Abstract: A system and methods are provided for verifying a hardware design for an electronic circuit. The method may include: providing a hardware design description for the electronic circuit; extracting a set of design constraints from the hardware design description, where the set of design constraints represents the electronic circuit in terms of signals and logical operations performed on the signals; creating an abstraction model from the set of design constraints, where the abstraction model abstracts one or more of the logical operations in the set of design constraints by replacing the abstracted logical operations with uninterpreted functions; and property checking the abstraction model in relation to one or more design properties. When a violation in the electronic circuit is detected by the property checking step, the feasibility of the violation is then checked and, if the violation is deemed infeasible, the abstraction model is refined.

Abstract: A system and methods are provided for verifying a hardware design for an electronic circuit. The method may include: providing a hardware design description for the electronic circuit; extracting a set of design constraints from the hardware design description, where the set of design constraints represents the electronic circuit in terms of signals and logical operations performed on the signals; creating an abstraction model from the set of design constraints, where the abstraction model abstracts one or more of the logical operations in the set of design constraints by replacing the abstracted logical operations with uninterpreted functions; and property checking the abstraction model in relation to one or more design properties. When a violation in the electronic circuit is detected by the property checking step, the feasibility of the violation is then checked and, if the violation is deemed infeasible, the abstraction model is refined.

Abstract: A system and methods are provided for verifying a hardware design for an electronic circuit. The method may include: providing a hardware design description for the electronic circuit; extracting a set of design constraints from the hardware design description, where the set of design constraints represents the electronic circuit in terms of signals and logical operations performed on the signals; creating an abstraction model from the set of design constraints, where the abstraction model abstracts one or more of the logical operations in the set of design constraints by replacing the abstracted logical operations with uninterpreted functions; and property checking the abstraction model in relation to one or more design properties. When a violation in the electronic circuit is detected by the property checking step, the feasibility of the violation is then checked and, if the violation is deemed infeasible, the abstraction model is refined.

Abstract: A system and methods are provided for verifying a hardware design for an electronic circuit. The method may include: providing a hardware design description for the electronic circuit; extracting a set of design constraints from the hardware design description, where the set of design constraints represents the electronic circuit in terms of signals and logical operations performed on the signals; creating an abstraction model from the set of design constraints, where the abstraction model abstracts one or more of the logical operations in the set of design constraints by replacing the abstracted logical operations with uninterpreted functions; and property checking the abstraction model in relation to one or more design properties. When a violation in the electronic circuit is detected by the property checking step, the feasibility of the violation is then checked and, if the violation is deemed infeasible, the abstraction model is refined.

Abstract: Methods and systems associated with online advertising campaigns are described. For example, systems and methods are described, which provide estimated advertising campaign statistics (e.g., in real-time) based on hypothetical online advertising campaign parameters entered by users. In certain implementations, the described systems combine pre-processed log data with real-time algorithms to estimate statistics for online advertising campaigns, which target a particular set of digital documents that display advertisements.