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In this chapter, we introduce a new fully generic computational paradigm for post-CMOS integrated circuits based on emerging wave-like physical phenomenon (e.g. spin waves), called Wave Interference Functions (WIF). Waves offer new features and opportunities for logic circuits with inherent support for multi-valued data representation, communication and computation. Multi-valued information processing occurs through wave interference, and multi-valued communication between processing elements is through wave propagation. We develop a formalism for multi-valued logic using WIF, and illustrate circuit designs using arithmetic circuits as examples. WIF circuits show tremendous benefits when compared to conventional CMOS technology in terms of area, power and delay. For instance, a 16-digit quaternary (radix 4) WIF full adder shows 63x density, 884x lower power and 3x performance improvement vs. 32-bit CMOS implementation in equivalent 45nm technology. WIF features and benefits open completely new avenues for designing post-CMOS integrated circuits at nanoscale.