Table 3 Axioms for ARCP
From: RETRACTED ARTICLE: An algebra of reversible computation
No. | Axiom |
|---|---|
RA6 | \(x+\delta = x\) |
RA7 | \(\delta \cdot x = \delta \) |
RA8 | \(x \cdot \delta = \delta \) |
RD1 | \(\upsilon \notin H\quad \partial _H(\upsilon ) = \upsilon \) |
RD2 | \(\upsilon [m]\notin H\quad \partial _H(\upsilon [m]) = \upsilon [m]\) |
RD3 | \(\upsilon \in H\quad \partial _H(\upsilon ) = \delta \) |
RD4 | \(\upsilon [m]\in H\quad \partial _H(\upsilon [m]) = \delta \) |
RD5 | \(\partial _H(\delta ) = \delta \) |
RD6 | \(\partial _H(x+y)=\partial _H(x)+\partial _H(y)\) |
RD7 | \(\partial _H(x\cdot y)=\partial _H(x)\cdot \partial _H(y)\) |
RD8 | \(\partial _H(x\mid y)=\partial _H(x)\mid \partial _H(y)\) |
RP8 | \(\delta \mid x=\delta \) |
RP9 | \(x\mid \delta =\delta \) |
RC18 | \(\delta \between x = \delta \) |
RC19 | \(x\between \delta = \delta \) |