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PURE REGULAR SYSTEMS
THE STRUCTURE OF THE SET OF THEOREMS OF A FRONTIER SYSTEM
A-accessible ai,pi aipi automata automaton sub(Z automaton with binary auxiliary alphabet auxiliary letters behavior p(A behaviors of finite called canonical system clearly congruences of finite construct a finite contraction of form corollary ctr(Z deduction defined definition of ZQ duction ec(y ec(z effectively construct elementary sets expansive system ext(X families of words finite automaton finite number finite rank finite set frontier system Furthermore implies inductive assumption initial int(B k-periodic KLeene lemma h length lg(v lg(y lg(z natural numbers obtain periodic description C,P production ax proof of lemma pure regular system R-family Rabin and Scott recursive recursive sets red(Z reduced regular system regular expression regular sets remark right-automaton right-congruence right-regular system set of axioms set of theorems set P(U sets of words shown Sj_lpX sp(u sp(x subset of Nk Suppose theorems t(C tion transition functions whereby z e Nk