Package com.github.javabdd

Class BDD

java.lang.Object

com.github.javabdd.BDD

Direct Known Subclasses:

BDDFactoryIntImpl.IntBDD

public abstract class BDD
extends Object

Binary Decision Diagrams (BDDs) are used for efficient computation of many common problems. This is done by giving a compact representation and a set of efficient operations on boolean functions f: {0,1}^n --> {0,1}.

Use an implementation of BDDFactory to create BDD objects.

See Also:

BDDFactory, BDDDomain.set()

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	BDD.AllSatIterator	Iterator that returns all satisfying assignments as byte arrays.
static class	BDD.BDDIterator	BDDIterator is used to iterate through the satisfying assignments of a BDD.
static class	BDD.BDDToString	BDDToString is used to specify the printing behavior of BDDs with domains.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	BDD()	Protected constructor.

Method Summary

Modifier and Type	Method	Description
BDD.AllSatIterator	allsat()	Finds all satisfying variable assignments.
BDD	and(BDD that)	Returns the logical 'and' of two BDDs.
BDD	andWith(BDD that)	Makes this BDD be the logical 'and' of two BDDs.
abstract BDD	apply(BDD that, BDDFactory.BDDOp opr)	Returns the result of applying the binary operator opr to the two BDDs.
abstract BDD	applyAll(BDD that, BDDFactory.BDDOp opr, BDDVarSet var)	Applies the binary operator opr to two BDDs and then performs a universal quantification of the variables from the variable set var.
abstract BDD	applyEx(BDD that, BDDFactory.BDDOp opr, BDDVarSet var)	Applies the binary operator opr to two BDDs and then performs an existential quantification of the variables from the variable set var.
abstract BDD	applyUni(BDD that, BDDFactory.BDDOp opr, BDDVarSet var)	Applies the binary operator opr to two BDDs and then performs a unique quantification of the variables from the variable set var.
abstract BDD	applyWith(BDD that, BDDFactory.BDDOp opr)	Makes this BDD be the result of the binary operator opr of two BDDs.
BDD	biimp(BDD that)	Returns the logical 'bi-implication' of two BDDs.
BDD	biimpWith(BDD that)	Makes this BDD be the logical 'bi-implication' of two BDDs.
abstract BDD	compose(BDD g, int var)	Functional composition.
abstract BDD	constrain(BDD that)	Generalized cofactor.
boolean	equals(Object o)
abstract boolean	equalsBDD(BDD that)	Returns true if this BDD equals that BDD, false otherwise.
abstract BDD	exist(BDDVarSet var)	Existential quantification of variables.
abstract BDD	forAll(BDDVarSet var)	Universal quantification of variables.
abstract void	free()	Frees this BDD.
abstract BDD	fullSatOne()	Finds one satisfying variable assignment.
abstract BDDFactory	getFactory()	Returns the factory that created this BDD.
abstract int	hashCode()
abstract BDD	high()	Gets the true branch of this BDD.
abstract BDD	id()	Identity function.
BDD	imp(BDD that)	Returns the logical 'implication' of two BDDs.
BDD	impWith(BDD that)	Makes this BDD be the logical 'implication' of two BDDs.
abstract boolean	isOne()	Returns true if this BDD is the one (true) BDD.
boolean	isUniverse()	Returns true if this BDD is the universe BDD.
abstract boolean	isZero()	Returns true if this BDD is the zero (false) BDD.
abstract BDD	ite(BDD thenBDD, BDD elseBDD)	if-then-else operator.
BDD.BDDIterator	iterator(BDDVarSet var)	Returns an iteration of the satisfying assignments of this BDD.
int	level()	Gets the level of this BDD.
double	logSatCount()	Calculates the logarithm of the number of satisfying variable assignments.
double	logSatCount(BDDVarSet varset)	Calculates the logarithm of the number of satisfying variable assignments to the variables in the given varset.
abstract BDD	low()	Gets the false branch of this BDD.
abstract int	nodeCount()	Counts the number of distinct nodes used for this BDD.
abstract BDD	not()	Negates this BDD by exchanging all references to the zero-terminal with references to the one-terminal and vice-versa.
BDD	or(BDD that)	Returns the logical 'or' of two BDDs.
BDD	orWith(BDD that)	Makes this BDD be the logical 'or' of two BDDs.
abstract double	pathCount()	Counts the number of paths leading to the true terminal.
void	printDot()	Prints this BDD in dot graph notation.
protected int	printdot_rec(PrintStream out, int current, boolean[] visited, HashMap<BDD,Integer> map)
void	printSet()	Prints the set of truth assignments specified by this BDD.
void	printSetWithDomains()	Prints this BDD using a set notation as in printSet() but with the index of the finite domain blocks included instead of the BDD variables.
BDD	relprod(BDD that, BDDVarSet var)	Relational product.
abstract BDD	replace(BDDPairing pair)	Returns a BDD where all variables are replaced with the variables defined by pair.
abstract BDD	replaceWith(BDDPairing pair)	Replaces all variables in this BDD with the variables defined by pair.
abstract BDD	restrict(BDD var)	Restrict a set of variables to constant values.
abstract BDD	restrictWith(BDD var)	Mutates this BDD to restrict a set of variables to constant values.
abstract double	satCount()	Calculates the number of satisfying variable assignments.
double	satCount(BDDVarSet varset)	Calculates the number of satisfying variable assignments to the variables in the given varset.
abstract BDD	satOne()	Finds one satisfying variable assignment.
abstract BDD	satOne(BDDVarSet var, boolean pol)	Finds one satisfying variable assignment.
BigInteger[]	scanAllVar()	Finds one satisfying assignment in this BDD of all the defined BDDDomain's.
BigInteger	scanVar(BDDDomain d)	Finds one satisfying assignment of the domain d in this BDD and returns that value.
abstract BDD	simplify(BDD d)	Coudert and Madre's restrict function.
abstract BDDVarSet	support()	Returns the variable support of this BDD.
String	toString()
String	toStringWithDomains()	Returns a string representation of this BDD using the defined domains.
String	toStringWithDomains(BDD.BDDToString ts)	Returns a string representation of this BDD on the defined domains, using the given BDDToString converter.
BDDVarSet	toVarSet()	Converts this BDD to a new BDDVarSet.
abstract BDD	unique(BDDVarSet var)	Unique quantification of variables.
abstract int	var()	Gets the variable labeling the BDD.
abstract int[]	varProfile()	Counts the number of times each variable occurs in this BDD.
abstract BDD	veccompose(BDDPairing pair)	Simultaneous functional composition.
BDD	xor(BDD that)	Returns the logical 'xor' of two BDDs.
BDD	xorWith(BDD that)	Makes this BDD be the logical 'xor' of two BDDs.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

