Module dfa

A module for building and searching with deterministic finite automata (DFAs).

Like other modules in this crate, DFAs support a rich regex syntax with Unicode features. DFAs also have extensive options for configuring the best space vs time trade off for your use case and provides support for cheap deserialization of automata for use in no_std environments.

If you’re looking for lazy DFAs that build themselves incrementally during search, then please see the top-level hybrid module.

Overview

This section gives a brief overview of the primary types in this module:

• A [regex::Regex] provides a way to search for matches of a regular expression using DFAs. This includes iterating over matches with both the start and end positions of each match.
• A [dense::DFA] provides low level access to a DFA that uses a dense representation (uses lots of space, but fast searching).
• A [sparse::DFA] provides the same API as a dense::DFA, but uses a sparse representation (uses less space, but slower searching).
• An [Automaton] trait that defines an interface that both dense and sparse DFAs implement. (A regex::Regex is generic over this trait.)
• Both dense DFAs and sparse DFAs support serialization to raw bytes (e.g., [dense::DFA::to_bytes_little_endian]) and cheap deserialization (e.g., [dense::DFA::from_bytes]).

There is also a onepass module that provides a one-pass DFA. The unique advantage of this DFA is that, for the class of regexes it can be built with, it supports reporting the spans of matching capturing groups. It is the only DFA in this crate capable of such a thing.

Example: basic regex searching

This example shows how to compile a regex using the default configuration and then use it to find matches in a byte string:

use regex_automata::{Match, dfa::regex::Regex};

let re = Regex::new(r"[0-9]{4}-[0-9]{2}-[0-9]{2}")?;
let text = b"2018-12-24 2016-10-08";
let matches: Vec<Match> = re.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(0, 0..10),
    Match::must(0, 11..21),
]);

Example: searching with regex sets

The DFAs in this module all fully support searching with multiple regexes simultaneously. You can use this support with standard leftmost-first style searching to find non-overlapping matches:

use regex_automata::{Match, dfa::regex::Regex};

let re = Regex::new_many(&[r"\w+", r"\S+"])?;
let text = b"@foo bar";
let matches: Vec<Match> = re.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(1, 0..4),
    Match::must(0, 5..8),
]);

Example: use sparse DFAs

By default, compiling a regex will use dense DFAs internally. This uses more memory, but executes searches more quickly. If you can abide slower searches (somewhere around 3-5x), then sparse DFAs might make more sense since they can use significantly less space.

Using sparse DFAs is as easy as using Regex::new_sparse instead of Regex::new:

use regex_automata::{Match, dfa::regex::Regex};

let re = Regex::new_sparse(r"[0-9]{4}-[0-9]{2}-[0-9]{2}").unwrap();
let text = b"2018-12-24 2016-10-08";
let matches: Vec<Match> = re.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(0, 0..10),
    Match::must(0, 11..21),
]);

If you already have dense DFAs for some reason, they can be converted to sparse DFAs and used to build a new Regex. For example:

use regex_automata::{Match, dfa::regex::Regex};

let dense_re = Regex::new(r"[0-9]{4}-[0-9]{2}-[0-9]{2}").unwrap();
let sparse_re = Regex::builder().build_from_dfas(
    dense_re.forward().to_sparse()?,
    dense_re.reverse().to_sparse()?,
);
let text = b"2018-12-24 2016-10-08";
let matches: Vec<Match> = sparse_re.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(0, 0..10),
    Match::must(0, 11..21),
]);

Example: deserialize a DFA

This shows how to first serialize a DFA into raw bytes, and then deserialize those raw bytes back into a DFA. While this particular example is a bit contrived, this same technique can be used in your program to deserialize a DFA at start up time or by memory mapping a file.

use regex_automata::{Match, dfa::{dense, regex::Regex}};

let re1 = Regex::new(r"[0-9]{4}-[0-9]{2}-[0-9]{2}").unwrap();
// serialize both the forward and reverse DFAs, see note below
let (fwd_bytes, fwd_pad) = re1.forward().to_bytes_native_endian();
let (rev_bytes, rev_pad) = re1.reverse().to_bytes_native_endian();
// now deserialize both---we need to specify the correct type!
let fwd: dense::DFA<&[u32]> = dense::DFA::from_bytes(&fwd_bytes[fwd_pad..])?.0;
let rev: dense::DFA<&[u32]> = dense::DFA::from_bytes(&rev_bytes[rev_pad..])?.0;
// finally, reconstruct our regex
let re2 = Regex::builder().build_from_dfas(fwd, rev);

