Package net.automatalib.util.automaton.procedural

Class SBAs

java.lang.Object

net.automatalib.util.automaton.procedural.SBAs

public final class SBAs
extends Object

Operations on SBAs.

Method Summary

Modifier and Type	Method	Description
static <I> Map<I,Word<I>>	computeAccessSequences(SBA<?,I> sba, ProceduralInputAlphabet<I> alphabet, Map<I,Word<I>> terminatingSequences)	Computes for a given SBA a set of access sequences using the given alphabet.
static <I> ATSequences<I>	computeATSequences(SBA<?,I> sba)	Computes a set of access sequences and terminating sequences for a given SBA.
static <I> ATSequences<I>	computeATSequences(SBA<?,I> sba, ProceduralInputAlphabet<I> alphabet)	Computes a set of access sequences and terminating sequences for a given SBA limited to the symbols of the given ProceduralInputAlphabet.
static <I> Map<I,Word<I>>	computeTerminatingSequences(SBA<?,I> sba, ProceduralInputAlphabet<I> alphabet)	Computes for a given SBA a set of terminating sequences using the given alphabet.
static <I> @Nullable Word<I>	findSeparatingWord(SBA<?,I> sba1, SBA<?,I> sba2, ProceduralInputAlphabet<I> alphabet)	Computes a separating word for the two given SBAs, if existent.
static <I> boolean	isValid(SBA<?,I> sba)	Checks whether the given SBA is valid, This is a convenience method for isValid(SBA, ProceduralInputAlphabet) that uses the input alphabet of the given SBA.
static <I> boolean	isValid(SBA<?,I> sba, ProceduralInputAlphabet<I> alphabet)	Checks whether the given SBA is valid with respect to the given ProceduralInputAlphabet, i.e., whether its procedures are prefix-closed, return-closed, and call-closed.
static <I> SPA<?,I>	reduce(SBA<?,I> sba)	Reduces a given SBA to its well-matched language.
static <I> SPA<?,I>	reduce(SBA<?,I> sba, ProceduralInputAlphabet<I> alphabet)	Reduces a given SBA to its well-matched language restricted to the symbols of the given ProceduralInputAlphabet.
static <I> boolean	testEquivalence(SBA<?,I> sba1, SBA<?,I> sba2, ProceduralInputAlphabet<I> alphabet)	Checks if the two given SBAs are equivalent, i.e. whether there exists a separating word for them.
static <I> ContextFreeModalProcessSystem<I,Void>	toCFMPS(SBA<?,I> sba)	Returns a ContextFreeModalProcessSystem-based view on the language of a given SBA such that there exists a w-labeled path in the returned CFMPS if and only if w is accepted by the given SBA.

Methods inherited from class java.lang.Object

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

Method Detail

computeATSequences

public static <I> ATSequences<I> computeATSequences(SBA<?,I> sba)

Computes a set of access sequences and terminating sequences for a given SBA. This is a convenience method for computeATSequences(SBA, ProceduralInputAlphabet) that automatically uses the input alphabet of the given sba.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA for which the sequences should be computed

Returns:

an ATSequences object which contains the respective sequences.

See Also:

computeATSequences(SBA, ProceduralInputAlphabet)

computeATSequences

public static <I> ATSequences<I> computeATSequences(SBA<?,I> sba,
                                                    ProceduralInputAlphabet<I> alphabet)

Computes a set of access sequences and terminating sequences for a given SBA limited to the symbols of the given ProceduralInputAlphabet.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA for which the sequences should be computed

alphabet - the ProceduralInputAlphabet whose symbols should be used for computing the respective sequences

Returns:

an ATSequences object which contains the respective sequences.

See Also:

computeAccessSequences(SBA, ProceduralInputAlphabet, Map), computeTerminatingSequences(SBA, ProceduralInputAlphabet)

computeTerminatingSequences

public static <I> Map<I,Word<I>> computeTerminatingSequences(SBA<?,I> sba,
                                                                   ProceduralInputAlphabet<I> alphabet)

Computes for a given SBA a set of terminating sequences using the given alphabet. Terminating sequences transfer a procedure from its initial state to a returnable state. This method furthermore checks that the hierarchy of calls is well-defined, i.e. it only includes procedural invocations p for determining a terminating sequence if p has a valid terminating sequence itself.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to analyze

alphabet - the ProceduralInputAlphabet whose symbols should be used for determining the terminating sequences

Returns:

A map from procedures (restricted to the call symbols of the given alphabet) to the terminating sequences. This map may be partial as some procedures may not have a well-defined terminating sequence for the given alphabet.

