MINI: A Heuristic Approach for Logic Minimization

Butler

2001

IEEE Trans. Comput.

AbstractÐIn 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.

“…For an n-variable function with m output values, Theorem 4.1 [15], [27], [29]. The number of AND gates in the minimum AND-OR two-level network for the function 3.…”

Section: Extension To Multiple-output Functionsmentioning

confidence: 99%

“…The 9SYM (or SYM9) [11], [15] function shown in [3, p. 165] is identical to WY Q. It has 1,680 PIs, (y X WY Q !…”

Section: Ny K Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Worst and best irredundant sum-of-products expressions

Butler

2001

IEEE Trans. Comput.

“…A positional cube [7] is convenient for manipulation of logic expressions by computers. In positional cube notation, an uncomplemented literal such a s x i is represented by 01, a complemented literal x i is represented by 10, and a don't care (missing variable in a product) is represented by 11.…”

Section: Positional Cube Notationmentioning

confidence: 99%

GRMIN: a heuristic simplification algorithm for generalized Reed-Muller expressions

Debnath

Proceedings of ASP-DAC'95/CHDL'95/VLSI'95 With EDA Technofair

Abstract| A generalized Reed-Muller expression (GRM) is a type of AND-EXOR expressions. In a GRM, each variable may appear both complemented and uncomplemented. Networks realized using GRMs are easily tested. This paper presents GR-MIN, a heuristic simplication algorithm for GRMs of multiple-output functions. GRMIN uses eight rules. As the primary objective, it reduces the number of products, and as the secondary objective, it reduces the number of literals. Experimental results show that, in most cases, GRMs require fewer products than conventional sum-of-products expressions (SOPs). GRMIN outperforms existing algorithms.

“…SOPs for CFNs are extensively used in logic synthesis [11]. They can be simplified by using multiplevalued logic minimizers such as MINI [7] and ESPRESSO-MV [9]. The CFN represents only non-zero input-output combinations, and SOPs for CFNs tend to be more compact than SOPs for CFs.…”

Section: Introductionmentioning

confidence: 99%

Compact SOP representations for multiple-output functions-an encoding method using multiple-valued logic

Proceedings 31st IEEE International Symposium on Multiple-Valued Logic