Abstract: Methods and apparatuses are described for sharing inductive invariants while performing formal verification of a circuit design. Specifically, some embodiments assume at least an inductive invariant for a property to be true while proving another property. According to one definition, an inductive invariant of a property is an inductive assertion such that all states that satisfy the inductive assertion also satisfy the property. According to one definition, an inductive assertion describes a set of states that includes all legal initial states of the circuit design and that is closed under a transition relation that models the circuit design.

Abstract: Methods and apparatuses are described for proving equivalence between two or more circuit designs that include one or more division circuits and/or one or more square-root circuits. Some embodiments analyze the circuit designs to determine an input relationship between the inputs of two division (or square-root) circuits. Next, the embodiments determine an output relationship between the outputs of two division (or square-root) circuits based on the input relationship. The embodiments then prove equivalence between the circuit designs by using the input and output relationships.

Abstract: Methods and apparatuses are described for proving equivalence between two or more circuit designs that include one or more division circuits and/or one or more square-root circuits. Some embodiments analyze the circuit designs to determine an input relationship between the inputs of two division (or square-root) circuits. Next, the embodiments determine an output relationship between the outputs of two division (or square-root) circuits based on the input relationship. The embodiments then prove equivalence between the circuit designs by using the input and output relationships.

Abstract: Methods and apparatuses are described for proving equivalence between two or more circuit designs that include one or more division circuits and/or one or more square-root circuits. Some embodiments analyze the circuit designs to determine an input relationship between the inputs of two division (or square-root) circuits. Next, the embodiments determine an output relationship between the outputs of two division (or square-root) circuits based on the input relationship. The embodiments then prove equivalence between the circuit designs by using the input and output relationships.

Abstract: Methods and apparatuses are described for sharing inductive invariants while performing formal verification of a circuit design. Specifically, some embodiments assume at least an inductive invariant for a property to be true while proving another property. According to one definition, an inductive invariant of a property is an inductive assertion such that all states that satisfy the inductive assertion also satisfy the property. According to one definition, an inductive assertion describes a set of states that includes all legal initial states of the circuit design and that is closed under a transition relation that models the circuit design.

Abstract: Methods and apparatuses are described for formally verifying a bit-serial division circuit design or a bit-serial square-root circuit design. Some embodiments formally verify a bit-serial division circuit design using a set of properties that can be efficiently proven using a bit-level solver. In some embodiments, the set of properties that are used for verifying a bit-serial division circuit design does not include any terms that multiply a w-bit partial quotient with the divisor. Some embodiments formally verify a bit-serial square-root circuit design using a set of properties that can be efficiently proven using a bit-level solver. In some embodiments, the set of properties that are used for verifying a bit-serial square-root circuit design does not include any terms that compute a square of a w-bit partial square-root.

Abstract: Methods and apparatuses are described for proving equivalence between two or more circuit designs that include one or more division circuits and/or one or more square-root circuits. Some embodiments analyze the circuit designs to determine an input relationship between the inputs of two division (or square-root) circuits. Next, the embodiments determine an output relationship between the outputs of two division (or square-root) circuits based on the input relationship. The embodiments then prove equivalence between the circuit designs by using the input and output relationships.

Abstract: Methods and apparatuses are described for formally verifying a bit-serial division circuit design or a bit-serial square-root circuit design. Some embodiments formally verify a bit-serial division circuit design using a set of properties that can be efficiently proven using a bit-level solver. In some embodiments, the set of properties that are used for verifying a bit-serial division circuit design does not include any terms that multiply a w-bit partial quotient with the divisor. Some embodiments formally verify a bit-serial square-root circuit design using a set of properties that can be efficiently proven using a bit-level solver. In some embodiments, the set of properties that are used for verifying a bit-serial square-root circuit design does not include any terms that compute a square of a w-bit partial square-root.

Abstract: A method for verifying an integrated circuit design using constraint information to develop a weighted data structure. In one embodiment, a binary decision diagram (BDD) includes a plurality of nodes (401, 402, 403, 404, 405, 406, 407, 420, and 430) representing signals and states in the circuit, and each node has a branching probability based on user-defined weights. The BDD represents the intersection of the input space and state space which satisfies the constraints. Current state information resulting from simulation is used to dynamically adjust the branching probabilities of the BDD on the fly. In one embodiment, the constraint information is applicable for formal verification of a portion of the circuit. In another embodiment, a simulation controller (12) receives design and constraint information and generates the program to control simulator (14).