Abstract: The present disclosure describes systems and methods for adjusting a logic network. The method includes adding, to the logic network, a first redundant node and determining a first adjustment to a first node of the logic network within a transitive fanin of the first redundant node. The method also includes making the first adjustment to the first node based on determining that a first gain based on the first adjustment satisfies a threshold.

Abstract: Embodiments herein describe selecting a gate in a mapped network and then un-mapping the gate from a library cell into a Boolean expression. Resubstitution can be performed on the gate to determine whether its logic can be simplified using, e.g., a don’t care set and candidate divisors within a window of the gate. If a new Boolean expression resulting from performing resubstitution has an equivalent function, the gate can be re-mapped using the new Boolean expression, which can reduce the area of a circuit design corresponding to the mapped network. These steps can be performed iteratively on the mapped network.

Abstract: A logic network for an integrated circuit is synthesized as follows. The logic network is mapped to a network of lookup tables (LUTs). The LUT mapping is based at least in part on estimated areas of the LUTs. The individual LUTs in the network are improved (LUT optimization), for example using various Boolean optimization techniques. The network of improved LUTs is then reduced to a gate-level netlist of standard cells.

Abstract: A system and method for SAT-sweeping is disclosed. According to one embodiment, a method includes determining gate classes by inputting simulation patterns to gates in an integrated circuit design, selecting a candidate gate based on an inverse topological ordering of the gates, and then selecting a driver gate belonging to the same gate class as the candidate gate. A SAT-solver is called based on the candidate gate and the driver gate to confirm equivalence. The candidate gate and the driver gate are then merged in the integrated circuit design.

Abstract: Techniques and systems for optimizing a logic network are described. Some embodiments automatically identify scenarios where Boolean methods are best driven by truth tables, binary decision diagrams (BDDs) or satisfiability (SAT). Some embodiments use circuit partitioning techniques that are based on hash-tables and topological sorting, and that are capable of grouping nodes with high simplification likelihood and still are able to efficiently scale to large circuits. Some embodiments feature a generalized resubstitution framework based on computing, and implementing, the Boolean difference between two nodes. Some embodiments include enhancements to (i) gradient-based and-inverter-graph (AIG) optimization, (ii) heterogeneous elimination for kerneling, and (iii) revisitation of maximum set of permissible functions (MSPF) computation with BDDs.

Abstract: A system and method for SAT-sweeping is disclosed. According to one embodiment, a method includes determining gate classes by inputting simulation patterns to gates in an integrated circuit design, selecting a candidate gate based on an inverse topological ordering of the gates, and then selecting a driver gate belonging to the same gate class as the candidate gate. A SAT-solver is called based on the candidate gate and the driver gate to confirm equivalence. The candidate gate and the driver gate are then merged in the integrated circuit design.

Abstract: Robust logic optimization on an IC design based on exclusive sum-of-products (ESOP) refactoring is described. ESOP expressions are two-level logic representation forms, similar to sum-of-product SOP representations. However, since ESOPs use exclusive-OR (XOR) instead of OR operators they can be exponentially more compact than sum-of-product (SOP) expressions for important classes of functions. In XOR heavy logic, ESOP expressions allow us to find optimizations that SOPs simply do not have access to.

Abstract: Systems and techniques are described for circuit optimization using Boolean resynthesis. Features described in this disclosure include (i) a theory of Boolean filtering, to drastically reduce the number of gates processed and still retain all possible optimization opportunities, (ii) a weaker notion of maximum set of permissible functions, which can be computed efficiently via truth tables, (iii) a parallel package for truth table computation tailored to speedup Boolean methods, (iv) a generalized refactoring engine which supports multiple representation forms and (v) a Boolean resynthesis flow, which combines these techniques.