BDD

protected BDD()

Protected constructor.

Method Detail

getFactory

public abstract BDDFactory getFactory()

Returns the factory that created this BDD.

Returns:

factory that created this BDD

isZero

public abstract boolean isZero()

Returns true if this BDD is the zero (false) BDD.

Returns:

true if this BDD is the zero (false) BDD

isOne

public abstract boolean isOne()

Returns true if this BDD is the one (true) BDD.

Returns:

true if this BDD is the one (true) BDD

isUniverse

public boolean isUniverse()

Returns true if this BDD is the universe BDD. The universal BDD differs from the one BDD in ZDD mode.

Returns:

true if this BDD is the universe BDD

toVarSet

public BDDVarSet toVarSet()

Converts this BDD to a new BDDVarSet.

This BDD must be a boolean function that represents the all-true minterm of the BDD variables of interest.

Returns:

the contents of this BDD as a new BDDVarSet

var

public abstract int var()

Gets the variable labeling the BDD.

Compare to bdd_var.

Returns:

the index of the variable labeling the BDD

level

public int level()

Gets the level of this BDD.

Compare to LEVEL() macro.

Returns:

the level of this BDD

high

public abstract BDD high()

Gets the true branch of this BDD.

Compare to bdd_high.

Returns:

true branch of this BDD

low

public abstract BDD low()

Gets the false branch of this BDD.

