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    <p>I'd go for a recursive algorithm with implicit backtracking. Function signature: <code>f: input -&gt; result</code>, with <code>input</code> being the string, <code>result</code> either <code>true</code> or <code>false</code> depending if the entire string can be tokenized correctly.</p> <p>Works like this:</p> <ol> <li>If <code>input</code> is the empty string, return <code>true</code>.</li> <li>Look at the length-one prefix of <code>input</code> (i.e., the first character). If it is in the dictionary, run <code>f</code> on the suffix of <code>input</code>. If that returns <code>true</code>, return <code>true</code> as well.</li> <li>If the length-one prefix from the previous step is not in the dictionary, or the invocation of <code>f</code> in the previous step returned <code>false</code>, make the prefix longer by one and repeat at step 2. If the prefix cannot be made any longer (already at the end of the string), return <code>false</code>.</li> <li>Rinse and repeat.</li> </ol> <p>For dictionaries with low to moderate amount of ambiguous prefixes, this <em>should</em> fetch a pretty good running time in practice (O(n) in the average case, I'd say), though in theory, pathological cases with O(2^n) complexity can probably be constructed. However, I doubt we can do any better since we need backtracking anyways, so the "instinctive" O(n) approach using a conventional pre-computed lexer is out of the question. ...I think.</p> <p><strong>EDIT:</strong> the estimate for the average-case complexity is likely incorrect, see my comment.</p> <p>Space complexity would be only stack space, so O(n) even in the worst-case.</p>
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    1. POTokenize valid words from a long string
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    1. COCan you clarify on the claim "average case O(n)"?
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    2. COHm, come to think about it, that average O(n) may have been a misjudgment on my part. For instance, if the algorithm sees the prefix 'a' in the dictionary (assuming a dictionary of English words for a minute), it would first try to tokenize the remaining input... likely adding the *entire* suffix character-by-character before deciding that this cannot be tokenized and reverting to expanding the 'a'. Looks more like something polynomial, then. Considering Cocke-Younger-Kasami has something like O(n^3), too... good question, then.
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    3. COCYK parsing algorithm. You remind me of my NLP course. :P
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