computeAccessSequences

public static <I> Map<I,Word<I>> computeAccessSequences(SBA<?,I> sba,
                                                              ProceduralInputAlphabet<I> alphabet,
                                                              Map<I,Word<I>> terminatingSequences)

Computes for a given SBA a set of access sequences using the given alphabet. An access sequence (for procedure p) transfers an SBA from its initial state to a state that is able to successfully execute a run of p. This method furthermore checks that potentially nested calls are well-defined, i.e. it only includes procedural invocations p for determining access sequences if p has a valid terminating sequence and therefore can be expanded correctly.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to analyze

alphabet - the ProceduralInputAlphabet whose symbols should be used for determining the access and return sequences

terminatingSequences - a Map of call symbols to terminating sequences used to expand nested invocations in access sequences

Returns:

A pair of maps from procedures (restricted to the call symbols of the given alphabet) to the access/return sequences. These maps may be partial as some procedures may not have well-defined access/terminating sequences for the given alphabet.

isValid

public static <I> boolean isValid(SBA<?,I> sba)

Checks whether the given SBA is valid, This is a convenience method for isValid(SBA, ProceduralInputAlphabet) that uses the input alphabet of the given SBA.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to analyze

Returns:

true if sba is valid, false otherwise.

See Also:

isValid(SBA, ProceduralInputAlphabet)

isValid

public static <I> boolean isValid(SBA<?,I> sba,
                                  ProceduralInputAlphabet<I> alphabet)

Checks whether the given SBA is valid with respect to the given ProceduralInputAlphabet, i.e., whether its procedures are prefix-closed, return-closed, and call-closed.

A procedure is considered prefix-closed iff any continuation of a rejected word is rejected as well.

A procedure is considered return-closed iff any continuation beyond the return symbol is rejected.

A procedure is considered call-closed iff any continuation beyond a non-terminating call symbol is rejected.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to analyze

alphabet - the ProceduralInputAlphabet whose symbols should be used for checking validity

Returns:

true if sba is valid, false otherwise.

testEquivalence

public static <I> boolean testEquivalence(SBA<?,I> sba1,
                                          SBA<?,I> sba2,
                                          ProceduralInputAlphabet<I> alphabet)

Checks if the two given SBAs are equivalent, i.e. whether there exists a separating word for them.

Type Parameters:

I - input symbol type

Parameters:

sba1 - the first SPMM

sba2 - the second SPMM

alphabet - the ProceduralInputAlphabet whose symbols should be used for checking equivalence

Returns:

true if the two SBAs are equivalent, false otherwise.

See Also:

findSeparatingWord(SBA, SBA, ProceduralInputAlphabet)

findSeparatingWord

public static <I> @Nullable Word<I> findSeparatingWord(SBA<?,I> sba1,
                                                       SBA<?,I> sba2,
                                                       ProceduralInputAlphabet<I> alphabet)

Computes a separating word for the two given SBAs, if existent. A separating word is a Word such that one SBA behaves different from the other.

Type Parameters:

I - input symbol type

Parameters:

sba1 - the first SBA

sba2 - the second SBA

alphabet - the ProceduralInputAlphabet whose symbols should be considered for computing the separating word

Returns:

a separating word, if existent, null otherwise.

reduce

public static <I> SPA<?,I> reduce(SBA<?,I> sba)

Reduces a given SBA to its well-matched language. This is a convenience method for reduce(SBA, ProceduralInputAlphabet) that uses the input alphabet of the given SBA.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to reduce

Returns:

the reduced SBA in form of an SPA

See Also:

reduce(SBA, ProceduralInputAlphabet)

reduce

public static <I> SPA<?,I> reduce(SBA<?,I> sba,
                                        ProceduralInputAlphabet<I> alphabet)

Reduces a given SBA to its well-matched language restricted to the symbols of the given ProceduralInputAlphabet. The reduced SBA only accepts a Word iff it is (minimally) well-matched and accepted by the original SBA as well.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to reduce

alphabet - the ProceduralInputAlphabet whose symbols should be considered for reduction

Returns:

the reduced SBA in form of an SPA

toCFMPS

public static <I> ContextFreeModalProcessSystem<I,Void> toCFMPS(SBA<?,I> sba)

Returns a ContextFreeModalProcessSystem-based view on the language of a given SBA such that there exists a w-labeled path in the returned CFMPS if and only if w is accepted by the given SBA. This allows one to model-check language properties of SBAs with tools such as M3C.

Type Parameters:

I - input symbol type

Parameters:

sba - the SBA to convert

Returns:

the ContextFreeModalProcessSystem-based view on the given sba.