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A transition to a shorter suffix match after an attempted extension fails. In a Knuth-Morris-Pratt automaton, the prefix function determines the next shorter matching prefix.

Kevin Wayne is a coauthor of Algorithms, 4th edition by Robert Sedgewick and others and Introduction to Programming in Java: An Interdisciplinary Approach by Robert Sedgewick and others. Their accompanying implementations connect abstract data types, algorithm invariants and resource analysis to executable programs. For example, the published Knuth-Morris-Pratt automaton implementation explicitly accounts for alphabet-dependent preprocessing and space.^[ref]

The Knuth-Morris-Pratt algorithm searches for a pattern using its proper prefix-suffix overlaps. After matching $j$ characters, a mismatch replaces $j$ by the length of the longest proper border of a string for that matched prefix, repeating until the next character can extend it or $j=0$. The text index never moves backward. Precomputing prefix failure links takes $O(m)$ time; during scanning each increase in $j$ can pay for a later decrease, giving $O(n+m)$ total character work and $O(m)$ auxiliary storage. A dense Knuth-Morris-Pratt automaton is a related implementation with alphabet-dependent preprocessing and storage.^[ref]

A Knuth-Morris-Pratt automaton records how much of a fixed pattern matches the suffix of the text seen so far. State $j$ means the longest such prefix has length $j$; reading a symbol moves to the longest compatible prefix state. Reaching state $m$ reports a full length-$m$ match. For pattern aba, state two records suffix ab; reading a completes the match, while reading b falls back to state zero. A dense table for an alphabet of size $R$ uses $O(mR)$ preprocessing and storage, then constant work per text symbol.^[ref]