Abstract: Techniques and systems for optimizing a logic network are described. Some embodiments automatically identify scenarios where Boolean methods are best driven by truth tables, binary decision diagrams (BDDs) or satisfiability (SAT). Some embodiments use circuit partitioning techniques that are based on hash-tables and topological sorting, and that are capable of grouping nodes with high simplification likelihood and still are able to efficiently scale to large circuits. Some embodiments feature a generalized resubstitution framework based on computing, and implementing, the Boolean difference between two nodes. Some embodiments include enhancements to (i) gradient-based and-inverter-graph (AIG) optimization, (ii) heterogeneous elimination for kerneling, and (iii) revisitation of maximum set of permissible functions (MSPF) computation with BDDs.

Abstract: A method for optimizing an implementation of a logic circuit, comprising steps of providing an interpretation of the logic circuit in terms of 3 Boolean variable majority operators M, with each of the majority operators being a function of a plurality of variables that returns a logic value assumed by more than half of the plurality of variables, and a single Boolean variable complementation operator ?. The method further comprises providing a commutativity, a majority (?.M), an associativity (?.A), a distributivity (?.D), an inverter propagation (?.I), a relevance (?.R), a complementary associativity (?.C), and a substitution (?.S) transformation; and combining the ?.M, ?.C, ?.A, ?.D, ?.I, ?.R, ?.C and ?.S transformations to reduce an area of the logic circuit via (i) a reshaping procedure consisting of the ?.A, ?.C, ?.D, ?.I, ?.R, ?.S and ?.

Abstract: We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consistent algebraic framework. However, when algebraic methods cannot improve a result quality, stronger Boolean methods are needed to attain further optimization. For this purpose, we propose MIG Boolean methods exploiting the error masking property of majority operators. Our MIG Boolean methods insert logic errors that strongly simplify an MIG while being successively masked by the voting nature of majority nodes. Thanks to the data-structure/methodology fitness, our MIG Boolean methods run in principle as fast as algebraic counterparts. Experiments show that our Boolean methodology combined with state-of-art MIG algebraic techniques enable superior optimization quality.

Abstract: Systems and techniques for optimizing an integrated circuit (IC) design are described. A logic-function identifier can be determined based on a fan-in combinational-logic-cone, wherein the logic-function identifier corresponds to a logic function that is implemented by the fan-in combinational-logic-cone. An arrival-time-pattern identifier can be determined based on a set of arrival times at inputs of the fan-in combinational-logic-cone. An optimized combinational-logic-cone can be obtained by performing, in addition to optionally other operations, a database lookup by using the logic-function identifier and the arrival-time-pattern identifier. Next, the fan-in combinational-logic-cone can be replaced with the optimized combinational-logic-cone in the IC design.

Abstract: Systems and techniques for optimizing an integrated circuit (IC) design are described. A logic-function identifier can be determined based on a fan-in combinational-logic-cone, wherein the logic-function identifier corresponds to a logic function that is implemented by the fan-in combinational-logic-cone. An arrival-time-pattern identifier can be determined based on a set of arrival times at inputs of the fan-in combinational-logic-cone. An optimized combinational-logic-cone can be obtained by performing, in addition to optionally other operations, a database lookup by using the logic-function identifier and the arrival-time-pattern identifier. Next, the fan-in combinational-logic-cone can be replaced with the optimized combinational-logic-cone in the IC design.

Abstract: Systems and techniques for optimizing timing of an integrated circuit (IC) design are described. A logic-function identifier can be determined based on a fan-in combinational-logic-cone, wherein the logic-function identifier corresponds to a logic function that is implemented by the fan-in combinational-logic-cone. An arrival-time-pattern identifier can be determined based on a set of arrival times at inputs of the fan-in combinational-logic-cone. A database lookup can be performed based on the logic-function identifier and the arrival-time-pattern identifier to obtain an optimized combinational-logic-cone. Next, the fan-in combinational-logic-cone can be replaced with the optimized combinational-logic-cone in the IC design.

