Abstract: Disclosed below are representative embodiments of methods, apparatus, and systems for performing formal verification. For example, certain embodiments can be used to formally verify a Booth multiplier. For instance, in one example embodiment, a specification of a Booth multiplier circuit is received; an initial model checking operation is performed for a smaller version of the Booth multiplier circuit; a series of subsequent model checking operations are performed for versions of the Booth multiplier circuit that are incrementally larger than the smaller version of the Booth multiplier circuit, wherein, for each incrementally larger Booth multiplier circuit, two or more model checking operations are performed, the two or more model checking operations representing decomposed proof obligations for showing; and a verification result of the Booth multiplier circuit is output.

Abstract: A mechanism is provided for efficiently determining Boolean satisfiability (SAT) using lazy constraints. A determination is made as to whether a SAT problem is satisfied without constraints in a list of constraints. Responsive to the SAT problem being satisfied without constraints, a set of variable assignments that are determined in satisfying the SAT problem without constraints are fixed. For each constraint in the list of constraints, a determination is made as to whether the SAT problem with the constraint results in the set of variable assignments remaining constant. Responsive to the SAT problem with the constraint resulting in the set of variable assignments remaining constant, the constraint is added to a list of non-affecting constraints and a satisfied result is returned.

Abstract: Disclosed below are representative embodiments of methods, apparatus, and systems for performing formal verification. For example, certain embodiments can be used to formally verify a Booth multiplier. For instance, in one example embodiment, a specification of a Booth multiplier circuit is received; an initial model checking operation is performed for a smaller version of the Booth multiplier circuit; a series of subsequent model checking operations are performed for versions of the Booth multiplier circuit that are incrementally larger than the smaller version of the Booth multiplier circuit, wherein, for each incrementally larger Booth multiplier circuit, two or more model checking operations are performed, the two or more model checking operations representing decomposed proof obligations for showing; and a verification result of the Booth multiplier circuit is output.

Abstract: A computer-implemented method simplifies a netlist, verifies the simplified netlist using induction, and remaps resulting inductive counterexamples via inductive trace lifting within a multi-algorithm verification framework. The method includes: a processor deriving a first unreachable state information that can be utilized to simplify the netlist; performing a simplification of the netlist utilizing the first unreachable state information; determining whether the first unreachable state information can be inductively proved on an original version of the netlist; and in response to the first unreachable state information not being inductively provable on the original netlist: projecting the first unreachable state information to a minimal subset; and adding the projected unreachable state information as an invariant to further constrain a child induction process.

Abstract: A mechanism is provided for efficiently determining Boolean satisfiability (SAT) using lazy constraints. A determination is made as to whether a SAT problem is satisfied without constraints in a list of constraints. Responsive to the SAT problem being satisfied without constraints, a set of variable assignments that are determined in satisfying the SAT problem without constraints are fixed. For each constraint in the list of constraints, a determination is made as to whether the SAT problem with the constraint results in the set of variable assignments remaining constant. Responsive to the SAT problem with the constraint resulting in the set of variable assignments remaining constant, the constraint is added to a list of non-affecting constraints and a satisfied result is returned.

Abstract: A computer-implemented method includes a processor identifying, within the netlist, at least one strongly connected components (SCCs) that has a reconvergent fanin input with at least two input paths from the reconvergent fanin input having a different propagation delay to the SCC. The method then computes an additive diameter for the netlist comprising at least one SCC, where the additive diameter includes a fanin additive diameter determined based on a propagation delay difference of the at least two input paths to a SCC and a number of complex feed-forward components within at least one input path. In response to the reconvergent fanin input to the SCC providing a binate function, the method computes a multiplicative diameter for the SCC utilizing a least common multiple (LCM) derived from one or more propagation delay differences across each reconvergent fanin input leading to the SCC.

Abstract: A mechanism is provided for increasing the scalability of transformation-based formal verification solutions through enabling the use of phase abstraction on logic models that include memory arrays. The mechanism manipulates the array to create a plurality of copies of its read and write ports, representing the different modulo time frames. The mechanism converts all write-before-read arrays to read-before-write and adds a bypass path around the array from write ports to read ports to capture any necessary concurrent read and write forwarding. The mechanism uses an additional set of bypass paths to ensure that the proper write data that becomes effectively concurrent through the unfolding inherent in phase abstraction is forwarded to the proper read port. If a given read port is disabled or fetches out-of-bounds data, the mechanism applies randomized data to the read port data output.

Abstract: A computer-implemented method includes receiving an input containing a candidate netlist, a target, and a number, K, of cycles of interest, where K represents a number of cycles required to be analyzed for the proof-based abstraction. In response to receiving the inputs, a computing device builds an inductively unrolled netlist, utilizing random, symbolic initial values, for K cycles and provides the unrolled netlist with a first initial value constraint to a satisfiability (SAT) solver, with the first initial value constraint empty. The method includes determining whether a result of the SAT solver is satisfiable, and in response to the result not being satisfiable, performing an abstraction on the netlist and outputting the abstraction. However, in response to the result being satisfiable, the method includes performing one of: (a) outputting a valid counterexample of the original netlist; and (b) lazily adding initial value constraints to avoid spurious counterexamples.

Abstract: A mechanism is provided for simplifying a netlist before computational resources are exceeded. For each of a set of suspected equivalences in a proof graph of a netlist, a determination is made as to whether equivalence holds for at least one of an equivalence or an equivalence class by identifying whether the equivalence or equivalence class is either affecting or non-affecting. Responsive to the equivalence or equivalence class being affecting, a proof dependency is recorded as an edge in a proof graph. For each node in the proof graph, a determination is made as to whether the node has a falsified dependency. Responsive to the node failing to have a falsified dependency, identification is made that all dependencies are satisfied and that the equivalences represented by the node in the proof graph are sequential equivalences. The netlist is then simplified by consuming the sequential equivalences.

