(int, int, int).
static Automaton	makeMaxInteger(String n)	See BasicAutomata.makeMaxInteger(String).
static Automaton	makeMinInteger(String n)	See BasicAutomata.makeMinInteger(String).
static Automaton	makeString(String s)	See BasicAutomata.makeString(String).
static Automaton	makeStringMatcher(String s)	See BasicAutomata.makeStringMatcher(String).
static Automaton	makeStringUnion(CharSequence... strings)	See BasicAutomata.makeStringUnion(CharSequence...).
static Automaton	makeTotalDigits(int i)	See BasicAutomata.makeTotalDigits(int).
void	minimize()	See MinimizationOperations.minimize(Automaton).
static Automaton	minimize(Automaton a)	See MinimizationOperations.minimize(Automaton).
Automaton	minus(Automaton a)	See BasicOperations.minus(Automaton, Automaton).
Automaton	optional()	See BasicOperations.optional(Automaton).
Automaton	overlap(Automaton a)	See SpecialOperations.overlap(Automaton, Automaton).
void	prefixClose()	See SpecialOperations.prefixClose(Automaton).
Automaton	projectChars(Set<Character> chars)	See SpecialOperations.projectChars(Automaton, Set).
void	reduce()	Reduces this automaton.
void	removeDeadTransitions()	Removes transitions to dead states and calls reduce() and clearHashCode().
Automaton	repeat()	See BasicOperations.repeat(Automaton).
Automaton	repeat(int min)	See BasicOperations.repeat(Automaton, int).
Automaton	repeat(int min, int max)	See BasicOperations.repeat(Automaton, int, int).
static Automaton	replaceWhitespace(Automaton a)	See SpecialOperations.replaceWhitespace(Automaton).
void	restoreInvariant()	Restores representation invariant.
boolean	run(String s)	See BasicOperations.run(Automaton, String).
static boolean	setAllowMutate(boolean flag)	Sets or resets allow mutate flag.
void	setDeterministic(boolean deterministic)	Sets deterministic flag for this automaton.
void	setInfo(Object info)	Associates extra information with this automaton.
void	setInitialState(State s)	Sets initial state.
static void	setMinimization(int algorithm)	Selects minimization algorithm (default: MINIMIZE_HOPCROFT).
static void	setMinimizeAlways(boolean flag)	Sets or resets minimize always flag.
Automaton	shuffle(Automaton a)	See ShuffleOperations.shuffle(Automaton, Automaton).
static String	shuffleSubsetOf(Collection<Automaton> ca, Automaton a, Character suspend_shuffle, Character resume_shuffle)	See ShuffleOperations.shuffleSubsetOf(Collection, Automaton, Character, Character).
Automaton	singleChars()	See SpecialOperations.singleChars(Automaton).
void	store(OutputStream stream)	Writes this Automaton to the given stream.
boolean	subsetOf(Automaton a)	See BasicOperations.subsetOf(Automaton, Automaton).
Automaton	subst(char c, String s)	See SpecialOperations.subst(Automaton, char, String).
Automaton	subst(Map<Character,Set<Character>> map)	See SpecialOperations.subst(Automaton, Map).
String	toDot()	Returns Graphviz Dot representation of this automaton.
String	toString()	Returns a string representation of this automaton.
Automaton	trim(String set, char c)	See SpecialOperations.trim(Automaton, String, char).
Automaton	union(Automaton a)	See BasicOperations.union(Automaton, Automaton).
static Automaton	union(Collection<Automaton> l)	See BasicOperations.union(Collection).

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Field Details

MINIMIZE_HUFFMAN

public static final int MINIMIZE_HUFFMAN

Minimize using Huffman's O(n²) algorithm. This is the standard text-book algorithm.

See Also:

• setMinimization(int)
• Constant Field Values

MINIMIZE_BRZOZOWSKI

public static final int MINIMIZE_BRZOZOWSKI

Minimize using Brzozowski's O(2ⁿ) algorithm. This algorithm uses the reverse-determinize-reverse-determinize trick, which has a bad worst-case behavior but often works very well in practice (even better than Hopcroft's!).

