PALMINI—fast Boolean minimizer for personal computers
DAC '87 Proceedings of the 24th ACM/IEEE Design Automation Conference
Two-level logic minimization: an overview
Integration, the VLSI Journal
Switching Theory for Logic Synthesis
Switching Theory for Logic Synthesis
Logic Design and Switching Theory
Logic Design and Switching Theory
Logic Design of Digital Systems
Logic Design of Digital Systems
Logic Minimization Algorithms for VLSI Synthesis
Logic Minimization Algorithms for VLSI Synthesis
A Remark on Minimal Polynomials of Boolean Functions
CSL '88 Proceedings of the 2nd Workshop on Computer Science Logic
A State-Machine Synthesizer—SMS
DAC '81 Proceedings of the 18th Design Automation Conference
An application of multiple-valued logic to a design of programmable logic arrays
MVL '78 Proceedings of the eighth international symposium on Multiple-valued logic
Logic Synthesis and Verification
Large-scale SOP minimization using decomposition and functional properties
Proceedings of the 40th annual Design Automation Conference
Towards finding path delay fault tests with high test efficiency using ZBDDs
ICCD '05 Proceedings of the 2005 International Conference on Computer Design
On the Use of ZBDDs for Implicit and Compact Critical Path Delay Fault Test Generation
Journal of Electronic Testing: Theory and Applications
A novel approach for fast covering the Boolean sets
ISTASC'08 Proceedings of the 8th conference on Systems theory and scientific computation
Advances in Engineering Software
Efficient transistor-level design of CMOS gates
Proceedings of the 23rd ACM international conference on Great lakes symposium on VLSI
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In an irredundant sum-of-products expression (ISOP), each product is a prime implicant (PI) and no product can be deleted without changing the function. Among the ISOPs for some function $f$, a worst ISOP (WSOP) is an ISOP with the largest number of PIs and a minimum ISOP (MSOP) is one with the smallest number. We show a class of functions for which the Minato-Morreale ISOP algorithm produces WSOPs. Since the ratio of the size of the WSOP to the size of the MSOP is arbitrarily large when $n$, the number of variables, is unbounded, the Minato-Morreale algorithm can produce results that are very far from minimum. We present a class of multiple-output functions whose WSOP size is also much larger than its MSOP size. For a set of benchmark functions, we show the distribution of ISOPs to the number of PIs. Among this set are functions where the MSOPs have almost as many PIs as do the WSOPs. These functions are known to be easy to minimize. Also, there are benchmark functions where the fraction of ISOPs that are MSOPs is small and MSOPs have many fewer PIs than the WSOPs. Such functions are known to be hard to minimize. For one class of functions, we show that the fraction of ISOPs that are MSOPs approaches 0 as $n$ approaches infinity, suggesting that such functions are hard to minimize.