Memristor-based nano-crossbar computing is a revolutionary computing paradigm that does away with the traditional Von Neumann architectural separation of memory and computation units. The computation of Boolean formulas using memristor circuits has been a subject of several recent investigations. Crossbar computing, in general, has also been a topic of active interest, but sneak paths have posed a hurdle in the design of pervasive general-purpose crossbar computing paradigms. Various embodiments are disclosed which demonstrate that sneak paths in nano-crossbar computing can be exploited to design a Boolean-formula evaluation strategy. Such nano-crossbar designs are also an effective approach for synthesizing high performance customized arithmetic and logic circuits.