Abstract
This paper generalizes the ALGOL-like theorem showing that every λ-free context-sensitive (recursive-enumerable) language is a component of the minimal solution of a system of equation X=F(X), where X=(X1,...,Xt), F=(F1,...,Ft), t⩾1 and Fi, 1⩽i⩽t are regular expressions over the alphabet of operations:{concatenation, reunion, kleene "+" closure, nonereasing finite substitution (arbitrary finite substitution), intersection}.
In the second part is presented a method which constructs for a monadic program a system of equations (in the above form) so that one of the components of the minimal solution of the system gives the partial function f computed by the program in a language form:
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References
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© 1979 Springer-Verlag Berlin Heidelberg
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Istrail, S. (1979). A fixed-point theorem for recursive-enumerable languages and some considerations about fixed-point semantics of monadic programs. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_23
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DOI: https://doi.org/10.1007/3-540-09510-1_23
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