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As research on developing assertion languages for the analog and mixed-signal (AMS) domain gains in momentum, it is increasingly being felt that extensions of existing assertion languages like property specification language and SystemVerilog assertions into the AMS domain are not adequate for expressing the analog design intent. This is largely due to the intricacy of the analog behavioral intent which cannot be captured purely in terms of logic. In this paper, we show that by using auxiliary forms of formal specifications such as abstract state machines and real-valued functions, called auxiliary functions, as references for AMS assertions, it becomes possible to model complex AMS behavioral properties. In addition, we present complexity results for the satisfiability problem of such specifications. This approach leverages the growing adoption of AMS behavioral modeling in the industry. This paper also shows that the use of auxiliary state machines allows us to separate out the scope of different analog assertions leading to significant performance gains in the assertion checking overhead.