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A Comparison of Algebraic and Map Methods for Solving General Boolean Equations

This paper identifies the main types of solutions of Boolean equations as subsumptive general solutions, parametric general solutions and particular solutions. The paper offers a tutorial exposition, review, and comparison of the three types of solutions by way of two illustrative examples solved by both map and algebraic techniques. Map techniques are demonstrated to be at least competitive with (and occasionally superior to) algebraic techniques, since they have a better control on the minimality of the pertinent function representations, and hence are more capable of producing more compact general parametric and subsumptive solutions.