Abstract: Systems and techniques for optimizing timing of an integrated circuit (IC) design are described. A logic-function identifier can be determined based on a fan-in combinational-logic-cone, wherein the logic-function identifier corresponds to a logic function that is implemented by the fan-in combinational-logic-cone. An arrival-time-pattern identifier can be determined based on a set of arrival times at inputs of the fan-in combinational-logic-cone. A database lookup can be performed based on the logic-function identifier and the arrival-time-pattern identifier to obtain an optimized combinational-logic-cone. Next, the fan-in combinational-logic-cone can be replaced with the optimized combinational-logic-cone in the IC design.

Abstract: A method for optimizing an implementation of a logic circuit, comprising steps of providing an interpretation of the logic circuit in terms of 3 Boolean variable majority operators M, with each of the majority operators being a function of a plurality of variables that returns a logic value assumed by more than half of the plurality of variables, and a single Boolean variable complementation operator ?. The method further comprises providing a commutativity, a majority (?.M), an associativity (?.A), a distributivity (?.D), an inverter propagation (?.I), a relevance (?.R), a complementary associativity (?.C), and a substitution (?.S) transformation; and combining the ?.M, ?.C, ?.A, ?.D, ?.I, ?.R, ?.C and ?.S transformations to reduce an area of the logic circuit via (i) a reshaping procedure consisting of the ?.A, ?.C, ?.D, ?.I, ?.R, ?.S and ?.

Abstract: A method for transforming a tautology check of an original logic circuit into a contradiction check of the original logic circuit and vice versa comprises interpreting the original logic circuit in terms of AND, OR, MAJ, MIN, XOR, XNOR, INV original logic operators; transforming the original circuit obtained from the interpreting, into a dual logic circuit enabled for a checking of contradiction in place of tautology and vice versa, by providing a set of switching rules configured to switch each respective one of the original logic operators INV, AND, OR, MAJ, XOR, XNOR, MIN into a respective switched logic operator INV, OR, AND, MAJ, XNOR, XOR, MIN; and complementing outputs of the original circuit by adding an INV at each output wire. The method further provides testing in parallel the satisfiability of the original logic circuit, and the satisfiability of the dual logic circuit with inverted outputs. Responsive to one of the parallel tests finishing, the other parallel test is caused to also stop.

Abstract: We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consistent algebraic framework. However, when algebraic methods cannot improve a result quality, stronger Boolean methods are needed to attain further optimization. For this purpose, we propose MIG Boolean methods exploiting the error masking property of majority operators. Our MIG Boolean methods insert logic errors that strongly simplify an MIG while being successively masked by the voting nature of majority nodes. Thanks to the data-structure/methodology fitness, our MIG Boolean methods run in principle as fast as algebraic counterparts. Experiments show that our Boolean methodology combined with state-of-art MIG algebraic techniques enable superior optimization quality.

Abstract: A method for transforming a tautology check of an original logic circuit into a contradiction check of the original logic circuit and vice versa comprises interpreting the original logic circuit in terms of AND, OR, MAJ, MIN, XOR, XNOR, INV original logic operators; transforming the original circuit obtained from the interpreting, into a dual logic circuit enabled for a checking of contradiction in place of tautology and vice versa, by providing a set of switching rules configured to switch each respective one of the original logic operators INV, AND, OR, MAJ, XOR, XNOR, MIN into a respective switched logic operator INV, OR, AND, MAJ, XNOR, XOR, MIN; and complementing outputs of the original circuit by adding an INV at each output wire. The method further provides testing in parallel the satisfiability of the original logic circuit, and the satisfiability of the dual logic circuit with inverted outputs. Responsive to one of the parallel tests finishing, the other parallel test is caused to also stop.

Abstract: A logic gate with three inputs A, B, and C, and one output implementing a function MAJ(A,B,C)=A*B+B*C+A*C comprising two mutually exclusive transmission gates (TGs) connected in series, based on two parallel double-gate controllable polarity devices, a polarity of each being controlled by input A and a conduction being controlled by input B, or vice-versa, in opposite polarities, and that route either an input A or C from one side of the transmission gates to the output.