docs: adr-046 add bisection algorithm details (#4496)

* docs: adr-046 add bisection algorithm details

Closes #4329

* format fig. 1 title

* docs: adr-046 we no longer download headers in TrustedHeader

https://github.com/tendermint/tendermint/pull/4496#issuecomment-592446054

docs/architecture/adr-046-light-client-implementation.md

@@ -3,6 +3,7 @@
 ## Changelog
 * 13-02-2020: Initial draft
 * 26-02-2020: Cross-checking the first header
+* 28-02-2020: Bisection algorithm details
 
 ## Context
 
@@ -67,9 +68,13 @@ required to respond: 1. Note the very first header (`TrustOptions.Hash`) is
 also cross-checked with witnesses for additional security.
 
 Due to bisection algorithm nature, some headers might be skipped. If the light
-client does not have a header for height `X` and `TrustedHeader(X)` or
-`TrustedValidatorSet(X)` methods are called, it will download the header from
-primary provider and perform a backwards verification.
+client does not have a header for height `X` and `VerifyHeaderAtHeight(X)` or
+`VerifyHeader(H#X)` methods are called, it will perform a backwards
+verification from the latest header back to the header at height `X`.
+
+`TrustedHeader`, `TrustedValidatorSet` only communicate with the trusted store.
+If some header is not there, an error will be returned indicating that
+verification is required.
 
 ```go
 type Provider interface {
@@ -127,6 +132,21 @@ cases of adjacent and non-adjacent headers. In the former case, it compares the
 hashes directly (2/3+ signed transition). Otherwise, it verifies 1/3+
 (`trustLevel`) of trusted validators are still present in new validators.
 
+### Bisection algorithm details
+
+Non-recursive bisection algorithm was implemented despite the spec containing
+the recursive version. There are two major reasons:
+
+1) Constant memory consumption => no risk of getting OOM (Out-Of-Memory) exceptions;
+2) Faster finality (see Fig. 1).
+
+_Fig. 1: Differences between recursive and non-recursive bisections_
+
+![Fig. 1](./img/adr-046-fig1.png)
+
+Specification of the non-recursive bisection can be found
+[here](https://github.com/tendermint/spec/blob/zm_non-recursive-verification/spec/consensus/light-client/non-recursive-verification.md).
+
 ## Status
 
 Accepted.