Package dk.brics.automaton

Class BasicOperations

java.lang.Object

dk.brics.automaton.BasicOperations

public final class BasicOperations
extends Object

Basic automata operations.

Method Summary

Modifier and Type	Method	Description
static void	addEpsilons(Automaton a, Collection<StatePair> pairs)	Adds epsilon transitions to the given automaton.
static Automaton	complement(Automaton a)	Returns a (deterministic) automaton that accepts the complement of the language of the given automaton.
static Automaton	concatenate(Automaton a1, Automaton a2)	Returns an automaton that accepts the concatenation of the languages of the given automata.
static Automaton	concatenate(List<Automaton> l)	Returns an automaton that accepts the concatenation of the languages of the given automata.
static void	determinize(Automaton a)	Determinizes the given automaton.
static String	getShortestExample(Automaton a, boolean accepted)	Returns a shortest accepted/rejected string.
static Automaton	intersection(Automaton a1, Automaton a2)	Returns an automaton that accepts the intersection of the languages of the given automata.
static boolean	isEmpty(Automaton a)	Returns true if the given automaton accepts no strings.
static boolean	isEmptyString(Automaton a)	Returns true if the given automaton accepts the empty string and nothing else.
static boolean	isTotal(Automaton a)	Returns true if the given automaton accepts all strings.
static Automaton	minus(Automaton a1, Automaton a2)	Returns a (deterministic) automaton that accepts the intersection of the language of a1 and the complement of the language of a2.
static Automaton	optional(Automaton a)	Returns an automaton that accepts the union of the empty string and the language of the given automaton.
static Automaton	repeat(Automaton a)	Returns an automaton that accepts the Kleene star (zero or more concatenated repetitions) of the language of the given automaton.
static Automaton	repeat(Automaton a, int min)	Returns an automaton that accepts min or more concatenated repetitions of the language of the given automaton.
static Automaton	repeat(Automaton a, int min, int max)	Returns an automaton that accepts between min and max (including both) concatenated repetitions of the language of the given automaton.
static boolean	run(Automaton a, String s)	Returns true if the given string is accepted by the automaton.
static boolean	subsetOf(Automaton a1, Automaton a2)	Returns true if the language of a1 is a subset of the language of a2.
static Automaton	union(Automaton a1, Automaton a2)	Returns an automaton that accepts the union of the languages of the given automata.
static Automaton	union(Collection<Automaton> l)	Returns an automaton that accepts the union of the languages of the given automata.

Methods inherited from class java.lang.Object

clone, equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

concatenate

public static Automaton concatenate(Automaton a1,
                                    Automaton a2)

Returns an automaton that accepts the concatenation of the languages of the given automata.

Complexity: linear in number of states.

concatenate

public static Automaton concatenate(List<Automaton> l)

Returns an automaton that accepts the concatenation of the languages of the given automata.

Complexity: linear in total number of states.

optional

public static Automaton optional(Automaton a)

Returns an automaton that accepts the union of the empty string and the language of the given automaton.

Complexity: linear in number of states.

repeat

public static Automaton repeat(Automaton a)

Returns an automaton that accepts the Kleene star (zero or more concatenated repetitions) of the language of the given automaton. Never modifies the input automaton language.

Complexity: linear in number of states.

repeat

public static Automaton repeat(Automaton a,
                               int min)

Returns an automaton that accepts min or more concatenated repetitions of the language of the given automaton.

Complexity: linear in number of states and in min.

repeat

public static Automaton repeat(Automaton a,
                               int min,
                               int max)

Returns an automaton that accepts between min and max (including both) concatenated repetitions of the language of the given automaton.

Complexity: linear in number of states and in min and max.

complement

public static Automaton complement(Automaton a)

Returns a (deterministic) automaton that accepts the complement of the language of the given automaton.

Complexity: linear in number of states (if already deterministic).

minus

public static Automaton minus(Automaton a1,
                              Automaton a2)

Returns a (deterministic) automaton that accepts the intersection of the language of a1 and the complement of the language of a2. As a side-effect, the automata may be determinized, if not already deterministic.

Complexity: quadratic in number of states (if already deterministic).

intersection

public static Automaton intersection(Automaton a1,
                                     Automaton a2)

Returns an automaton that accepts the intersection of the languages of the given automata. Never modifies the input automata languages.

Complexity: quadratic in number of states.

subsetOf

public static boolean subsetOf(Automaton a1,
                               Automaton a2)

Returns true if the language of a1 is a subset of the language of a2. As a side-effect, a2 is determinized if not already marked as deterministic.

Complexity: quadratic in number of states.

union

public static Automaton union(Automaton a1,
                              Automaton a2)

Returns an automaton that accepts the union of the languages of the given automata.

Complexity: linear in number of states.

union

public static Automaton union(Collection<Automaton> l)

Returns an automaton that accepts the union of the languages of the given automata.

Complexity: linear in number of states.

determinize

public static void determinize(Automaton a)

Determinizes the given automaton.

Complexity: exponential in number of states.

addEpsilons

public static void addEpsilons(Automaton a,
                               Collection<StatePair> pairs)

Adds epsilon transitions to the given automaton. This method adds extra character interval transitions that are equivalent to the given set of epsilon transitions.

Parameters:

pairs - collection of StatePair objects representing pairs of source/destination states where epsilon transitions should be added

isEmptyString

public static boolean isEmptyString(Automaton a)

Returns true if the given automaton accepts the empty string and nothing else.

isEmpty

public static boolean isEmpty(Automaton a)

Returns true if the given automaton accepts no strings.

isTotal

public static boolean isTotal(Automaton a)

Returns true if the given automaton accepts all strings.

getShortestExample

public static String getShortestExample(Automaton a,
                                        boolean accepted)

Returns a shortest accepted/rejected string. If more than one shortest string is found, the lexicographically first of the shortest strings is returned.

Parameters:

accepted - if true, look for accepted strings; otherwise, look for rejected strings

Returns:

the string, null if none found

run

public static boolean run(Automaton a,
                          String s)

Returns true if the given string is accepted by the automaton.

Complexity: linear in the length of the string.

Note: for full performance, use the RunAutomaton class.