Abstract: A method and product for solving a Constraint Satisfaction Problem (CSP) having a constraint associated with a string variable, comprising: defining a string variable using a string domain data structure representing a domain of string values for string variables, the structure represents the domain as a Deterministic Finite Automaton (DFA) with no back loops longer than 1 and edges representing characters; defining a constraint for the CSP, wherein the constraint involves the variable and is to be complied with by a solution to the CSP; invoking a CSP solver using the string variable while complying with the constraint, and to invoke operations performed over the domain, wherein the solver: propagates values into the domain of string values, wherein the value propagation reduces the domain size; or selects values from the domain thus reducing the domain to a singleton domain, whereby value propagation to domains of other variables is invoked by the solver.

Abstract: A method and product for solving a Constraint Satisfaction Problem (CSP) having a constraint associated with a string variable, comprising: defining a string variable using a string domain data structure representing a domain of string values for string variables, the structure represents the domain as a Deterministic Finite Automaton (DFA) with no back loops longer than 1 and edges representing characters; defining a constraint for the CSP, wherein the constraint involves the variable and is to be complied with by a solution to the CSP; invoking a CSP solver using the string variable while complying with the constraint, and to invoke operations performed over the domain, wherein the solver: propagates values into the domain of string values, wherein the value propagation reduces the domain size; or selects values from the domain thus reducing the domain to a singleton domain, whereby value propagation to domains of other variables is invoked by the solver.

Abstract: A method, apparatus and product for encoding a cardinality constraint in Conjunctive Normal Form (CNF). The method comprising: having a Boolean formula comprising a cardinality constraint, wherein the cardinality constraint relating to a set of Boolean variables, the set of variables consisting of N variables, the cardinality constraint given in a non-Conjunctive Normal Form; and encoding the cardinality constraint in Conjunctive Normal Form based on a mapping by a Perfect Hash Family, whereby said memory is modified to retain the CNF encoded cardinality constraint.

Abstract: A method, apparatus and product for encoding a cardinality constraint in Conjunctive Normal Form (CNF). The method comprising: having a Boolean formula comprising a cardinality constraint, wherein the cardinality constraint relating to a set of Boolean variables, the set of variables consisting of N variables, the cardinality constraint given in a non-Conjunctive Normal Form; and encoding the cardinality constraint in Conjunctive Normal Form based on a mapping by a Perfect Hash Family, whereby said memory is modified to retain the CNF encoded cardinality constraint.