Table 2 Axioms for RPAP
From: RETRACTED ARTICLE: An algebra of reversible computation
No. | Axiom |
|---|---|
RP1 | \(x\parallel y = x\mid y + x\between y\) |
RP2 | \(x\mid x = x\) |
RP3 | \((x\mid y)\mid z = x\mid (y\mid z)\) |
RP4 | \(x \mid (y + z) = x\mid y + x\mid z\) |
RP5 | \((x + y) \mid z = x\mid z + y\mid z\) |
RP6 | \(x \cdot (y \mid z) = x\cdot y \mid x\cdot z\) |
RP7 | \((x \mid y) \cdot z = x\cdot z \mid y\cdot z\) |
RC8 | \(\upsilon \between \omega =\gamma (\upsilon ,\omega )\) |
RC9 | \(\upsilon [m]\between \omega [m]=\gamma (\upsilon ,\omega )[m]\) |
RC10 | \(\upsilon \between (\omega \cdot y) = \gamma (\upsilon ,\omega )\cdot y\) |
RC11 | \(\upsilon [m]\between (\omega [m]\cdot y) = \gamma (\upsilon ,\omega )[m]\cdot y\) |
RC12 | \((\upsilon \cdot x)\between \omega = \gamma (\upsilon ,\omega )\cdot x\) |
RC13 | \((\upsilon [m]\cdot x)\between \omega [m] = \gamma (\upsilon ,\omega )[m]\cdot x\) |
RC14 | \((\upsilon \cdot x)\between (\omega \cdot y) = \gamma (\upsilon ,\omega )\cdot (x\parallel y)\) |
RC15 | \((\upsilon [m]\cdot x)\between (\omega [m]\cdot y) = \gamma (\upsilon ,\omega )[m]\cdot (x\parallel y)\) |
RC16 | \((x + y)\between z = x\between z + y\between z\) |
RC17 | \(x\between (y+z) = x\between y + x\between z\) |