See Also:

• setMinimization(int)
• Constant Field Values

MINIMIZE_HOPCROFT

public static final int MINIMIZE_HOPCROFT

Minimize using Hopcroft's O(n log n) algorithm. This is regarded as one of the most generally efficient algorithms that exist.

See Also:

• setMinimization(int)
• Constant Field Values

MINIMIZE_VALMARI

public static final int MINIMIZE_VALMARI

Minimize using Valmari's O(n + m log m) algorithm.

See Also:

• setMinimization(int)
• Constant Field Values

Constructor Details

Automaton

public Automaton()

Constructs a new automaton that accepts the empty language. Using this constructor, automata can be constructed manually from State and Transition objects.

See Also:

• setInitialState(State)
• State
• Transition

Method Details

setMinimization

public static void setMinimization(int algorithm)

Selects minimization algorithm (default: MINIMIZE_HOPCROFT).

Parameters:

algorithm - minimization algorithm

setMinimizeAlways

public static void setMinimizeAlways(boolean flag)

Sets or resets minimize always flag. If this flag is set, then minimize() will automatically be invoked after all operations that otherwise may produce non-minimal automata. By default, the flag is not set.

Parameters:

flag - if true, the flag is set

setAllowMutate

public static boolean setAllowMutate(boolean flag)

Sets or resets allow mutate flag. If this flag is set, then all automata operations may modify automata given as input; otherwise, operations will always leave input automata languages unmodified. By default, the flag is not set.

Parameters:

flag - if true, the flag is set

Returns:

previous value of the flag

getSingleton

public String getSingleton()

Returns the singleton string for this automaton. An automaton that accepts exactly one string may be represented in singleton mode. In that case, this method may be used to obtain the string.

Returns:

string, null if this automaton is not in singleton mode.

setInitialState

public void setInitialState(State s)

Sets initial state.

Parameters:

s - state

getInitialState

public State getInitialState()

Gets initial state.

Returns:

state

isDeterministic

public boolean isDeterministic()

Returns deterministic flag for this automaton.

Returns:

true if the automaton is definitely deterministic, false if the automaton may be nondeterministic

setDeterministic

public void setDeterministic(boolean deterministic)

Sets deterministic flag for this automaton. This method should (only) be used if automata are constructed manually.

Parameters:

deterministic - true if the automaton is definitely deterministic, false if the automaton may be nondeterministic

setInfo

public void setInfo(Object info)

Associates extra information with this automaton.

Parameters:

info - extra information

getInfo

public Object getInfo()

Returns extra information associated with this automaton.

Returns:

extra information

See Also:

• setInfo(Object)

getStates

public Set<State> getStates()

Returns the set of states that are reachable from the initial state.

Returns:

set of State objects

getAcceptStates

public Set<State> getAcceptStates()

Returns the set of reachable accept states.

Returns:

set of State objects

restoreInvariant

public void restoreInvariant()

Restores representation invariant. This method must be invoked before any built-in automata operation is performed if automaton states or transitions are manipulated manually.

See Also:

• setDeterministic(boolean)

reduce

public void reduce()

Reduces this automaton. An automaton is "reduced" by combining overlapping and adjacent edge intervals with same destination.

getLiveStates

public Set<State> getLiveStates()

Returns the set of live states. A state is "live" if an accept state is reachable from it.

Returns:

set of State objects

removeDeadTransitions

public void removeDeadTransitions()

Removes transitions to dead states and calls reduce() and clearHashCode(). (A state is "dead" if no accept state is reachable from it.)

expandSingleton

public void expandSingleton()

Expands singleton representation to normal representation. Does nothing if not in singleton representation.

getNumberOfStates

public int getNumberOfStates()

Returns the number of states in this automaton.

getNumberOfTransitions

public int getNumberOfTransitions()

Returns the number of transitions in this automaton. This number is counted as the total number of edges, where one edge may be a character interval.

equals

public boolean equals(Object obj)

Returns true if the language of this automaton is equal to the language of the given automaton. Implemented using hashCode and subsetOf.