Compare to bdd_low.

Returns:

false branch of this BDD

id

public abstract BDD id()

Identity function. Returns a copy of this BDD. Use as the argument to the "xxxWith" style operators when you do not want to have the argument consumed.

Compare to bdd_addref.

Returns:

copy of this BDD

not

public abstract BDD not()

Negates this BDD by exchanging all references to the zero-terminal with references to the one-terminal and vice-versa.

Compare to bdd_not.

Returns:

the negated BDD

and

public BDD and(BDD that)

Returns the logical 'and' of two BDDs. This is a shortcut for calling "apply" with the "and" operator.

Compare to bdd_and.

Parameters:

that - BDD to 'and' with

Returns:

the logical 'and' of two BDDs

andWith

public BDD andWith(BDD that)

Makes this BDD be the logical 'and' of two BDDs. The "that" BDD is consumed, and can no longer be used. This is a shortcut for calling "applyWith" with the "and" operator.

Compare to bdd_and and bdd_delref.

Parameters:

that - the BDD to 'and' with

Returns:

the logical 'and' of the two BDDs

or

public BDD or(BDD that)

Returns the logical 'or' of two BDDs. This is a shortcut for calling "apply" with the "or" operator.

Compare to bdd_or.

Parameters:

that - the BDD to 'or' with

Returns:

the logical 'or' of two BDDs

orWith

public BDD orWith(BDD that)

Makes this BDD be the logical 'or' of two BDDs. The "that" BDD is consumed, and can no longer be used. This is a shortcut for calling "applyWith" with the "or" operator.

Compare to bdd_or and bdd_delref.

Parameters:

that - the BDD to 'or' with

Returns:

the logical 'or' of the two BDDs

xor

public BDD xor(BDD that)

Returns the logical 'xor' of two BDDs. This is a shortcut for calling "apply" with the "xor" operator.

Compare to bdd_xor.

Parameters:

that - the BDD to 'xor' with

Returns:

the logical 'xor' of two BDDs

xorWith

public BDD xorWith(BDD that)

Makes this BDD be the logical 'xor' of two BDDs. The "that" BDD is consumed, and can no longer be used. This is a shortcut for calling "applyWith" with the "xor" operator.

Compare to bdd_xor and bdd_delref.

Parameters:

that - the BDD to 'xor' with

Returns:

the logical 'xor' of the two BDDs

imp

public BDD imp(BDD that)

Returns the logical 'implication' of two BDDs. This is a shortcut for calling "apply" with the "imp" operator.

Compare to bdd_imp.

Parameters:

that - the BDD to 'implication' with

Returns:

the logical 'implication' of two BDDs

impWith

public BDD impWith(BDD that)

Makes this BDD be the logical 'implication' of two BDDs. The "that" BDD is consumed, and can no longer be used. This is a shortcut for calling "applyWith" with the "imp" operator.

Compare to bdd_imp and bdd_delref.

Parameters:

that - the BDD to 'implication' with

Returns:

the logical 'implication' of the two BDDs

biimp

public BDD biimp(BDD that)

Returns the logical 'bi-implication' of two BDDs. This is a shortcut for calling "apply" with the "biimp" operator.

Compare to bdd_biimp.

Parameters:

that - the BDD to 'bi-implication' with

Returns:

the logical 'bi-implication' of two BDDs

biimpWith

public BDD biimpWith(BDD that)

Makes this BDD be the logical 'bi-implication' of two BDDs. The "that" BDD is consumed, and can no longer be used. This is a shortcut for calling "applyWith" with the "biimp" operator.

Compare to bdd_biimp and bdd_delref.

Parameters:

that - the BDD to 'bi-implication' with

Returns:

the logical 'bi-implication' of two BDDs

ite

public abstract BDD ite(BDD thenBDD,
                        BDD elseBDD)

if-then-else operator.

Compare to bdd_ite.

Parameters:

thenBDD - the 'then' BDD

elseBDD - the 'else' BDD

Returns:

the result of the if-then-else operator on the three BDDs

relprod

public BDD relprod(BDD that,
                   BDDVarSet var)

Relational product. Calculates the relational product of the two BDDs as this AND that with the variables in var quantified out afterwards. Identical to applyEx(that, and, var).

