Caret anchor (ˆ) support for Noir

[ewynx]

Description

Note: proposed change here is an addition of a single line, the rest is the original Noir support @olehmisar built.

^ causes the DFA to contain an extra state beforehand that has a transition for 255, which marks the start of the input byte array. In the regex_match function the input is then prefixed with 255 to execute the check. This implementation follows the one of circom. As checked in the TG group, this assumes 255 won't appear in the rest of the input byte string as valid ASCII.

If the regex doesn't start with a "ˆ" this doesn't do anything because then the mapping is to 0.

Note that ^ is only taken into consideration in the decomposed mode.

Example test input for ˆ[0-9]{2}/[0-9]{2}/[0-9]{4}:

{
  "parts": [
      {
          "is_public": false,
          "regex_def": "^"
      },
      {
          "is_public": true,
          "regex_def": "[0-9]{2}/[0-9]{2}/[0-9]{4}"
      }
  ]
}

With cargo run --bin zk-regex decomposed -d <filepath>.json --noir-file-path caret_anchor_test.nr

Problem*

Resolves

Summary*

Additional Context

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[ewynx]

#8 contains this feature, closing this PR.