| S.C. Kleene: General recursive functions of natural numbers, Mathematische Annalen 112, 5 (1936), pp. 727-742 |
....(2i 1) AB p(J (2i 1) KL We test, whether z x: If yes, a complementation step occurs, the cycle is nished, and we go to point 5 k , otherwise the cycle continues. 4 k C z S(AB) f i (z;y) D x (KL) y p(S) j p(C) EFA j[1] p(A) A j[2] p(B) p(D) GH p(K) A j[3] p(L) IJ We generate a starting string of f j : All other symbols in w i are balanced so that jw i j PUR i = jw i j PYR i : EF ) z j A z j[1] A f i (z;y) j[2] A y j[3] GH) x (IJ) y . p(E) E p(F ) F f i (z 1; y) f j (z; f i (z; y) y) is computed ....
.... f i (z;y) D x (KL) y p(S) j p(C) EFA j[1] p(A) A j[2] p(B) p(D) GH p(K) A j[3] p(L) IJ We generate a starting string of f j : All other symbols in w i are balanced so that jw i j PUR i = jw i j PYR i : EF ) z j A z j[1] A f i (z;y) j[2] A y j[3] (GH) x (IJ) y . p(E) E p(F ) F f i (z 1; y) f j (z; f i (z; y) y) is computed via p j : EF ) z # j Z f i (z 1;y) j (GH) x (IJ) y p(# j ) EFS (0) p(Z j ) B (0) We assign z : z 1 and run a complementation step to break the sleeping state of w i ; which ....
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S. Kleene: General recursive functions on natural numbers. Mathematische Annalen 112, 727-742 (1936).
....23, 1935, but had definitely been established by March. Church wrote on July 15, 1935 his next letter to Bernays and pointed to a number of developments that had taken place in the meantime ; these developments had led to a(n impressive) list of papers, including his own [8] and [10] Kleene s [43] and [44] Rosser s [55] and the joint papers with Kleene, respectively Rosser. Contrary to Davis s impression , the equivalence was known already in March of 1935 when the abstract was submitted: if the inclusion of # definability in recursiveness had not also been known by then, the thesis ....
, General recursive functions of natural numbers, Mathematische Annalen, vol. 112 (1936), pp. 727--42. 180 WILFRIED SIEG
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S.C. Kleene: General recursive functions of natural numbers, Mathematische Annalen 112, 5 (1936), pp. 727-742
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