Compare to bdd_relprod.

Parameters:

that - the BDD to 'and' with

var - the BDDVarSet to existentially quantify with

Returns:

the result of the relational product

See Also:

BDDDomain.set()

compose

public abstract BDD compose(BDD g,
                            int var)

Functional composition. Substitutes the variable var with the BDD that in this BDD: result = f[g/var].

Compare to bdd_compose.

Parameters:

g - the function to use to replace

var - the variable number to replace

Returns:

the result of the functional composition

veccompose

public abstract BDD veccompose(BDDPairing pair)

Simultaneous functional composition. Uses the pairs of variables and BDDs in pair to make the simultaneous substitution: f [g1/V1, ... gn/Vn]. In this way one or more BDDs may be substituted in one step. The BDDs in pair may depend on the variables they are substituting. BDD.compose() may be used instead of BDD.replace() but is not as efficient when gi is a single variable, the same applies to BDD.restrict(). Note that simultaneous substitution is not necessarily the same as repeated substitution.

Compare to bdd_veccompose.

Parameters:

pair - the pairing of variables to functions

Returns:

BDD the result of the simultaneous functional composition

constrain

public abstract BDD constrain(BDD that)

Generalized cofactor. Computes the generalized cofactor of this BDD with respect to the given BDD.

Compare to bdd_constrain.

Parameters:

that - the BDD with which to compute the generalized cofactor

Returns:

the result of the generalized cofactor

exist

public abstract BDD exist(BDDVarSet var)

Existential quantification of variables. Removes all occurrences of this BDD in variables in the set var by existential quantification.

Compare to bdd_exist.

Parameters:

var - BDDVarSet containing the variables to be existentially quantified

Returns:

the result of the existential quantification

See Also:

BDDDomain.set()

forAll

public abstract BDD forAll(BDDVarSet var)

Universal quantification of variables. Removes all occurrences of this BDD in variables in the set var by universal quantification.

Compare to bdd_forall.

Parameters:

var - BDDVarSet containing the variables to be universally quantified

Returns:

the result of the universal quantification

See Also:

BDDDomain.set()

unique

public abstract BDD unique(BDDVarSet var)

Unique quantification of variables. This type of quantification uses a XOR operator instead of an OR operator as in the existential quantification.

Compare to bdd_unique.

Parameters:

var - BDDVarSet containing the variables to be uniquely quantified

Returns:

the result of the unique quantification

See Also:

BDDDomain.set()

restrict

public abstract BDD restrict(BDD var)

Restrict a set of variables to constant values. Restricts the variables in this BDD to constant true if they are included in their positive form in var, and constant false if they are included in their negative form.

Note that this is quite different than Coudert and Madre's restrict function.

Compare to bdd_restrict.

Parameters:

var - BDD containing the variables to be restricted

Returns:

the result of the restrict operation

See Also:

simplify(BDD)

restrictWith

public abstract BDD restrictWith(BDD var)

Mutates this BDD to restrict a set of variables to constant values. Restricts the variables in this BDD to constant true if they are included in their positive form in var, and constant false if they are included in their negative form. The "that" BDD is consumed, and can no longer be used.

Note that this is quite different than Coudert and Madre's restrict function.

Compare to bdd_restrict and bdd_delref.

Parameters:

var - BDD containing the variables to be restricted

Returns:

the result of the restrict operation

See Also:

BDDDomain.set()

simplify

public abstract BDD simplify(BDD d)

Coudert and Madre's restrict function. Tries to simplify the BDD f by restricting it to the domain covered by d. No checks are done to see if the result is actually smaller than the input. This can be done by the user with a call to nodeCount().

Compare to bdd_simplify.

Parameters:

d - BDDVarSet containing the variables in the domain

Returns:

the result of the simplify operation

support

public abstract BDDVarSet support()

Returns the variable support of this BDD. The support is all the variables that this BDD depends on.

Compare to bdd_support.

