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Regular Expression Matching

Matches text against patterns with operators such as choice, repetition, and character classes.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Pattern Matching
Difficulty: Intermediate
Family: Automaton Matching
Tier: Core
Status: Verified
Review: Source Checked
Sources: 2
Formulas: 1
Relationships: 3
Code example: Ready
Visualization: Ready
Aliases: Regex Matching

Overview

Regular Expression Matching compiles or interprets a pattern and checks whether text follows that pattern language.

Core Concepts

pattern comparisonstring sequencefinite-state automatonautomaton matchingsequence scanpattern statematch verification

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n)

Average

O(nm)

Worst

O(2^n)

Space

O(m)

When to Use

Use Regular Expression Matching when you need to represent pattern states.
Use it for input validation with inputs like regular expression.
Use it when exact, fuzzy, or structured patterns must be found in sequences.
Use it when the Automaton Matching tradeoff is acceptable for the problem size.

When Not to Use

Avoid it when preprocessing cost is larger than a one-off simple scan.
Avoid it when O(2^n) worst-case behavior is too costly for the expected input size.
Avoid it when the required output is not match result.

What It Does

Represents pattern states
Consumes text according to regex operators

Use Cases

Input validation
Text extraction
Search tools

Inputs

Regular expression
Text

Outputs

Match result
Capture groups when supported

Key Formulas (1)

Automaton transition

next_states = ε_closure(move(current_states, character))

next_states = epsilon_closure(move(current_states, character))

Advances all active pattern states for one input character.

Pseudocode

1.Parse or compile the regular expression
2.Create matching states
3.Feed text characters through the matcher
4.Track active states or backtracking choices
5.Return matches that reach accepting states

Canonical Example

Input: text = 'abracadabra', pattern = 'abra'
Output: matches at positions [0, 7]
Explanation: Regular Expression Matching: The algorithm scans the sequence and reports where the pattern appears.

Implementation Notes

Keep the input contract explicit: Regular expression; Text.
Use this step as the implementation spine: Parse or compile the regular expression.
Then preserve the next state change: Create matching states.
Decide whether indexes mean bytes, code units, characters, or tokens.
Test overlapping matches, empty patterns, repeated characters, and no-match inputs.

Common Pitfalls

Backtracking regex engines can have exponential cases unless patterns are constrained.
Indexing by bytes instead of characters can break text with multibyte characters.
Reporting a match before verifying collisions, boundaries, or full-pattern alignment.
Returning match result without handling empty, invalid, or boundary inputs.

Interactive Mechanism Walkthrough

Sequence Window & Automaton Alignment

Show text moving through pattern states and accepting matches.

Input:ABABABCABAB

Window:ABAB

Step 1 of 5: Parse or compile the regular expression

regex-states

Notes

Regular Expression Matching operates in O(nm) time and O(m) space within the Automaton Matching family. Key governing relation: next_states = epsilon_closure(move(current_states, character)). Often compared with Aho-Corasick and Naive String Search.