Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

Finite adaptive composition

Errors, finite composition, locality, and transport › Finite adaptive composition · lines 1817–1833

X-J-ST@1#eq:telescoping

For compatible complete implementations, telescoping gives

d_{⋄} (Γ, Γ) \leq min {1, e_{prep} + e_{table} + j \sum e_{j} + e_{decode}} .

Each $e_{j}$ concerns the complete fixed interface of one component. The estimate follows from channel contraction and the triangle inequality Watrous. It does not prove exact causality of a faulty implementation.

Displayed formulas in this passage

X-J-ST@1#eq:telescoping · line 1821
$d_{⋄} (Γ, Γ) \leq min {1, e_{prep} + e_{table} + j \sum e_{j} + e_{decode}} .$

Nearby in this section

theorem: Theorem: Complete finite composition
section: Finite adaptive composition
corollary: Corollary: When a gap survives a continuation