Using a recent result of ***, an extention of Ackermann-Peter hierarchy of unary primitive recursive functions to string-functions is obtained. The resulting hierarchy classifies the string-functions according to thei...
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Pure Lisp style recursive function programs are represented in a new way by sentences and schemata of first order logic. This permits easy and natural proofs of extensional properties of such programs by methods that ...
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In this paper we summarize our approach and findings in a point-free setting for recursive topology and recursive analysis. recursive analysis has received intensive attention recently and our approach, while differin...
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As the reliance of businesses and organizations on online operations continues to grow, the importance of addressing software security vulnerabilities becomes increasingly critical. This paper delves into the phenomen...
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A capacitor bank of appropriate capacitance value helps in self-excitation of Standalone Asynchronous Generator. İn order to determine the appropriate value of the capacitor to be connected in real time systems, simul...
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This article presents the design of a library for attaching and checking executable contracts to code written in the Elixir programming language. In addition to classical contract constructs such as preconditions and ...
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This article presents the design of a library for attaching and checking executable contracts to code written in the Elixir programming language. In addition to classical contract constructs such as preconditions and postconditions, the library allows specifying exceptional behaviour (i.e., which exceptions are thrown and under which conditions), detecting non-termination issues in recursive functions by specifying a strictly decreasing order in function arguments, and associating timers with function calls to detect slow computations. The library also focuses on language-specific features, enabling the association of contracts with the reception of messages sent by processes and the attachment of constraints to variable names (useful due to variable shadowing in Elixir). Moreover, stateful contracts (i.e., with a model state) permit specifying the behaviour of stateful APIs whose operations can be linearized. Using the stateful contracts, a monitor can be employed to check that the observed state can be explained in terms of possible linearizations.
Corresponding to the definition of mu-recursive functions we introduce a class of recursive relations in metric spaces such that each relation is generated from a class of basic relations by a finite number of applica...
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Corresponding to the definition of mu-recursive functions we introduce a class of recursive relations in metric spaces such that each relation is generated from a class of basic relations by a finite number of applications of some specified operators. We prove that our class of recursive relations essentially coincides with our class of densely computable relations, defined via Turing machines. In the special case of the real numbers our subclass of recursive functions coincides with the classical class of computable real-valued functions, defined via Turing machines by Grzegorczyk, Lacombe and others.
Hofstadter’s G function is recursively defined via G(0) = 0 and then G(n) = n − G(G(n − 1)). Following Hofstadter, a family (Fk) of similar functions is obtained by varying the number k of nested recursive calls in t...
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Constant-recursive sequences are those which satisfy a linear recurrence, so that later terms can be obtained as a linear combination of the previous ones. The rank of a constant-recursive sequence is the minimal numb...
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We reconstruct some of the development in Richard Bird’s [2008] paper Zippy Tabulations of recursive functions, using dependent types and string diagrams rather than mere simple types. This paper serves as an intuiti...
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