Recursive Functions [antikvár]

PREFACE TO THE ENGLISH EDITION The English translation of this book was begun in 1960. At that time I have made no changes in the text, save for the addition of an Appendix, dealing with an extensive generalization of the theory of recursive functions which was the subject of a lecture, delivered by me in Warsaw on the occasion of an international symposium in September 1959. (This generalization contains as a special case also the theory of recursive functions, defined on the word set over an arbitrary alphabet.) My article on this subject, received in the same month by the Acta Math. Acad. Sci. Hungaricae, appeared in the meantime in two parts in Vols 12 and 13 of this periodical; some corrections followed in Vol. 14 in my paper on a certain range of the numerous applications of the theory. These applications also affect the field I have made mention of in 1956 in the preface of the second German edition of my book. At that time I did not enter into the details ofthe rôle ofthe recursive functions in the theory of relay contact systems, in that of computers and other automatic systems, as well as in the theory of translating machines, because the appropriate study of the respective foreign literature was made impossible by the momentary situation in those days. At present it is on account of the abundance of the actually existing material which would require a special volume that I cannot even think of doing this. I am indebted to the Publishing House of the Hungarian Academy of Sciences for having prepared the English edition of the book, as well as to tlie Academic Press for overcoming all emerging difficulties, causing a great time-lag, thus making possible the appearance of my book in close English translation. Budapest, 1966 Rózsa Péter