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The increasing complexity of modern processors poses many challenges to existing hardware verification tools and methodologies for detecting security-critical bugs. Recent attacks on processors have shown the fatal consequences of uncovering and exploiting hardware vulnerabilities. Fuzzing has emerged as a promising technique for detecting software vulnerabilities. Recently, a few hardware fuzzing techniques have been proposed. However, they suffer from several limitations, including non-applicability to commonly used Hardware Description Languages (HDLs) like Verilog and VHDL, the need for significant human intervention, and inability to capture many intrinsic hardware behaviors, such as signal transitions and floating wires. In this paper, we present the design and implementation of a novel hardware fuzzer, TheHuzz, that overcomes the aforementioned limitations and significantly improves the state of the art. We analyze the intrinsic behaviors of hardware designs in HDLs and then measure the coverage metrics that model such behaviors. TheHuzz generates assembly-level instructions to increase the desired coverage values, thereby finding many hardware bugs that are exploitable from software. We evaluate TheHuzz on four popular open-source processors and achieve 1.98x and 3.33x the speed compared to the industry-standard random regression approach and the state-of-the-art hardware fuzzer, DiffuzRTL, respectively. Using TheHuzz, we detected 11 bugs in these processors, including 8 new vulnerabilities, and we demonstrate exploits using the detected bugs. We also show that TheHuzz overcomes the limitations of formal verification tools from the semiconductor industry by comparing its findings to those discovered by the Cadence JasperGold tool.