Key Phrases - Statistically Improbable Phrases (SIPs):
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sequential machines, infinite words, evaluation theorem, minimal automata, internal shuffle product, unitary monoid, very fine morphism, locally finite monoid, principal factorization, gsp function, unambiguous subset, linear sequential machines, single terminal state, recurrence polynomial, fine morphisms, recognizable subset, quotient criterion, rational subset, maximal base, recognizable iff, action monoid, minimal automaton, free submonoid, complete semirings, complete automaton
Key Phrases - Capitalized Phrases (CAPs):
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Kleene's Theorem, New York, Basic Definitions, Proof Let, Use Exercise, Structure of Recognizable Sets, Systems Theory, Composition Theorem, The Integers, Academic Press, The Decomposition Algorithm, Second Factorization Theorem, First Factorization Theorem, The Equality Theorem, Maximal Prefixes, Examples of Syntactic Monoids, K-Recognizable Power Series, Positive Analytic Functions, Arbitrary Monoids, Expansion of Real Numbers, The Quotient Criterion, The Strong Minimization Problem, Use Proposition
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