Returns:

the variable support of this BDD

apply

public abstract BDD apply(BDD that,
                          BDDFactory.BDDOp opr)

Returns the result of applying the binary operator opr to the two BDDs.

Compare to bdd_apply.

Parameters:

that - the BDD to apply the operator on

opr - the operator to apply

Returns:

the result of applying the operator

applyWith

public abstract BDD applyWith(BDD that,
                              BDDFactory.BDDOp opr)

Makes this BDD be the result of the binary operator opr of two BDDs. The "that" BDD is consumed, and can no longer be used. Attempting to use the passed in BDD again will result in an exception being thrown.

Compare to bdd_apply and bdd_delref.

Parameters:

that - the BDD to apply the operator on

opr - the operator to apply

Returns:

the result of applying the operator

applyAll

public abstract BDD applyAll(BDD that,
                             BDDFactory.BDDOp opr,
                             BDDVarSet var)

Applies the binary operator opr to two BDDs and then performs a universal quantification of the variables from the variable set var.

Compare to bdd_appall.

Parameters:

that - the BDD to apply the operator on

opr - the operator to apply

var - BDDVarSet containing the variables to quantify

Returns:

the result

See Also:

BDDDomain.set()

applyEx

public abstract BDD applyEx(BDD that,
                            BDDFactory.BDDOp opr,
                            BDDVarSet var)

Applies the binary operator opr to two BDDs and then performs an existential quantification of the variables from the variable set var.

Compare to bdd_appex.

Parameters:

that - the BDD to apply the operator on

opr - the operator to apply

var - BDDVarSet containing the variables to quantify

Returns:

the result

See Also:

BDDDomain.set()

applyUni

public abstract BDD applyUni(BDD that,
                             BDDFactory.BDDOp opr,
                             BDDVarSet var)

Applies the binary operator opr to two BDDs and then performs a unique quantification of the variables from the variable set var.

Compare to bdd_appuni.

Parameters:

that - the BDD to apply the operator on

opr - the operator to apply

var - BDDVarSet containing the variables to quantify

Returns:

the result

See Also:

BDDDomain.set()

satOne

public abstract BDD satOne()

Finds one satisfying variable assignment. Finds a BDD with at most one variable at each level. The new BDD implies this BDD and is not false unless this BDD is false.

Compare to bdd_satone.

Returns:

one satisfying variable assignment

fullSatOne

public abstract BDD fullSatOne()

Finds one satisfying variable assignment. Finds a BDD with exactly one variable at all levels. The new BDD implies this BDD and is not false unless this BDD is false.

Compare to bdd_fullsatone.

Returns:

one satisfying variable assignment

satOne

public abstract BDD satOne(BDDVarSet var,
                           boolean pol)

Finds one satisfying variable assignment. Finds a minterm in this BDD. The var argument is a set of variables that must be mentioned in the result. The polarity of these variables in the result - in case they are undefined in this BDD - are defined by the pol parameter. If pol is false, then all variables will be in negative form. Otherwise they will be in positive form.

Compare to bdd_satoneset.

Parameters:

var - BDDVarSet containing the set of variables that must be mentioned in the result

pol - the polarity of the result

Returns:

one satisfying variable assignment

See Also:

BDDDomain.set()

allsat

public BDD.AllSatIterator allsat()

Finds all satisfying variable assignments.

Compare to bdd_allsat.

Returns:

all satisfying variable assignments

scanVar

public BigInteger scanVar(BDDDomain d)

Finds one satisfying assignment of the domain d in this BDD and returns that value.

Compare to fdd_scanvar.

Parameters:

d - domain to scan

Returns:

one satisfying assignment for that domain

scanAllVar

public BigInteger[] scanAllVar()

Finds one satisfying assignment in this BDD of all the defined BDDDomain's. Each value is stored in an array which is returned. The size of this array is exactly the number of BDDDomain's defined.

Compare to fdd_scanallvar.

Returns:

array containing one satisfying assignment of all the defined domains

iterator

public BDD.BDDIterator iterator(BDDVarSet var)

Returns an iteration of the satisfying assignments of this BDD. Returns an iteration of minterms. The var argument is the set of variables that will be mentioned in the result.

