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On the complexity of some problems concerning the use of procedures. II

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Summary

We consider programming languages which allow procedures to be declared dynamically and to be passed as parameters. The influence of these two features on the decidability of “formal parameter correctness”, “formal recursivity”, and other properties relevant for debugging and optimization has been studied in [1, 2, 4–9]. In this paper we study the feasibility of such decision procedures in those cases where decidability has been proven. Thus this paper presents a complexity-theoretic refinement of some of the recursion-theoretic work from [1, 2, 4–9].

In contrast to part I [10], this part is concerned with restricted classes of programs. The main results presented in this part are:

  1. 1)

    Deciding whether or not a program has the “formal most-recent-property” is a P-space-complete problem even for programs with no more than 4 parameters per procedure (Theorem 7).

  2. 2)

    Deciding formal parameter correctness, formal recursivity and reachability of procedures, and the formal macro-property are all P-space complete problems for the class of programs without procedure nesting (Theorem 4). Detecting the presence of recursive procedures is an NP-complete problem for this class of programs (Theorem 4).

  3. 3)

    In finite-mode programs, detecting the presence of formally recursive procedures is an NP-complete problem; deciding whether or not a procedure is formally recursive, deciding whether or not a procedure is formally reachable, and deciding whether or not a program has the formal macro-property are P-space-hard problems; and deciding whether or not a program has the formal most-recent-property is a P-space-complete problem (Theorem 5).

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References

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Authors and Affiliations

  1. Computer Science Department, Washington State University, 99164-1210, Pullman, Washington, USA

    Karl Winklmann

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  1. Karl Winklmann
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Supported by the Purdue Research Foundation and by the National Science Foundation through Grants GJ27127A1 and MCS8004128

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Winklmann, K. On the complexity of some problems concerning the use of procedures. II. Acta Informatica 18, 411–430 (1983). https://doi.org/10.1007/BF00289578

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