Update README's roadmap and add more info about the trace/memory comparisons

README.md

@@ -66,6 +66,20 @@ To run the factorial demo:
 make demo_factorial
 ```
 
+These demos compare the trace and memory files generated by the `Go` and `Rust` VM implementations to make sure they coincide. We have more general Makefile targets that do this comparison for every program we use for testing. You can check out a list of all these programs under the `cairo_programs` directory. The targets to run these comparisons are
+
+```
+make compare_trace_memory
+```
+
+and
+
+```
+make compare_proof_trace_memory
+```
+
+The first one does the comparison for normal executions, while the second one does it with *proof mode* enabled.
+
 ## Project Guidelines
 
 - PRs addressing performance are forbidden. We are currently concerned with making it work without bugs and nothing more.
@@ -90,53 +104,45 @@ The milestone includes:
 - Writing of the memory into files with the correct format.
 - Make the fibonacci and factorial tests pass, comparing our own memory with the Rust VM one, making sure they match.
 
-## Roadmap
-
-### Cairo 0/Cairo 1
-
-The above will work for Cairo 0 programs. Cairo 1 has the following extra issues to address:
-
-- There is no `Json` representation of a Cairo 1 Program, so we can only run contracts. This means we will have to add functions to run cairo contracts (aka implement run_from_entrypoint).
-- Cairo 1 contracts use the `range_check` builtin by default, so we need to implement it.
-
-### Full VM implementation
-
-To have a full implementation, we will need the following:
-
-- Builtins. Add the `BuiltinRunner` logic, then implement each builtin:
-  - `Range check (RC)`
-  - `Output`
-  - `Bitwise`
-  - `Ec_op`
-  - `Pedersen`
-  - `Keccak`
-  - `Poseidon`
-  - `Signature`
-  - `Segment Arena`
-- Memory layouts. This is related to builtins but we will do it after implementing them.
-- Hints. Add the `HintProcessor` logic, then implement each hint. Hints need to be documented extensively, implementing them is super easy since it's just porting code; what's not so clear is what they are used for. Having explanations and examples for each is important. List of hints below:
-  - [Parsing of references](https://github.com/lambdaclass/cairo-vm/tree/main/docs/references_parsing)
-  - [`CommonLib`](https://github.com/starkware-libs/cairo-lang/tree/master/src/starkware/cairo/common)
-  - `Secp`
-  - `Vrf`
-  - `BigInt`
-  - `Blake2`
-  - `DictManager`
-  - `EcRecover`
-  - `Field Arithmetic`
-  - `Garaga`
-  - `set_add`
-  - `sha256 utils`
-  - `ECDSA verification`
-  - `uint384` and `uint384 extension`
-  - `uint512 utils`
-  - `Cairo 1` hints.
-- Proof mode. It's important to explain in detail what this is when we do it. It's one of the most obscure parts of the VM in my experience.
-- Air Public inputs. (Tied to Proof-mode)
-- Temporary segments.
-- Program tests from Cairo VM in Rust.
-- Fuzzing/Differential fuzzing.
-
+### Second Milestone: Full VM implementation
+
+Below is a list of requirements to have a full implementation along with their progress:
+
+- ✅ Builtins. Add the `BuiltinRunner` logic, then implement each builtin:
+  - ✅ `Range check (RC)`
+  - ✅ `Output`
+  - ✅ `Bitwise`
+  - ✅ `Ec_op`
+  - ✅ `Pedersen`
+  - ✅ `Keccak`
+  - ✅ `Poseidon`
+  - ✅ `Signature`
+  - ✅ `Segment Arena`
+- ✅ Memory layouts. This is related to builtins but we will do it after implementing them.
+- Hints. 
+    - ✅ Add the `HintProcessor` logic
+    - ✅ [Parsing of references](https://github.com/lambdaclass/cairo-vm/tree/main/docs/references_parsing)
+    - Implement each hint. This is a long task which we divided into milestones. You can check out their progress [here](https://github.com/lambdaclass/cairo-vm_in_go/milestones).
+- ✅ Proof mode. It's important to explain in detail what this is when we do it. It's one of the most obscure parts of the VM in my experience.
+- ✅ Program tests from Cairo VM in Rust.
+- Print debug information on failure (i.e. introduce the concept of a `VmException`)
+- Air Public inputs. (Tied to Proof mode)
+- Starknet integration:
+    - Running cairo contracts (i.e. implement `RunFromEntrypoint`)
+    - Tracking `ExecutionResources` and `RunResources`.
+- Cairo 1 support. This requires:
+    - Parsing Cairo 1 contracts. There is no `Json` representation of a Cairo 1 Program, so we can only run contracts. This means this depends on the `RunFromEntrypoint` feature above. 
+    - Implementing Cairo 1 builtin (`Segment Arena`)
+    - Implementing Cairo 1 Hints
+- Support for `CairoPie` (Cairo Position Independent Code).
+
+
+### Other Stuff: Performance and Fuzzing
+
+Things that are out of the second milestone but we want to have:
+
+- Add benchmarks to track performance and compare against the Rust implementation.
+- Add Fuzzing and Differential fuzzing to catch errors that our regular tests don't and compare ourselves against the Rust VM.
 ## Documentation
 
 ### High Level Overview