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Events and Languages Arto Salomaa Professor Arto Salomaa received his Ph.D. in 1960 and has b een Professor of Mathe- matics at the UniversityofTurku since 1965. He has authored more than 400 scienti c publications in ma jor journals, as well as ten b o oks, some of whichhave app eared also in French, German, Japanese, Romanian, Russian, Vietnamese and Chinese transla- tions. Prof. Salomaa holds the degree of do ctor honoris causa at six universities. He has b een an invited sp eaker at numerous conferences in computer science and math- ematics, and a program committee member or chairman for ma jor computer science conferences, including STOC, ICALP,MFCS, FCT. Prof. Salomaa was EATCS Pres- ident 1979-85 and is currently the editor-in-chief of the EATCS Monograph Series published by Springer-Verlag, as well as an editor of eight international journals of Computer Science. Festival conferences \Salo days in Theoretical Computer Science" Bucharest 1992, \Salo days in Auckland" Auckland, NZ, 1994 and \Imp ortant Re- sults and Trends in Theoretical Computer Science" Graz, 1994 have b een arranged in his honor. Prof. Salomaa is a memb er of the Academy of Sciences of Finland, the Swedish Academy of Sciences of Finland and Academia Europaea 92. Currently,heisa Research Professor at the Academy of Finland and the head of the Academy's research pro ject on mathematical structures in computer science. Events and Languages Early computer science It is customary to b egin a pap er with an abstract or a summary. The purp ose of this article is to tell ab out some people and ideas in the early history of computer 254 Salomaa science, roughly up to 1970. The article has a very sub jective avor: I will tell only ab out events and p ersons I have in some sense come into contact with. Since my p oint of view is over formal languages and automata, the happ enings and phenomena rep orted in the sequel will b e from these and related areas of theoretical computer science, rather than from the theory of algorithms and complexity. The relative imp ortance of the latter areas has increased very much since the 1970s. Although there have b een many attempts of uni cation and clari cation, it is still not at all clear what should be called computer science and what is theoretical computer science. Opinions and esp ecially p oints of emphasis vary remarkably from place to place, country to country. Of course the setup was even less clear and more obscure in the 60s when imp ortant ideas were emerging or just ab out to emerge. However, by the end of the 60s well-established com- puter science curricula existed already at numerous universities. An indication of the ideological unclarity is the Finnish word for \computer science", \tieto- jenkasittelyoppi", still prevalent in Finland. Literally translated the word means \discipline of data pro cessing". I opp osed this term very muchin the 60s but without success. I was in the 60s also in London, Canada, for a long p erio d. Here are some excerpts from my writing at the UniversityofWestern Ontario, in connection with a prop osed Ph.D. program in computer science: Likeanyyoung and growing discipline, Computer Science is far from b eing saturated and, therefore, one should b e prepared to add new ar- eas to the program. When launching the program, one should consider simultaneously with the areas of study also the availability of sta mem- b ers in these areas. ::: Formal language and automata theory is in a rather central p osition in every Ph.D. program in Computer Science I know of and, thus, I don't see to o much harm in this resp ect in a con ict with other universities in the province. ::: The main part of computer combinatorics would consist of the theory of graphs and networks but also other combinatorial problems with applications in computers could b e included. ::: Appliedareas could include some of the following: infor- mation retrieval, symb olic computation, arti cial intelligence, theorem proving by computer, pattern recognition, learning theory CAI, simu- lation, organization and design of systems for sequential, concurrent and time-shared pro cessing b oth on line and o line, design of system comp o- nents for assembly and compilation, computational linguistics. Any list like this is op en-ended and in selecting the areas the availability of sta should b e kept in mind. In all of the suggested areas, co op eration with other departments is p ossible and sometimes even necessary. Some such departments could be: mathematics recursive function theory, combi- natorics, applied mathematics