Parameters:

var - set of variables to mention in result

Returns:

an iteration of minterms

See Also:

BDDDomain.set()

replace

public abstract BDD replace(BDDPairing pair)

Returns a BDD where all variables are replaced with the variables defined by pair. Each entry in pair consists of a old and a new variable. Whenever the old variable is found in this BDD then a new node with the new variable is inserted instead.

Compare to bdd_replace.

Parameters:

pair - pairing of variables to the BDDs that replace those variables

Returns:

result of replace

replaceWith

public abstract BDD replaceWith(BDDPairing pair)

Replaces all variables in this BDD with the variables defined by pair. Each entry in pair consists of a old and a new variable. Whenever the old variable is found in this BDD then a new node with the new variable is inserted instead. Mutates the current BDD.

Compare to bdd_replace and bdd_delref.

Parameters:

pair - pairing of variables to the BDDs that replace those variables

Returns:

result of replace

printSet

public void printSet()

Prints the set of truth assignments specified by this BDD.

Compare to bdd_printset.

printSetWithDomains

public void printSetWithDomains()

Prints this BDD using a set notation as in printSet() but with the index of the finite domain blocks included instead of the BDD variables.

Compare to fdd_printset.

printDot

public void printDot()

Prints this BDD in dot graph notation.

Compare to bdd_printdot.

printdot_rec

protected int printdot_rec(PrintStream out,
                           int current,
                           boolean[] visited,
                           HashMap<BDD,Integer> map)

nodeCount

public abstract int nodeCount()

Counts the number of distinct nodes used for this BDD.

Compare to bdd_nodecount.

Returns:

the number of distinct nodes used for this BDD

pathCount

public abstract double pathCount()

Counts the number of paths leading to the true terminal.

Compare to bdd_pathcount.

Returns:

the number of paths leading to the true terminal

satCount

public abstract double satCount()

Calculates the number of satisfying variable assignments.

Compare to bdd_satcount.

Returns:

the number of satisfying variable assignments

satCount

public double satCount(BDDVarSet varset)

Calculates the number of satisfying variable assignments to the variables in the given varset. ASSUMES THAT THE BDD DOES NOT HAVE ANY ASSIGNMENTS TO VARIABLES THAT ARE NOT IN VARSET. You will need to quantify out the other variables first.

Compare to bdd_satcountset.

Parameters:

varset - the given varset

Returns:

the number of satisfying variable assignments

logSatCount

public double logSatCount()

Calculates the logarithm of the number of satisfying variable assignments.

Compare to bdd_satcount.

Returns:

the logarithm of the number of satisfying variable assignments

logSatCount

public double logSatCount(BDDVarSet varset)

Calculates the logarithm of the number of satisfying variable assignments to the variables in the given varset.

Compare to bdd_satcountset.

Parameters:

varset - the given varset

Returns:

the logarithm of the number of satisfying variable assignments

varProfile

public abstract int[] varProfile()

Counts the number of times each variable occurs in this BDD. The result is stored and returned in an integer array where the i'th position stores the number of times the i'th printing variable occurred in the BDD.

Compare to bdd_varprofile.

Returns:

the variable profile

equalsBDD

public abstract boolean equalsBDD(BDD that)

Returns true if this BDD equals that BDD, false otherwise.

Parameters:

that - the BDD to compare with

Returns:

true iff the two BDDs are equal

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public abstract int hashCode()

Overrides:

hashCode in class Object

toString

public String toString()

Overrides:

toString in class Object

toStringWithDomains

public String toStringWithDomains()

Returns a string representation of this BDD using the defined domains.

Returns:

string representation of this BDD using the defined domains

toStringWithDomains

public String toStringWithDomains(BDD.BDDToString ts)

Returns a string representation of this BDD on the defined domains, using the given BDDToString converter.

Parameters:

ts - the given BDDToString converter

Returns:

string representation of this BDD using the given BDDToString converter

See Also:

BDD.BDDToString

free

public abstract void free()

Frees this BDD. Further use of this BDD will result in an exception being thrown.