Innovative nano-scale devices have been developed to enhance future circuit design to overcome physical barriers hindering complementary metal-oxide semiconductor (CMOS) technology. Among the emerging nanodevices, resonant tunneling diodes (RTDs) have demonstrated promising electronic features due to their high speed switching capability and functional versatility. Great circuit functionality can be achieved through integrating heterostructure field-effect transistors (HFETs) in conjunction with RTDs to modulate effective negative differential resistance (NDR). However, RTDs are intrinsically suitable for implementing threshold logic rather than Boolean logic which has dominated CMOS technology in the past. To fully take advantage of such emerging nanotechnology, efficient design methodologies and design automation tools for threshold logic therefore become essential. In this thesis, we first propose novel programmable logic elements (PLEs) implemented in threshold gates (TGs) and multi-threshold threshold gates (MTTGs) by exploring RTD/ HFET monostable-bistable transition logic element (MOBILE) principles. Our three-input PLE can be configured through five control bits to realize all the three-variable logic functions, which is, to the best of our knowledge, the first single RTD-based structure that provides complete logic implementation. It is also a more efficient reconfigurable circuit element than a general look-up table which requires eight configuration bits for three-variable functions. We further extend the design concept to construct a more versatile four-input PLE. A comprehensive comparison of three- and four-input PLEs provides an insightful view of design tradeoffs between performance and area. We present the mathematical proof of PLE's logic completeness based on Shannon Expansion, as well as the HSPICE simulation results of the programmable and primitive RTD/HFET gates that we have designed. An efficient control bit generating algorithm is developed by using a special encoding scheme to implement any given logic function. In addition, we propose novel techniques of formulating a given threshold logic in conjunctive normal form (CNF) that facilitates efficient SAT-based equivalence checking for threshold logic networks. Three different strategies of CNF generation from threshold logic representations are implemented. Experimental results based on MCNC benchmarks are presented as a complete comparison. Our hybrid algorithm, which takes into account input symmetry as well as input weight order of threshold gates, can efficiently generate CNF formulas in terms of both SAT solving time and CNF generating time. / Master of Science