numerical analysis, linguistics natural language asp ects of formal languages, electrical engineering, library sci- ence. That is my authentic writing from 1968, mayb e still preserved in some les at the University of Western Ontario. I would still agree with some of it but Events and Languages 255 obviously many things in it have b ecome obsolete. However, I do not wantto dwell on this topic longer; no nal answers can b e given anyway. Formal languages: Are they formal and are they languages? Grzegorz Rozenb erg { I will talk more ab out him later { published a pap er \Decision problems for quasi-uniform events" which had b een presented to the Bulletin of the Polish Academy of Sciences by Andrzej Mostowski on August 7, 1967. In this pap er we read: Let = f ; ;:::; g be a nite nonempty alphabet xed for 1 2 n all our considerations. The elements of are called symbols. Finite se- quences of symb ols are called tapes. The length of any tap e x is de ned to be the number of letters in the tap e and is denoted by lgx. The set of all tap es over including the empty sequence is denoted by T . We shall identify tap es of length 1 with symb ols of .If x and y are tap es, then xy denotes the concatenation of x and y . ::: If P; Q are subsets of T , then P; Q are called events.For arbitrary events P and Q, P [ Q is de ned as the set union, the complex pro duct PQ as 1 k 0 PQ = fxy : x 2 P; y 2 Qg, and P as [ P , where P = f0g and k =0 i+1 i P = P P i 0. It is obvious that T = . ::: An event P is fundamental if there exists a subset B of such that P = B . Everything is very well presented, mayb e some of the terms sound strange nowadays. Indeed, formal languages were earlier mostly called events. I used the latter term in all of my rst pap ers. The double meaning of the word \event" is re ected also in the title of this writing. Apparently, the usage of the word \event" in this sense stems from Kleene, [20]. I switched to \languages" in 1966{ 67. \Events" do not o ccur any more in my rst book \Theory of Automata" which was written in 1966{67 but, due to my complete ignorance ab out the publishers, was delayed for more than twoyears by the publisher. But do es it make more sense to call subsets of \formal languages" than \events"? Probably not. Most of the subsets lackany form whatso ever { how could they b e called \formal"? And most of them do not serveany purp ose in any kind of communication { how could they b e called \languages"? Let us go backto the quoted passage of Rozenb erg, [13]. It is very mathe- matical in avor. Moreover, the in uence of the great Polish scho ol of logicians b ecomes apparent in statements such as \We shall identify tap es of length 1 with symb ols of ". In general, most of the early investigators of computer sci- ence, no matter how the term is understo o d, were mathematically trained and oriented. Thus it is very natural that typical mathematical topics, suchasthe e ect of certain well-de ned op erations on languages, were studied early in the game. This tradition has continued, at least to some extent. Currentinvestigators should not just continue the tradition for its own sake. They should rather make sure that their topic is of some practical imp ortance, or else really signi cant mathematically. 256 Salomaa I met a few times the aforementioned Andrzej Mostowski, a famous repre- sentative of the Polish scho ol. He wore very elegant suits at conferences, quite unlike the casual so-and-so attire currently in use. He was also p olite and consid- erate. He was chairing a session in 1962, where I gave a talk ab out in nite-valued truth functions. I was somewhat nervous, and apparently this was noticed by Mostowski. There were some simple questions after my talk but Mostowski did not want to embarrass me with his dicult question. Instead, he came to me much later and asked \I would like to knowhowyou actually obtain the decid- ability". In the early days of formal language theory, the motivation and the b elief in the usefulness of the theory were quite strong. Let us lo ok at some examples from well-known sources. They tell also what di erent p eople thought language theory was ab out. Noam Chomsky, [3], wrote in 1959: A language is a collection of sentences of nite length all constructed from a nite alphab et or, where our concern is limited to syntax, a nite vo cabulary of symb ols. Since any language L in whichwe are likely to be interested is an in nite set, we can investigate the structure of L only through the study of the nite devices grammars which are capable of enumerating its sentences.
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