This brief proposes the use of four-level forms in the memristive material implication (M-IMP) logic. M-IMP is a promising approach to perform stateful logic in memristive nonvolatile memories. In such a design technique, a given Boolean function is evaluated as a sequence of instructions, making logic synthesis methods necessary to attain the shortest sequence. In comparison to previous work, experimental results have shown an average reduction of 40% when evaluating the tradeoff between the numbers of instructions and memristive devices.

In this paper, a straightforward and effective method to identify threshold logic function (TLF) is presented. Threshold logic is a promising alternative to conventional Boolean logic due to its suitability for emerging technologies, like memristors, quantum-dot cellular automata, resonant tunneling device, and spintronic devices. Identification and synthesis of TLF are essential tasks in a design flow based on such a logic strategy. The proposed method relies on irredundant sum-of-products Boolean function description form and exploits both ordering of variables and system of inequalities to assign the variable weights and the function threshold value. This is the first heuristic algorithm able to identify all threshold functions with up to six variables, being also more effective than other heuristic methods for functions with a larger number of variables. For functions obtained from k -cuts of benchmark circuits, experimental results demonstrated effectiveness near to 100% when compared to exact methods, even when the number of function variables increases. The execution time of the proposed approach is similar to related heuristic methods, being faster than integer linear programming-based algorithms.

Transistor network optimization represents an effective way of improving VLSI circuits. This paper proposes a novel method to automatically generate networks with minimal transistor count, starting from an irredundant sum-of-products expression as the input. The method is able to deliver both series-parallel (SP) and non-SP switch arrangements, improving speed, power dissipation, and area of CMOS gates. Experimental results demonstrate expected gains in comparison with related approaches.

This paper presents a new approach for Boolean decomposition based on the Boolean difference and cofactor analysis. Two simple tests provide sufficient and necessary conditions to identify AND and exclusive-OR (XOR) decompositions. The proposed method can decompose an n-input function in O(n • log n) cofactor and O(n) equivalence test operations. Recently, 2-to-1 multiplexers (MUX) have also been used to perform such decomposition. However, MUX with more inputs has been neglected. We provide sufficient and necessary conditions to obtain MUX decompositions of functions with an arbitrary number of inputs.

This work presents an efficient algorithm to obtain a material implication (IMPLY) expression from a sum-of-products (SOP). The resulting expression is computable with two work memristors. The proposed method has linear time complexity with respect to the SOP size. Comparison to previous work shows a reduction on the average number of IMPLY operations when applying the proposed method.

This paper presents two contributions to logic synthesis for memristive stateful logic. Firstly, we demonstrate the necessity to correct results provided by existing logic synthesis methods to ensure the expected computation. Secondly, we propose the concept of multi-memristor implication as a generalization of multi-input implication. Experimental results have shown a reduction of 6.5% in the number of operations when compared to previous works.

The transistor arrangement optimization is an effective possibility to improve VLSI design, especially when generating CMOS logic gates to be inserted in standard cell libraries. This paper addresses this issue and presents a new methodology to generate efficient transistor networks. Starting from an input ISOP, the proposed method is capable to deliver series-parallel and non-series-parallel arrangements with reduced transistor count. By applying the proposed approach, it is possible to achieve optimized transistor arrangements since greedy choices are avoided during part of the generation process. The performed experiments have demonstrated the efficiency of this methodology when comparing to other available techniques.

Every Boolean function has a unique property called Minimum Decision Chain (MDC). This paper proposes an effective way to compute this property for arbitrary functions. The proposed method is very efficient when compared to a more direct and intuitive approach, that is used as the reference for performance analysis. Different examples have been evaluated, and the results are discussed. The proposed method is able to compute the MDC value in order of milliseconds, allowing the use of MDC computation to guide logic synthesis algorithms.