Overrides:

equals in class Object

hashCode

public int hashCode()

Returns hash code for this automaton. The hash code is based on the number of states and transitions in the minimized automaton. Invoking this method may involve minimizing the automaton.

Overrides:

hashCode in class Object

toString

public String toString()

Returns a string representation of this automaton.

Overrides:

toString in class Object

toDot

public String toDot()

Returns Graphviz Dot representation of this automaton.

clone

public Automaton clone()

Returns a clone of this automaton.

Overrides:

clone in class Object

load

public static Automaton load(URL url)
                      throws IOException,
ClassCastException,
ClassNotFoundException

Retrieves a serialized Automaton located by a URL.

Parameters:

url - URL of serialized automaton

Throws:

IOException - if input/output related exception occurs

ClassCastException - if the data is not a serialized Automaton

ClassNotFoundException - if the class of the serialized object cannot be found

load

public static Automaton load(InputStream stream)
                      throws IOException,
ClassCastException,
ClassNotFoundException

Retrieves a serialized Automaton from a stream.

Parameters:

stream - input stream with serialized automaton

Throws:

IOException - if input/output related exception occurs

ClassCastException - if the data is not a serialized Automaton

ClassNotFoundException - if the class of the serialized object cannot be found

store

public void store(OutputStream stream)
           throws IOException

Writes this Automaton to the given stream.

Parameters:

stream - output stream for serialized automaton

Throws:

IOException - if input/output related exception occurs

makeEmpty

public static Automaton makeEmpty()

See BasicAutomata.makeEmpty().

makeEmptyString

public static Automaton makeEmptyString()

See BasicAutomata.makeEmptyString().

makeAnyString

public static Automaton makeAnyString()

See BasicAutomata.makeAnyString().

makeAnyChar

public static Automaton makeAnyChar()

See BasicAutomata.makeAnyChar().

makeChar

public static Automaton makeChar(char c)

See BasicAutomata.makeChar(char).

makeCharRange

public static Automaton makeCharRange(char min,
 char max)

See BasicAutomata.makeCharRange(char, char).

makeCharSet

public static Automaton makeCharSet(String set)

See BasicAutomata.makeCharSet(String).

makeInterval

public static Automaton makeInterval(int min,
 int max,
 int digits)
                              throws IllegalArgumentException

See BasicAutomata.makeInterval(int, int, int).

Throws:

IllegalArgumentException

makeString

public static Automaton makeString(String s)

See BasicAutomata.makeString(String).

makeStringUnion

public static Automaton makeStringUnion(CharSequence... strings)

See BasicAutomata.makeStringUnion(CharSequence...).

makeMaxInteger

public static Automaton makeMaxInteger(String n)

See BasicAutomata.makeMaxInteger(String).

makeMinInteger

public static Automaton makeMinInteger(String n)

See BasicAutomata.makeMinInteger(String).

makeTotalDigits

public static Automaton makeTotalDigits(int i)

See BasicAutomata.makeTotalDigits(int).

makeFractionDigits

public static Automaton makeFractionDigits(int i)

See BasicAutomata.makeFractionDigits(int).

makeIntegerValue

public static Automaton makeIntegerValue(String value)

See BasicAutomata.makeIntegerValue(String).

makeDecimalValue

public static Automaton makeDecimalValue(String value)

See BasicAutomata.makeDecimalValue(String).

makeStringMatcher

public static Automaton makeStringMatcher(String s)

See BasicAutomata.makeStringMatcher(String).

concatenate

public Automaton concatenate(Automaton a)

See BasicOperations.concatenate(Automaton, Automaton).

concatenate

public static Automaton concatenate(List<Automaton> l)

See BasicOperations.concatenate(List).

optional

public Automaton optional()

See BasicOperations.optional(Automaton).

