Module for manipulating Binary Decision Diagrams.

It contains programs for building BDDs, for computing probabilities and for performing Expectation Maximization.

author

- Fabrizio Riguzzi

copyright

- Fabrizio Riguzzi

license

- Artistic License 2.0 https://opensource.org/licenses/Artistic-2.0

 init_em(--Context:int) is det

Initializes a data structure for performing parameter learning. It returns an integer in Context that is a pointer to a context data structure for performing the EM algorithm.

 end_em(++Context:int) is det

Terminates the context data structure for performing parameter learning. Context is a pointer to a context data structure for performing the EM algorithm. Context must have been returned by a call to init_em/1. It frees the memory occupied by Context.

 init_ex(++Context:int, --Environment:int) is det

Initializes an enviroment data structure for storing a BDD. Context is an integer that is a pointer to a context data structure created using init_em/1. Returns an integer Environment that is a pointer to a data structure for storing a single BDD to be used for the EM algorithm.

 end_ex(++Environment:int) is det

Terminates the evnironment data structure for storing a BDD. Environment is a pointer to a data structure returned by init_ex/2. It frees the memory occupied by the BDD.

 init(--Environment:int) is det

Initializes a data structure for storing a single BDD. Returns an integer Environment that is a pointer to a data structure for storing a single BDD to be used for inference only (no learning).

 end(++Environment:int) is det

Terminates the environment data structure for storing a single BDD. Environment is a pointer to a data structure returned by a call to init/1.

 one(++Environment:int, --One:int) is det

Returns in One a pointer to a BDD belonging to environment Environment representing the one Boolean function.

 zero(++Environment:int, --Zero:int) is det

Returns in Zero a pointer to a BDD belonging to environment Environment representing the zero Boolean function.

 and(++Environment:int, ++A:int, ++B:int, --AandB:int) is det

Returns in AandB a pointer to a BDD belonging to environment Environment representing the conjunction of BDDs A and B.

 or(++Environment:int, ++A:int, ++B:int, --AorB:int) is det

Returns in AorB a pointer to a BDD belonging to environment Environment representing the disjunction of BDDs A and B.

 ret_prob(++Environment:int, ++BDD:int, -Probability:float) is det

Returns the Probability of BDD belonging to environment Environment.

 ret_map_prob(++Environment:int, ++BDD:int, -Probability:float, -MAPState:list) is det

Returns the MAP state MPAState of BDD and its Probability. BDD belongs to environment Environment.

 ret_abd_prob(++Environment:int, ++BDD:int, -Probability:float, -Explanation:list) is det

Returns the abductive Explanation of BDD and its Probability. BDD belongs to environment Environment.

 bdd_not(++Environment:int, ++A:int, --NotA:int) is det

Returns in NotA a pointer to a BDD belonging to environment Environment representing the negation of BDD A.

 equality(++Environment:int, ++Variable:int, ++Value:int, --BDD:int) is det

Returns in BDD the BDD belonging to environment Environment that represents the equation Variable=Value.

 em(++Context:int, ++RuleInfo:list, ++ListOfBDDs:list, ++EA:float, ++ER:float, ++Iterations:int, -LL:float, -Parameters:list, -ExampleProbabilities:list) is det

NumberOfHeads is a list of terms, one for each rule. Each term is either an integer, indicating the number of head atoms in the rule, or a list [N] where N is the number of head atoms. In the first case, the parameters of the rule are tunable, in the latter they are fixed.

Performs EM learning. Takes as input the Context, information on the rules, a list of BDDs each representing one example, the minimum absolute difference EA and relative difference ER between the log likelihood of examples in two different iterations and the maximum number of iterations Iterations. RuleInfo is a list of elements, one for each rule, with are either

• an integer, indicating the number of heads, in which case the parameters of the corresponding rule should be randomized,
• a list of floats, in which case the parameters should be set to those indicated in the list and not changed during learning (fixed parameters)
• [a list of floats], in which case the initial values of the parameters should be set to those indicated in the list and changed during learning (initial values of the parameters) Returns the final log likelihood of examples LL, the list of new Parameters and a list with the final probabilities of each example. Parameters is a list whose elements are of the form [N,P] where N is the rule number and P is a list of probabilities, one for each head atom of rule N, in reverse order.

 add_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new random variable in Environment with NumberOHeads values and probability distribution ProbabilityDistribution.