// we can use it like normal
let text = b"2018-12-24 2016-10-08";
let matches: Vec<Match> = re2.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(0, 0..10),
    Match::must(0, 11..21),
]);

There are a few points worth noting here:

• We need to extract the raw DFAs used by the regex and serialize those. You can build the DFAs manually yourself using [dense::Builder], but using the DFAs from a Regex guarantees that the DFAs are built correctly. (In particular, a Regex constructs a reverse DFA for finding the starting location of matches.)
• To convert the DFA to raw bytes, we use the to_bytes_native_endian method. In practice, you’ll want to use either [dense::DFA::to_bytes_little_endian] or [dense::DFA::to_bytes_big_endian], depending on which platform you’re deserializing your DFA from. If you intend to deserialize on either platform, then you’ll need to serialize both and deserialize the right one depending on your target’s endianness.
• Safely deserializing a DFA requires verifying the raw bytes, particularly if they are untrusted, since an invalid DFA could cause logical errors, panics or even undefined behavior. This verification step requires visiting all of the transitions in the DFA, which can be costly. If cheaper verification is desired, then [dense::DFA::from_bytes_unchecked] is available that only does verification that can be performed in constant time. However, one can only use this routine if the caller can guarantee that the bytes provided encoded a valid DFA.

The same process can be achieved with sparse DFAs as well:

use regex_automata::{Match, dfa::{sparse, regex::Regex}};

let re1 = Regex::new(r"[0-9]{4}-[0-9]{2}-[0-9]{2}").unwrap();
// serialize both
let fwd_bytes = re1.forward().to_sparse()?.to_bytes_native_endian();
let rev_bytes = re1.reverse().to_sparse()?.to_bytes_native_endian();
// now deserialize both---we need to specify the correct type!
let fwd: sparse::DFA<&[u8]> = sparse::DFA::from_bytes(&fwd_bytes)?.0;
let rev: sparse::DFA<&[u8]> = sparse::DFA::from_bytes(&rev_bytes)?.0;
// finally, reconstruct our regex
let re2 = Regex::builder().build_from_dfas(fwd, rev);

// we can use it like normal
let text = b"2018-12-24 2016-10-08";
let matches: Vec<Match> = re2.find_iter(text).collect();
assert_eq!(matches, vec![
    Match::must(0, 0..10),
    Match::must(0, 11..21),
]);

Note that unlike dense DFAs, sparse DFAs have no alignment requirements. Conversely, dense DFAs must be aligned to the same alignment as a StateID.

Support for no_std and alloc-only

This crate comes with alloc and std features that are enabled by default. When the alloc or std features are enabled, the API of this module will include the facilities necessary for compiling, serializing, deserializing and searching with DFAs. When only the alloc feature is enabled, then implementations of the std::error::Error trait are dropped, but everything else generally remains the same. When both the alloc and std features are disabled, the API of this module will shrink such that it only includes the facilities necessary for deserializing and searching with DFAs.

The intended workflow for no_std environments is thus as follows:

• Write a program with the alloc or std features that compiles and serializes a regular expression. You may need to serialize both little and big endian versions of each DFA. (So that’s 4 DFAs in total for each regex.)
• In your no_std environment, follow the examples above for deserializing your previously serialized DFAs into regexes. You can then search with them as you would any regex.

Deserialization can happen anywhere. For example, with bytes embedded into a binary or with a file memory mapped at runtime.

The regex-cli command (found in the same repository as this crate) can be used to serialize DFAs to files and generate Rust code to read them.

Syntax

This module supports the same syntax as the regex crate, since they share the same parser. You can find an exhaustive list of supported syntax in the documentation for the regex crate.