Abstract: A mechanism is provided in an integrated circuit simulator for tracking array data contents across three-value read and write operations. The mechanism accounts for write operations with data values and address values having X symbols. The mechanism performs writes to a tree data structure that is used to store the three-valued contents to the array. The simulator includes functionality for updating the array contents for a three-valued write and to read data for a three-valued read. The simulator also includes optimizations for dynamically reducing the size of the data structure when possible in order to save memory in the logic simulator.

Abstract: A method, system, and computer program product for reducing the size of a logic network design, prior to verification of the logic network design. The method includes eliminating registers to reduce the size of the logic network design; thereby, increasing the speed and functionality of the verification process, and decreasing the size of the logic network design. The system identifies one or more compatible resubstitutions of a selected register, wherein the compatible resubstitution expresses the selected register as one or more pre-existing registers of fixed initial state. The resubstitutions are refined utilizing design invariants. When one more resubstitutions are preformed, the system eliminates the selected registers to reduce the size of the logic network design. As a result of the resubstitution process, a logic network design of reduced size is generated.

Abstract: A technique for performing an analysis of a logic design (that includes a native memory array embodied in a netlist) includes detecting an initial transient behavior in the logic design as embodied in the netlist. The technique also includes determining a duration of the initial transient behavior and gathering reduction information on the logic design based on the initial transient behavior. The netlist is then modified based on the reduction information.

Abstract: A logic synthesis program, method and system for simplifying and/or reducing a logic design receives output from a logic simulator that uses symbolic values for stimulus and contains symbolic values in the logic simulator output. Relationships between the nodes dependent on symbolic values can be used to merge nodes or otherwise simplify the logic design. Behaviors such as oscillators, transient values, identical signals, dependent logical states and chicken-switch determined states that depend on the symbolic values can be detected in the simulation results and the netlist simplified using the results of the detection. The netlist can be simplified by inserting registers to represent nodes that assume a symbolic value or combination based on symbolic values either statically or after an initial transient.

Abstract: Methods and systems are provided for reducing an original circuit design into a simplified circuit design by merging gates that may not be equivalent but can be demonstrated to preserve target assertability with respect to the original circuitry design. A composite netlist is created from the simplified netlist and the original netlist. The composite netlist includes a number of targets that imply the existence of a target in the simplified netlist and a corresponding target in the original netlist. The implications are verified and then validated to ensure the simplified circuit design is a suitable replacement for the original circuit design.

Abstract: A mechanism is provided for simplifying a netlist before computational resources are exceeded. For each of a set of suspected equivalences in a proof graph of a netlist, a determination is made as to whether equivalence holds for at least one of an equivalence or an equivalence class by identifying whether the equivalence or equivalence class is either affecting or non-affecting. Responsive to the equivalence or equivalence class being affecting, a proof dependency is recorded as an edge in a proof graph. For each node in the proof graph, a determination is made as to whether the node has a falsified dependency. Responsive to the node failing to have a falsified dependency, identification is made that all dependencies are satisfied and that the equivalences represented by the node in the proof graph are sequential equivalences. The netlist is then simplified by consuming the sequential equivalences.

Abstract: Mechanisms are provided in a design environment for eliminating, coalescing, or bypassing ports. The design environment comprises one mechanism to eliminate unnecessary ports in arrays using disabled and disconnected pin information. The design environment may comprise another mechanism to combine and reduce the number of array ports using address comparisons. The design environment may comprise another mechanism to combine and reduce the number of array ports using disjoint enable comparisons. The design environment may comprise one mechanism to combine and reduce the number of array ports using “don't care” computations. The design environment may comprise another mechanism to reduce the number of array ports through bypassing write-to-read paths around arrays.

Abstract: A technique for performing an analysis of a logic design includes detecting an initial transient behavior in a logic design embodied in a netlist. A duration of the initial transient behavior is also determined. Reduction information on the logic design is gathered based on the initial transient behavior. The netlist is then modified based on the reduction information.

Abstract: A logic synthesis program, method and system for simplifying and/or reducing a logic design receives output from a logic simulator that uses symbolic values for stimulus and contains symbolic values in the logic simulator output. Relationships between the nodes dependent on symbolic values can be used to merge nodes or otherwise simplify the logic design. Behaviors such as oscillators, transient values, identical signals, dependent logical states and chicken-switch determined states that depend on the symbolic values can be detected in the simulation results and the netlist simplified using the results of the detection. The netlist can be simplified by inserting registers to represent nodes that assume a symbolic value or combination based on symbolic values either statically or after an initial transient.

Abstract: A logic simulation program, method and system for obtaining a set of reachable states for a logic design that can be used to provide input to other algorithms that simplify the netlist describing the logic design or perform other types of processing, provides an efficient, compact behavior when simulating large designs. Rather than simulating using ternary input and state value representations that are restricted to true, false and unknown, the techniques of the present invention use input symbolic values that are retained in the set of reachable states retained as the output. Behaviors such as oscillators, transient values, identical signals, dependent logical states and chicken-switch determined states can be detected in the simulation results and the netlist simplified using the results of the detection.

Abstract: Mechanisms are provided in a design environment for minimizing memory array representations for enhanced synthesis and verification. The design environment comprises one mechanism to compress the width of arrays using disconnected pin information. The design environment comprises another mechanism to simplify the enable conditions of array ports using “don't care” computations. The design environment comprises yet another mechanism to reduce address pins from an array through analysis of limitations of readable addresses.