 add_abd_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new abducible random variable in Environment with NumberOHeads values and probability distribution ProbabilityDistribution.

 add_query_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new random variable to be queried in MAP inference with NumberOHeads values and probability distribution ProbabilityDistribution. The variable belongs to Environment.

 make_query_var(++Environment:int, +Variable:int, --BDD:int) is det

Makes Variable belonging to Environment a query random variable for MAP inference. Returns in BDD the diagram of the formula encoding the required constraints among the Boolean random variable that represent Variable.

 create_dot_string(++Env:int, ++BDD:int, -Dot:string) is det

The predicate returns the BDD in dot format.

 create_dot(++Env:int, ++BDD:int, ++File:string) is det

The predicate writes the BDD in dot format to to file FileName.

 rand_seed(+Seed:int) is det

The pseudo-random number generator is initialized using the argument passed as Seed. It calls the C function srand.

 orc(++A:couple, ++B:couple, --AorB:couple) is det

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AorB a couple (Environment, BDDAorB) where BDDAorB is pointer to a BDD belonging to environment Environment representing the disjunction of BDDs BDDA and BDDB.

 onec(++Environment:int, --One:couple) is det

Returns in One a couple (Environment,BDD) where BDD is pointer to a BDD belonging to environment Environment representing the one Boolean function

 zeroc(++Environment:int, --Zero:couple) is det

Returns in Zero a couple (Environment,BDD) where BDD is pointer to a BDD belonging to environment Environment representing the zero Boolean function

 andc(++Environment:int, ++A:couple, ++B:couple, --AandB:couple) is semidet

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AandB a couple (Environment, BDDAandB) where BDDAandB is pointer to a BDD belonging to environment Environment representing the conjunction of BDDs BDDA and BDDB. fails if BDDB represents the zero function

 andcnf(++Environment:int, ++A:couple, ++B:couple, --AandB:couple) is semidet

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AandB a couple (Environment, BDDAandB) where BDDAandB is pointer to a BDD belonging to environment Environment representing the conjunction of BDDs BDDA and BDDB.

 bdd_notc(++Environment:int, ++EBDD:couple, --NotEBDD:couple) is det

EBDD is a couple (Environment,A) Returns in NotEBDD a couple (Environment,NotA) where NotA is pointer to a BDD belonging to environment Environment representing the negation of BDD A

 equalityc(++Environment:int, ++Variable:int, ++Value:int, --EBDD:couple) is det

Returns in EBDD a couple (Environment,BDD) where BDD belongs to environment Environment and represents the equation Variable=Value.

 ret_probc(++Environment:int, ++EBDD:couple, -Probability:float) is det

EBDD is a couple (Environment,BDD) Returns the Probability of BDD belonging to environment Environment Uses

 initial_values(++Environment:int, ++Alpha:float) is det

Sets the type of parameter initialization for EM on Environment: if Alpha is 0.0, it uses a truncated Dirichlet process if Alpha is a float > 0.0, it uses a symmetric Dirichlet distribution with that value as parameter

 or_list(++ListOfBDDs:list, ++Environment, --BDD:int) is det

Returns in BDD a pointer to a BDD belonging to environment Environment representing the disjunction of all the BDDs in ListOfBDDs

 or_listc(++ListOfBDDs:list, ++Environment, --BDD:int) is det

Returns in BDD a couple (Env,B) with B a pointer to a BDD belonging to environment Environment representing the disjunction of all the BDDs in ListOfBDDs (a list of couples (Env,BDD))

Undocumented predicates

The following predicates are exported, but not or incorrectly documented.

 gamma_sample(Arg1, Arg2, Arg3)

 gauss_sample(Arg1, Arg2, Arg3)

 uniform_sample(Arg1)

 dirichlet_sample(Arg1, Arg2)

 symmetric_dirichlet_sample(Arg1, Arg2, Arg3)

 discrete_sample(Arg1, Arg2)

 add_decision_var(Arg1, Arg2, Arg3)

 probability_dd(Arg1, Arg2, Arg3)

 add_prod(Arg1, Arg2, Arg3, Arg4)

 add_sum(Arg1, Arg2, Arg3, Arg4)

 ret_strategy(Arg1, Arg2, Arg3, Arg4)

 debug_cudd_var(Arg1, Arg2)