A fixed-point theorem for recursive-enumerable languages and some considerations about fixed-point semantics of monadic programs

  • Sorin Istrail
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)


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:
$$\left\{ {a^{n + 1} \# b^{f(n) + 1} |n \in Dom f} \right\}.$$


Partial Function Minimal Solution Free Monoid Exit Node Formal Language Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Sorin Istrail
    • 1
  1. 1.Computer CenterUniversity "Al.I.Cuza"IaşiRomania

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