We present a generic proof methodology to automatically prove correctness of design transformations introduced at the Register-Transfer Level (RTL) to achieve lower power dissipation in hardware systems. We also introduce a new algorithm to reduce switching activity power dissipation in microprocessors. We further apply our technique in a completely different domain of dynamic power management of Systems-on-Chip (SoCs). We demonstrate our methodology on real-life circuits. In this thesis, we address the dual problem of transforming hardware systems at higher levels of abstraction to achieve lower power dissipation, and a reliable way to verify the correctness of the afore-mentioned transformations. The thesis is in three parts. The first part introduces Instruction-driven Slicing, a new algorithm to automatically introduce RTL/System level annotations in microprocessors to achieve lower switching power dissipation. The second part introduces Dedicated Rewriting, a rewriting based generic proof methodology to automatically prove correctness of such high-level transformations for lowering power dissipation. The third part implements dedicated rewriting in the context of dynamically managing power dissipation of mobile and hand-held devices. We first present instruction-driven slicing, a new technique for annotating microprocessor descriptions at the Register Transfer Level in order to achieve lower power dissipation. Our technique automatically annotates existing RTL code to optimize the circuit for lowering power dissipated by switching activity. Our technique can be applied at the architectural level as well, achieving similar power gains. We first demonstrate our technique on architectural and RTL models of a 32-bit OpenRISC pipelined processor (OR1200), showing power gains for the SPEC2000 benchmarks. These annotations achieve reduction in power dissipation by changing the logic of the design. We further extend our technique to an out-of-order superscalar core and demonstrate power gains for the same SPEC2000 benchmarks on architectural and RTL models of PUMA, a fixed point out-of-order PowerPC microprocessor. We next present dedicated rewriting, a novel technique to automatically prove the correctness of low power transformations in hardware systems described at the Register Transfer Level. We guarantee the correctness of any low power transformation by providing a functional equivalence proof of the hardware design before and after the transformation. Dedicated rewriting is a highly automated deductive verification technique specially honed for proving correctness of low power transformations. We provide a notion of equivalence and establish the equivalence proof within our dedicated rewriting system. We demonstrate our technique on a non-trivial case study. We show equivalence of a Verilog RTL implementation of a Viterbi decoder, a component of the DRM System-On-Chip (SoC), before and after the application of multiple low power transformations. We next apply dedicated rewriting to a broader context of holistic power management of SoCs. This in turn creates a self-checking system and will automatically flag conflicting constraints or rules. Our system will manage power constraint rules using dedicated rewriting specially honed for dynamic power management of SoC designs. Together, this provides a common platform and representation to seamlessly cooperate between hardware and software constraints to achieve maximum platform power optimization dynamically during execution. We demonstrate our technique in multiple contexts on an SoC design of the state-of-the-art next generation Intel smartphone platform. Finally, we give a proof of instruction-driven slicing. We first prove that the annotations automatically introduced in the OR1200 processor preserve the original functionality of the machine using the ACL2 theorem prover. Then we establish the same proof within our dedicated rewriting system, and discuss the merits of such a technique and a framework. In the context of today's shrinking hardware and mobile internet devices, lowering power dissipation is a key problem. Verifying the correctness of transformations which achieve that is usually a time-consuming affair. Automatic and reliable methods of verification that are easy to use are extremely important. In this thesis we have presented one such transformation, and a generic framework to prove correctness of that and similar transformations. Our methodology is constructed in a manner that easily and seamlessly fits into the design cycle of creating complicated hardware systems. Our technique is also general enough to be applied in a completely different context of dynamic power management of mobile and hand-held devices. / text