There are two things that are not supported by the DFAs in this module:

• Capturing groups. The DFAs (and Regexes built on top of them) can only find the offsets of an entire match, but cannot resolve the offsets of each capturing group. This is because DFAs do not have the expressive power necessary.
• Unicode word boundaries. These present particularly difficult challenges for DFA construction and would result in an explosion in the number of states. One can enable [dense::Config::unicode_word_boundary] though, which provides heuristic support for Unicode word boundaries that only works on ASCII text. Otherwise, one can use (?-u:\b) for an ASCII word boundary, which will work on any input.

There are no plans to lift either of these limitations.

Note that these restrictions are identical to the restrictions on lazy DFAs.

Differences with general purpose regexes

The main goal of the regex crate is to serve as a general purpose regular expression engine. It aims to automatically balance low compile times, fast search times and low memory usage, while also providing a convenient API for users. In contrast, this module provides a lower level regular expression interface based exclusively on DFAs that is a bit less convenient while providing more explicit control over memory usage and search times.

Here are some specific negative differences:

• Compilation can take an exponential amount of time and space in the size of the regex pattern. While most patterns do not exhibit worst case exponential time, such patterns do exist. For example, [01]*1[01]{N} will build a DFA with approximately 2^(N+2) states. For this reason, untrusted patterns should not be compiled with this module. (In the future, the API may expose an option to return an error if the DFA gets too big.)
• This module does not support sub-match extraction via capturing groups, which can be achieved with the regex crate’s “captures” API.
• While the regex crate doesn’t necessarily sport fast compilation times, the regexes in this module are almost universally slow to compile, especially when they contain large Unicode character classes. For example, on my system, compiling \w{50} takes about 1 second and almost 15MB of memory! (Compiling a sparse regex takes about the same time but only uses about 1.2MB of memory.) Conversely, compiling the same regex without Unicode support, e.g., (?-u)\w{50}, takes under 1 millisecond and about 15KB of memory. For this reason, you should only use Unicode character classes if you absolutely need them! (They are enabled by default though.)
• This module does not support Unicode word boundaries. ASCII word bondaries may be used though by disabling Unicode or selectively doing so in the syntax, e.g., (?-u:\b). There is also an option to heuristically enable Unicode word boundaries, where the corresponding DFA will give up if any non-ASCII byte is seen.
• As a lower level API, this module does not do literal optimizations automatically. Although it does provide hooks in its API to make use of the Prefilter trait. Missing literal optimizations means that searches may run much slower than what you’re accustomed to, although, it does provide more predictable and consistent performance.
• There is no &str API like in the regex crate. In this module, all APIs operate on &[u8]. By default, match indices are guaranteed to fall on UTF-8 boundaries, unless either of syntax::Config::utf8 or thompson::Config::utf8 are disabled.

With some of the downsides out of the way, here are some positive differences:

• Both dense and sparse DFAs can be serialized to raw bytes, and then cheaply deserialized. Deserialization can be done in constant time with the unchecked APIs, since searching can be performed directly on the raw serialized bytes of a DFA.
• This module was specifically designed so that the searching phase of a DFA has minimal runtime requirements, and can therefore be used in no_std environments. While no_std environments cannot compile regexes, they can deserialize pre-compiled regexes.
• Since this module builds DFAs ahead of time, it will generally out-perform the regex crate on equivalent tasks. The performance difference is likely not large. However, because of a complex set of optimizations in the regex crate (like literal optimizations), an accurate performance comparison may be difficult to do.
• Sparse DFAs provide a way to build a DFA ahead of time that sacrifices search performance a small amount, but uses much less storage space. Potentially even less than what the regex crate uses.
• This module exposes DFAs directly, such as [dense::DFA] and [sparse::DFA], which enables one to do less work in some cases. For example, if you only need the end of a match and not the start of a match, then you can use a DFA directly without building a Regex, which always requires a second DFA to find the start of a match.
• This module provides more control over memory usage. Aside from choosing between dense and sparse DFAs, one can also choose a smaller state identifier representation to use less space. Also, one can enable DFA minimization via [dense::Config::minimize], but it can increase compilation times dramatically.

Modules

• onepass
  A DFA that can return spans for matching capturing groups.