Verification of Mixed-Signal Systems with Affine Arithmetic Assertions

Table 2

AAF+A operators.

AAF+A operators	Symbols	Operator meaning
Arithmetic operators	⊖∈{+,−,∗,/,^∧}	Symbols for the usual arithmetic operations
Relation operators	•∈{<,>,≤,≥,==}	The usual relation operations
Logic operators	⊘∈{&&,‖,→}; !	Logic and, or, implies not
Affine analog operator	IN	Compares two affine terms 𝑎 and 𝑏
Affine analog frequency operator	AFO∈{FIN,GFIN}; min,max	Compares two affine terms 𝑎 and 𝑏 within specified frequency interval, FIN assigns eventually; GIN assigns always; Min finds frequency component with minimum amplitude value within specified frequency interval; max finds frequency component with maximum amplitude value within specified frequency interval
Slope operator	DV	Calculates slope of a signal
Temporal operators	□∈{𝐺,𝐹}	Always, eventually
Affine analog time interval	Time∈AAF,time=𝑡0+𝜀Δ𝑡,𝑡0,Δ𝑡∈ℝ	Specified signal time interval of affine analog signal
Verification time interval	[𝑡],𝑡∈ℝ	Specified time within which the assertion is verified