Dana S. Scott

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Finite automata are considered in this paper a s instruments for classifying finite tapes. Each onetape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical(More)
The purpose of the theory of domains is to give models for spaces on which to define computable functions. The kinds of spaces needed for denotational sematics involve not only spaces of higher type (e.g. function spaces) but also spaces defined reeursively (e.g. reflexive domains). Also required are many special domain constructs (or functors) in order to(More)
Let R be the set of all sets of natural numbers. A collection (ü of subsets of R satisfies a reduction principle if, for every A and 5 G d , there are A' and B'E® such that A'QA^B'QB, A'UB'=*AUB, and AC\B' is empty. For n>0 let Hi and S« be, respectively the set of u i subsets of R and the set of 2£ subsets of R. It is known that Ilj and S2 satisfy(More)
This paper represents a continuation of the program sketched in Outline of a Mathematical Theory of Computation (PRG 2), The language under consideration is the elementary languag~ of flow diagrams where the level of analysis concerns the flo'~ of control but not any questions of storage, assignment. block structure or the use of parameters. A new feature(More)