Axilog: language support for approximate hardware design

Relaxing the traditional abstraction of "near-perfect" accuracy in hardware design can yield significant gains in efficiency, area, and performance. To exploit this opportunity, there is a need for design abstractions and synthesis tools that can ...

All the results given in the paper hold true. In the proof of Theorem 1, change steps IV, V, and VI to

IV. for every $a,b,c \in T$ , add $(\langle a\rangle,\langle b \rangle,\langle c \rangle,\$) \rightarrow (\langle 0a \rangle,\langle 0b \rangle,\langle 0c \rangle,\S)$ to P ;

V. for every $a,b,c,d \in T$ , add $(Y, \langle 0a \rangle, Y, \langle 0b \rangle, Y, \langle 0c \rangle, \S) \rightarrow \# , \langle 0a \rangle, X, \langle 0b \rangle, Y, \langle 0c \rangle, \S)$ , $(\langle 0a\rangle, \langle 0b \rangle, \langle 0c \rangle, \S) \rightarrow (\langle 4a \rangle, \langle 1b \rangle, \langle 2c \rangle, \S)$ , $(\langle 4a \rangle, X, \langle 1b \rangle, Y, \langle 2c \rangle, \S) \rightarrow (\langle 4a \rangle, \# , \langle 1b \rangle, X, \langle 2c \rangle, \S)$ , $(\langle 4a \rangle, \langle 1b \rangle, \langle 2c \rangle, \langle d \rangle, \S \rightarrow (a, \langle 4b \rangle, \langle 1c \rangle, \langle 2d \rangle, \S)$ , $(\langle 4a \rangle, \langle 1b \rangle, \langle 2c \rangle, \S) \rightarrow (a, \langle 1b \rangle, \langle 3c \rangle, \S)$ , $(\langle 1a \rangle, X, \langle 3b \rangle, Y, \S) \rightarrow (\langle 1a \rangle, \# , \langle 3b \rangle, \# , \S)$ to P ;

VI. for every $a, b \in T$ , add $(\langle 1a \rangle, X, \langle 3b \rangle, \S) \rightarrow (a, \# , b, \# )$ to P .