repeat

public Automaton repeat()

See BasicOperations.repeat(Automaton).

repeat

public Automaton repeat(int min)

See BasicOperations.repeat(Automaton, int).

repeat

public Automaton repeat(int min,
 int max)

See BasicOperations.repeat(Automaton, int, int).

complement

public Automaton complement()

See BasicOperations.complement(Automaton).

minus

public Automaton minus(Automaton a)

See BasicOperations.minus(Automaton, Automaton).

intersection

public Automaton intersection(Automaton a)

See BasicOperations.intersection(Automaton, Automaton).

subsetOf

public boolean subsetOf(Automaton a)

See BasicOperations.subsetOf(Automaton, Automaton).

union

public Automaton union(Automaton a)

See BasicOperations.union(Automaton, Automaton).

union

public static Automaton union(Collection<Automaton> l)

See BasicOperations.union(Collection).

determinize

public void determinize()

See BasicOperations.determinize(Automaton).

addEpsilons

public void addEpsilons(Collection<StatePair> pairs)

See BasicOperations.addEpsilons(Automaton, Collection).

isEmptyString

public boolean isEmptyString()

See BasicOperations.isEmptyString(Automaton).

isEmpty

public boolean isEmpty()

See BasicOperations.isEmpty(Automaton).

isTotal

public boolean isTotal()

See BasicOperations.isTotal(Automaton).

getShortestExample

public String getShortestExample(boolean accepted)

See BasicOperations.getShortestExample(Automaton, boolean).

run

public boolean run(String s)

See BasicOperations.run(Automaton, String).

minimize

public void minimize()

See MinimizationOperations.minimize(Automaton).

minimize

public static Automaton minimize(Automaton a)

See MinimizationOperations.minimize(Automaton). Returns the automaton being given as argument.

overlap

public Automaton overlap(Automaton a)

See SpecialOperations.overlap(Automaton, Automaton).

singleChars

public Automaton singleChars()

See SpecialOperations.singleChars(Automaton).

trim

public Automaton trim(String set,
 char c)

See SpecialOperations.trim(Automaton, String, char).

compress

public Automaton compress(String set,
 char c)

See SpecialOperations.compress(Automaton, String, char).

subst

public Automaton subst(Map<Character,Set<Character>> map)

See SpecialOperations.subst(Automaton, Map).

subst

public Automaton subst(char c,
 String s)

See SpecialOperations.subst(Automaton, char, String).

homomorph

public Automaton homomorph(char[] source,
 char[] dest)

See SpecialOperations.homomorph(Automaton, char[], char[]).

projectChars

public Automaton projectChars(Set<Character> chars)

See SpecialOperations.projectChars(Automaton, Set).

isFinite

public boolean isFinite()

See SpecialOperations.isFinite(Automaton).

getStrings

public Set<String> getStrings(int length)

See SpecialOperations.getStrings(Automaton, int).

getFiniteStrings

public Set<String> getFiniteStrings()

See SpecialOperations.getFiniteStrings(Automaton).

getFiniteStrings

public Set<String> getFiniteStrings(int limit)

See SpecialOperations.getFiniteStrings(Automaton, int).

getCommonPrefix

public String getCommonPrefix()

See SpecialOperations.getCommonPrefix(Automaton).

prefixClose

public void prefixClose()

See SpecialOperations.prefixClose(Automaton).

hexCases

public static Automaton hexCases(Automaton a)

See SpecialOperations.hexCases(Automaton).

replaceWhitespace

public static Automaton replaceWhitespace(Automaton a)

See SpecialOperations.replaceWhitespace(Automaton).

shuffleSubsetOf

public static String shuffleSubsetOf(Collection<Automaton> ca,
 Automaton a,
 Character suspend_shuffle,
 Character resume_shuffle)

See ShuffleOperations.shuffleSubsetOf(Collection, Automaton, Character, Character).

shuffle

public Automaton shuffle(Automaton a)

See ShuffleOperations.shuffle(Automaton, Automaton).